IRAK4 inhibitors and methods for their topical use

Abstract

The present invention relates to compositions comprising an IRAK4 inhibitor useful for treating dermatological disorders or conditions characterized by inflammation. The present invention also relates to methods for treating dermatological disorders or conditions.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Application No. 63 / 046,531, filed June 30, 2020, the disclosure of which is incorporated herein by reference. [Background technology]

[0002] background Dermatological disorders associated with hyperactive innate inflammation, such as rosacea, psoriasis, and atopic dermatitis, are common dermatological conditions affecting many people. For example, rosacea is a common and chronic inflammatory skin disease affecting over 10 million Americans. Rosacea manifests with at least one of the following symptoms: flushing (transient redness), non-transient redness, papules, pustules, and telangiectasias (visible small dilated blood vessels). While clinically heterogeneous, rosacea phenotypes are all related to the presence of chronic facial skin inflammation. Until recently, the pathophysiology of this disease was poorly understood and limited to explanations of factors that exacerbate or improve the condition. Recent molecular studies suggest that altered innate immune responses are involved in the pathogenesis of vascular and inflammatory disorders seen in rosacea patients. Currently available treatments for rosacea include vasoconstrictors such as alpha- or beta-blockers, antibiotics, phototherapy, and laser therapy.

[0003] Currently, there is a need for fast-acting, effective, and safe dermatological treatments for dermatological disorders characterized by inflammation. Summary of the Invention

[0004] overview Described herein are topical compositions comprising inhibitors of IRAK4 and TrkA, which may also have low inhibitory activity against VEGFR, and methods of using IRAK4 inhibitors for the treatment of dermatological disorders or conditions characterized by inflammation, such as rosacea.

[0005] In one aspect, the present disclosure provides a topical composition comprising a dermatologically acceptable excipient and a pharmaceutically effective amount of an IRAK4 inhibitor (e.g., a compound having Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) below).

[0006] In a further aspect, the present disclosure provides a method for treating a dermatological disorder, the method comprising topically administering to a subject in need thereof a topical composition having a therapeutically effective amount of an IRAK4 inhibitor of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) and a dermatologically acceptable excipient.

[0007] In a further aspect, the present disclosure provides a method for reducing inflammation in mammalian skin, the method comprising topically administering to the mammalian skin a topical composition comprising an effective amount of an IRAK4 inhibitor of a compound of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) to a subject in need thereof.

[0008] In a further aspect, the present disclosure provides a method for reducing inflammation and vascular dysfunction in mammalian skin, the method comprising topically administering to the mammalian skin a topical composition comprising a therapeutically effective amount of an IRAK4 inhibitor that is a compound of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) to a subject in need thereof. [The present invention 1001] A pharmaceutically effective amount of: N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, 2-(2-((2,2-difluoroethyl)amino)pyridin-4-yl)-N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-1,3-oxazole-4-carboxamide, N-(3-((3S,4S)-4-hydroxy-3-methyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(1-methyl-3-(2-oxoimidazolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(1-methyl-3-((3S)-3-methyl-2-oxopyrrolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, 2-(2-((cyclopropylmethyl)amino)pyridin-4-yl)-N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3,3-dimethyl-4-((methylamino)methyl)-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3,3-dimethyl-4-((methylamino)methyl)-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3-isopropyl-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((dimethylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3-(2-hydroxypropyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((dimethylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((cyclopropylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, and N-(3-(3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-(oxetan-3-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, or a stereoisomer, tautomer, or pharmaceutically acceptable salt thereof and a compound selected from a solvent system comprising one or more solvents; Antioxidants and 1. A topical composition comprising: [The present invention 1002] The topical composition of the present invention 1001, wherein the solvent system comprises one or more solvents selected from polyethers, polyethylene glycols (e.g., PEG 400), polyether alcohols (e.g., diethylene glycol monoethyl ether; Transcutol® P), ethers, and alcohols; e.g., PEG 400 and diethylene glycol monoethyl ether (Transcutol® P). [The present invention 1003] The topical composition of claim 1001 or 1002, wherein the solvent system comprises PEG 400 in an amount of about 20% to about 70% by weight of the composition, or about 35% to about 70% by weight of the composition, or about 35% to about 50% by weight of the composition, or about 40% to about 45% by weight of the composition, or about 55% to about 65% by weight of the composition, or about 40%, about 45%, about 50%, about 55%, or about 60% by weight of the composition. [The present invention 1004] Any of the preceding topical compositions of the present invention, wherein the solvent system comprises diethylene glycol monoethyl ether (Transcutol® P) in an amount of about 10% to about 45% by weight of the composition, or about 10% to about 20% by weight of the composition, or about 20% to about 30% by weight of the composition, or about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, or about 45% by weight of the composition. [The present invention 1005] Any of the preceding topical compositions of the invention, wherein the solvent system further comprises one or more preservatives, for example, an alcohol having 2 to 10 carbon atoms, for example, benzyl alcohol or phenoxyethanol. [The present invention 1006] Any of the preceding topical compositions of the present invention, wherein the solvent system further comprises one or more preservatives in an amount from about 0.01% to about 20% by weight of the composition, or from about 0.1% to about 10% by weight of the composition, or from about 0.5% to about 5% by weight of the composition, or from about 1% to about 3% by weight of the composition, or about 2% by weight of the composition. [The present invention 1007] Any of the preceding topical compositions of the present invention, wherein the solvent system is present in an amount of about 50% to about 90% by weight of the composition, or about 75% to about 90% by weight of the composition, or about 80% to about 90% by weight of the composition, or about 85% to about 90% by weight of the composition, or about 55% to about 65% by weight of the composition, or about 55% to about 60% by weight of the composition. [The present invention 1008] Any of the preceding topical compositions of the present invention, wherein the antioxidant is selected from one or more of butylated hydroxytoluene (BHT), sodium metabisulfite, ascorbic acid, propyl gallate, and / or alpha tocopherol (vitamin E), and is present in an amount of about 0.001 wt. % to about 1 wt. %, e.g., about 0.01 wt. % to about 1 wt. %, e.g., about 0.2 wt. %, based on the total weight of the composition. [The present invention 1009] Any of the preceding topical compositions of the present invention, further comprising a non-solvent. [The present invention 1010] 1009. The topical composition of claim 1009, wherein the non-solvent is water, a silicone oil (e.g., dimethicone 350), or a mixture thereof. [The present invention 1011] The topical composition of the present invention, wherein the water is present in an amount of about 5% to about 30% by weight of the composition, or about 5% to about 15% by weight of the composition, or about 15% to about 25% by weight of the composition, or about 10%, or about 15%, or about 20% by weight of the composition, and the silicone oil is Dimethicone 350 and is present in an amount of about 0.01% to about 2% by weight of the composition, or about 0.1% to about 1.5% by weight of the composition, or about 0.5% to about 1% by weight of the composition, or about 0.75% by weight of the composition. [The present invention 1012] Any of the preceding topical compositions of the present invention, wherein the composition further comprises a polymeric gelling agent selected from one or both of crosslinked polyacrylic acid and nonionic cellulose ethers, such as Carbopol polymers and hydroxypropyl cellulose, e.g., one or more of Carbopol 980 NF and HPC HF, wherein the gelling agent is present in an amount of from 0.01% to about 5% by weight of the composition, or from about 0.1% to about 3% by weight of the composition, or from about 0.5% to about 2% by weight of the composition, or from about 0.75% to about 1.25% by weight of the composition, or about 1% by weight of the composition. [The present invention 1013] Any of the preceding topical compositions of the present invention, further comprising a skin conditioning agent, such as diisopropyl adipate or a silicone oil, such as dimethicone 350, wherein the skin conditioning agent is present in an amount of from 0.1% to about 15% by weight of the composition, or from about 0.1% to about 5% by weight of the composition, or from about 0.1% to about 2% by weight of the composition, or from about 5% to about 15% by weight of the composition, or about 1% by weight of the composition, or about 10% by weight of the composition. [The present invention 1014] Any of the preceding topical compositions of the present invention further comprising an emollient, e.g., the emollient is a triglyceride, e.g., a medium chain triglyceride, e.g., Crodamol GTCC, in an amount of from 0.1% to about 15% by weight of the composition, or from about 0.1% to about 5% by weight of the composition, or from about 0.1% to about 2% by weight of the composition, or from about 5% to about 15% by weight of the composition, or about 1% by weight of the composition, or about 10% by weight of the composition. [The present invention 1015] For example, one or more C 14 -C 30 fatty alcohols, celluloses, acrylate polymers or crosspolymers, or carbomers; for example, hydroxypropyl cellulose, hydroxymethyl cellulose, hydroxypropyl methylcellulose (e.g., Benecel E4M), cetostearyl alcohol, poloxamers (Pluronic PF127), carbomers (e.g., Carbomer 980, Carbomer 1342, and Carbomer 940), more specifically, hydroxypropyl cellulose (e.g., hydroxypropyl cellulose Klucel® EF, GF, MF, and / or HF having a molecular weight of 850,000 to 1,150,000 daltons), Pluronic PF127, Carbomer 980, and / or Carbomer 1342 (Pemulen® TR-1, TR-2, and / or Carbopol® ETD) 2020); any of the preceding topical compositions of the present invention, further comprising a viscosity enhancer selected from, for example, cetostearyl alcohol, wherein the viscosity enhancer is present in an amount of from 0.1% to about 15% by weight of the composition, or from about 1% to about 10% by weight of the composition, or from about 3% to about 7% by weight of the composition, or about 5% by weight of the composition. [The present invention 1016] Any of the preceding topical compositions of the present invention further comprising a surfactant, e.g., the surfactant is selected from one or more of polyoxyethylene fatty ethers; nonoxynol, polysorbate, polyoxyethylene alcohols, polyoxyethylene fatty acid esters, sodium lauryl sulfate, and sorbitan monostearate; e.g., Brij S2 or Brij S 20, and the surfactant is present in an amount of 0.1% to about 15% by weight of the composition, or about 1% to about 5% by weight of the composition, or about 1%, about 2%, about 3%, about 4%, about 5%, about 7%, or about 10% by weight of the composition. [The present invention 1017] For example, C 1-20 Alkanols (e.g., oleyl alcohol, cetyl alcohol, octyldodecanol, cetostearyl alcohol, benzyl alcohol), saturated or unsaturated fatty acid esters, saturated or unsaturated fatty acid esters, polyoxyethylene fatty ethers, polyoxyethylene fatty acid esters, diethylene glycol monoethyl ether, 1,3-dimethyl-2-imidazolidinone, and / or dimethyl isosorbide; e.g., oleyl alcohol, cetyl alcohol, octyldodecanol, cetostearyl alcohol, mineral oil, benzyl alcohol, isopropyl myristate, diisopropyl adipate, ethylhexyl hydroxystearate, steareth-2 (Brij S2), steareth-20 (Brij S3), S20), glyceryl stearate, stearic acid, magnesium stearate, diethylene glycol monoethyl ether, 1,3-dimethyl-2-imidazolidinone, and / or dimethyl isosorbide; for example, one or more of propylene glycol, oleyl alcohol, diisopropyl adipate, and isopropyl myristate; for example, propylene glycol, wherein the penetration enhancer is present in an amount of from 0.1% to about 20% by weight of the composition, or from about 1% to about 15% by weight of the composition, or from about 5% to about 15% by weight of the composition, or about 10% by weight of the composition. [The present invention 1018] Any of the preceding topical compositions of the present invention in the form of a cream, lotion, foam, aqueous gel, non-aqueous gel, spray, or ointment (e.g., a polyethylene glycol-based ointment). [The present invention 1019] Any of the preceding topical compositions of the present invention having an apparent pH of about 3.5 to about 7.5, about 4 to about 7, about 4.5 to about 6.5, or about 5 to about 6.5, or about 5.5 to 6.5, or about 6. [The present invention 1020] Any of the preceding topical compositions of the present invention, wherein the composition is applied to the patient's skin three times a day, twice a day, once a day, every other day, once a week, or once a month. [The present invention 1021] Any of the topical compositions of the preceding invention administered to a patient suffering from a dermatological condition characterized by inflammation, e.g., rosacea, psoriasis, atopic dermatitis, hidradenitis suppurativa, seborrheic dermatitis, contact dermatitis, urticaria, dermatitis herpetiformis, nummular eczema, lichen planus, pityriasis rosea, cutaneous lupus, acne, cancer of the skin (e.g., cutaneous T-cell lymphoma), or miliaria. [The present invention 1022] Any of the topical compositions of the preceding invention, wherein said skin is mammalian skin (e.g., human skin). [The present invention 1023] Any of the preceding topical compositions of the present invention, wherein the topical composition is an aqueous gel, the solvent system comprises PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is about 0.7 to about 1.1, e.g., about 0.8 to about 1.0, e.g., about 0.9. [The present invention 1024] Any of the preceding topical compositions of the invention, wherein the topical composition is a non-aqueous gel, the solvent system comprises PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is about 2.2 to about 2.6, e.g., about 2.3 to about 2.5, e.g., about 2.4. [The present invention 1025] Any of the preceding topical compositions of the present invention, wherein the topical composition is a cream, the solvent system comprises PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is about 2.6 to about 3.2, e.g., about 2.7 to about 3.1, e.g., about 2.9. [The present invention 1026] Any of the preceding topical compositions of the present invention, wherein the topical composition is an ointment, the solvent system comprises PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is about 3.5 to about 4.5, e.g., about 3.8 to about 4.2, e.g., about 4. [The present invention 1027] A method for treating an inflammatory dermatological disorder, comprising topically administering to a subject in need thereof any of the preceding topical compositions of the present invention. [The present invention 1028] A method for reducing inflammation in mammalian skin, comprising topically administering to the mammalian skin an effective amount of any of the topical compositions of inventions 1001-1026. [The present invention 1029] A method for reducing inflammation and vascular dysfunction in mammalian skin, comprising topically administering to the mammalian skin an effective amount of any of the topical compositions of inventions 1001 to 1026. [The present invention 1030] 1029. The method of any of claims 1027 to 1029, wherein the inflammatory dermatological disorder is rosacea, psoriasis, atopic dermatitis, hidradenitis suppurativa, seborrheic dermatitis, contact dermatitis, urticaria, dermatitis herpetiformis, nummular eczema, lichen planus, pityriasis rosea, cutaneous lupus, acne, cancer of the skin (e.g., cutaneous T-cell lymphoma), or miliaria. [Brief explanation of the drawings]

[0009] [Figure 1]

[0023] Figure 1 shows the performance of an IRAK4 inhibitor (Compound 1) according to the present disclosure in various vehicle formulations in sRICA. The vehicles prepared are summarized in Tables 29-32. [Figure 2]

[0023] Figure 1 shows the performance of an IRAK4 inhibitor (compound 2) according to the present disclosure in various vehicle formulations in sRICA. The vehicles prepared are summarized in Tables 29-32. DETAILED DESCRIPTION OF THE INVENTION

[0010] Detailed Description Provided herein are topical compositions for treating dermatological conditions characterized by inflammation. In particular, the pharmaceutical compositions contain compounds that are dual inhibitors of interleukin-1 receptor-associated kinase 4 (IRAK4) and tropomyosin receptor kinase A (TrkA). IRAK4 is a protein involved in signal transduction of innate immune responses downstream of Toll-like receptors (except TLR3) and IL-1 family cytokine receptors (all MyD88-dependent). TrkA is a high-affinity catalytic receptor for nerve growth factor (NGF). Without wishing to be bound by theory, inhibition of IRAK4 and TrkA can potently reverse the excessive innate inflammatory state of the skin and reduce cutaneous vascular abnormalities and sensitivity. Topical compositions of IRAK4 / TrkA inhibitors are particularly capable of addressing all three major components of rosacea pathology, including innate inflammation, redness, and sensitivity.

[0011] Dual IRAK4 and TrkA inhibitor The present disclosure provides compositions comprising compounds with IRAK4 inhibitory properties that also target TrkA.

[0012] In one aspect, the present disclosure provides a topical composition comprising a pharmaceutically effective amount of an IRAK4 inhibitor (e.g., an IRAK4 inhibitor of the present disclosure, e.g., a compound having Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) below), a solvent system comprising one or more solvents, and an antioxidant.

[0013] In some embodiments, the compound for use in the methods or compositions described herein has Formula I, in free or pharmaceutically acceptable salt form, including its racemates, enantiomers, and diastereomers: TIFF0007813733000001.tif44128In formula, Ring A is a monocyclic heteroaryl; R 1 is an optionally substituted monocyclic or bicyclic heteroaryl; R 2 -CONH2, -CONH-R 0 , -CONH-R 00 -OH, phenyl, oxadiazolyl, tetrazolyl, etc. R 3 is H, heterocycloalkyl (R 0 , which may be substituted with halogen, etc.), R 0 is lower alkyl, R 00 is a lower alkylene.

[0014] In some embodiments, the present disclosure provides a topical composition comprising a compound according to Formula II [Compound 1], in free or pharmaceutically acceptable salt form, including its racemate, enantiomers, and diastereomers: TIFF0007813733000002.tif67128In formula, R 1 is an optionally substituted aromatic heterocyclic group, or an optionally substituted C 6-14 is an aryl group, R 2 is a hydrogen atom or a substituent, R 3 and R 4 are independently a hydrogen atom or a substituent, or R 3 and R 4 may combine to form an optionally substituted ring, R 5 and R 6 are independently a hydrogen atom or a substituent, or R 5 and R 6 may combine to form an optionally substituted ring, X is CR7 R 8 , N.R. 9 , O, or S; R 7 and R 8 are independently a hydrogen atom or a substituent, or R 7 and R 8 may combine to form an optionally substituted ring, R 9 is a hydrogen atom or a substituent.

[0015] The present disclosure further provides compounds of Formula II: 1.1 Compound 1, wherein: R 1 is an aromatic heterocyclic group or C 6-14 aryl groups, each of which may contain a halogen atom, optionally substituted C 1-6 alkyl group, optionally substituted C 6-14 an aryl group, an optionally substituted heterocyclic group, C 3-10 Cycloalkylsulfonyl group, C 1-6 optionally substituted by 1 to 3 substituents selected from an alkyl-carbonyl group, an aromatic heterocyclylsulfonyl group, and a halogenated sulfanyl group; R 2 may be substituted C 1-6 alkyl group, optionally substituted C 3-10 a cycloalkyl group or an optionally substituted non-aromatic heterocyclic group, R 3 and R 4 are independently a hydrogen atom or an optionally substituted C 1-6 is an alkyl group, R 5 and R 6 are independently (1) a hydrogen atom, (2) a hydroxy group, or (3) an optionally substituted C 1-6 (4) an optionally substituted C 1-6 (5) (i) optionally substituted C 1-6 (ii) an optionally substituted C 1-6an amino group optionally mono- or di-substituted by a substituent selected from an alkyl-carbonyl group, and (iii) an optionally substituted C alkylsulfonyl group; (6) an optionally substituted non-aromatic heterocyclic group; (7) a carboxy group; or (8) a C 1-6 a carbamoyl group optionally mono- or disubstituted by alkyl groups, or R5 and R6 taken together form an optionally substituted non-aromatic heterocycle or an optionally substituted C 3-10 may form a cycloalkane, X is CR 7 R 8 , N.R. 9 , O, or S; R 7 and R 8 are independently a hydrogen atom, a cyano group, an optionally substituted C 1-6 is an alkyl group or a hydroxy group, or R 7 and R 8 are combined to form optionally substituted C 3-10 may form a cycloalkane or an optionally substituted non-aromatic heterocycle, R 9 is a hydrogen atom, optionally substituted C 1-6 alkyl group, optionally substituted C 2-6 an alkenyl group or an optionally substituted C 7-16 is an aralkyl group, Compound 1. 1.2 In the formula, X is CR 7 R 8 or NR 9 and R 3 and R 4 are both hydrogen atoms, Compound 1 or 1.1. 1.3 N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide or a salt thereof, Compound 1 or a compound of 1.1 to 1.2. 1.4 N-(1-methyl-3-(2-oxoimidazolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide or a salt thereof, Compound 1 or a compound of 1.1 to 1.2. 1.5 N-(1-methyl-3-((3S)-3-methyl-2-oxopyrrolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide or a salt thereof, Compound 1 or a compound of 1.1 to 1.2.

[0016] Each symbol in formula II is explained below.

[0017] R 1 represents an optionally substituted aromatic heterocyclic group or an optionally substituted C 6-14 It is an aryl group.

[0018] R 1 Regarding "optionally substituted aromatic heterocyclic group", "aromatic heterocyclic group" and "optionally substituted C 6-14 "C" in "Aryl group" 6-14 Each "aryl group" may have 1 to 3 substituents at substitutable positions. When the number of substituents is plural, the respective substituents may be the same or different.

[0019] In one embodiment, R 1 Regarding the "optionally substituted aromatic heterocyclic group", the "substituents" of the "aromatic heterocyclic group" and the "optionally substituted C 6-14 "C" in "Aryl group" 6-14Examples of the "substituent" of the "aryl group" include a halogen atom, a cyano group, a nitro group, an optionally substituted hydrocarbon group, an optionally substituted heterocyclic group (the "heterocyclic group" may have a substituent selected from Substituent Group A (the substituent may be further substituted with a substituent selected from Substituent Group A)), an acyl group, an optionally substituted amino group, an optionally substituted carbamoyl group, an optionally substituted thiocarbamoyl group, an optionally substituted sulfamoyl group, an optionally substituted hydroxy group, an optionally substituted sulfanyl (SH) group, and an optionally substituted silyl group.

[0020] R 1 Regarding the "optionally substituted aromatic heterocyclic group", the "substituents" of the "aromatic heterocyclic group" and the "optionally substituted C 6-14 "C" in "Aryl group" 6-14 Preferred examples of the "substituent" of the "aryl group" include: (1) an optionally substituted hydrocarbon group (for example, a hydrocarbon group optionally having a substituent selected from Substituent Group A), (2) optionally substituted heterocyclic groups (for example, heterocyclic groups optionally having a substituent selected from Substituent Group A (the substituent may be further substituted with a substituent selected from Substituent Group A)), and (3) Acyl group Examples include:

[0021] In another embodiment, R 1 Regarding the "optionally substituted aromatic heterocyclic group", the "substituents" of the "aromatic heterocyclic group" and the "optionally substituted C 6-14 "C" in "Aryl group" 6-14 Examples of the "substituent" of the "aryl group" include a halogen atom, a cyano group, a nitro group, an optionally substituted hydrocarbon group, an optionally substituted heterocyclic group (the "heterocyclic group" may have a substituent selected from Substituent Group A and a thioxo group (the substituent is selected from Substituent Group A, an azide group, and a mono- or di-C 1-6 Alkylamino group (alkyl is C 3-10and an optionally substituted silyl group).

[0022] R 1 Regarding the "optionally substituted aromatic heterocyclic group", the "substituents" of the "aromatic heterocyclic group" and the "optionally substituted C 6-14 "C" in "Aryl group" 6-14 Preferred examples of the "substituent" of the "aryl group" include: (1) a halogen atom, (2) an optionally substituted hydrocarbon group (for example, a hydrocarbon group optionally having a substituent selected from Substituent Group A), (3) A heterocyclic group which may have a substituent selected from the group consisting of the substituents A and a thioxo group (the substituents are the group consisting of the substituents A, an azido group, and a mono- or di-C 1-6 Alkylamino group (alkyl is C 3-10 substituted by a substituent selected from a cycloalkyl group and a halogen atom); (4) acyl groups, and (5) an optionally substituted sulfanyl (SH) group Examples include:

[0023] In one embodiment, R 1 is preferably an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group) or C 6-14 Aryl groups, each of which may be substituted with 1 to 3 substituents selected from the following: (1) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), (2) optionally substituted C 6-14 An aryl group (e.g., C optionally having a substituent selected from Substituent Group A) 6-14 aryl group), (3) an optionally substituted heterocyclic group (for example, a heterocyclic group optionally having a substituent selected from Substituent Group A (the substituent may be further substituted with a substituent selected from Substituent Group A)), (4) C 3-10 cycloalkylsulfonyl groups, (5) C 1-6 alkyl-carbonyl groups, and (6) An aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group).

[0024] R 1 is more preferably an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group or an 8- to 14-membered fused polycyclic aromatic heterocyclic group) (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)), or C 6-14 and aryl groups (eg, phenyl), each of which may be substituted with 1 to 3 substituents selected from the following: (1) The following: (i) a halogen atom (e.g., a fluorine atom), and (ii) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (2) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 5-14 aryl groups (e.g., phenyl); (3) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 1-6an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., ethyl); (4) 1 to 3 Cs 1-6 a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl) optionally substituted by an alkyl group (e.g., methyl); (5) C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), (6) C 1-6 alkyl-carbonyl groups (e.g., acetyl), and (7) An aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl group) (for example, thiazolylsulfonyl).

[0025] R 1 is even more preferably an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- or 6-membered monocyclic aromatic heterocyclic group or an 8- to 14-membered fused polycyclic aromatic heterocyclic group) optionally substituted by 1 to 3 substituents selected from the following (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)). (i) Below: (a) a halogen atom (e.g., a fluorine atom), and (b) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (ii) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 6-14aryl groups (e.g., phenyl); (iii) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 1-6 an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., ethyl); (iv) 1 to 3 C 1-6 a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl) optionally substituted by an alkyl group (e.g., methyl); (v) C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and (vi) C 1-6 an alkyl-carbonyl group (e.g., acetyl), or (2) The following: (I C 1-6 alkyl groups (e.g., methyl); (ii) C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and (iii) an aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl group) (e.g., thiazolylsulfonyl) C optionally substituted by 1 to 3 substituents selected from 6-14 Aryl groups (e.g., phenyl).

[0026] R 1 is particularly preferably C optionally substituted by 1 to 3 halogen atoms (for example, fluorine atoms). 1-6and aromatic heterocyclic groups (preferably 5- to 14-membered aromatic heterocyclic groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclic groups) (e.g., oxazolyl) optionally substituted by aromatic heterocyclic groups (preferably 5- to 14-membered aromatic heterocyclic groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclic groups) (e.g., pyridyl) optionally substituted by amino groups which may be mono- or di-substituted by alkyl groups (e.g., methyl, ethyl).

[0027] In another embodiment, R 1 is more preferably an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group or an 8- to 14-membered fused polycyclic aromatic heterocyclic group) (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)), or C 6-14 and aryl groups (eg, phenyl), each of which may be substituted with 1 to 3 substituents selected from the following: (1) The following: (i) a halogen atom (e.g., a fluorine atom), and (ii) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (2) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 6-14 aryl groups (e.g., phenyl); (3) The following: (i) a halogen atom (e.g., a fluorine atom), and (ii) C 3-10 cycloalkyl groups (e.g., cyclopropyl) C optionally substituted by 1 to 3 substituents selected from 1-6an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); (4) 1 to 3 Cs 1-6 a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl) optionally substituted by an alkyl group (e.g., methyl); (5) C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), (6) C 1-6 alkyl-carbonyl groups (e.g., acetyl), and (7) An aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl group) (for example, thiazolylsulfonyl).

[0028] R 1 is even more preferably an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- or 6-membered monocyclic aromatic heterocyclic group or an 8- to 14-membered fused polycyclic aromatic heterocyclic group) optionally substituted by 1 to 3 substituents selected from the following (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)). (i) Below: (a) a halogen atom (e.g., a fluorine atom), and (b) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (ii) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms)6-14 aryl groups (e.g., phenyl); (iii) Below: (a) a halogen atom (e.g., a fluorine atom), and (b)C 3-10 cycloalkyl groups (e.g., cyclopropyl) C optionally substituted by 1 to 3 substituents selected from 1-6 an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); (iv) 1 to 3 C 1-6 a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl) optionally substituted by an alkyl group (e.g., methyl); (v) C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and (vi) C 1-5 an alkyl-carbonyl group (e.g., acetyl), or (2) The following: (I C 1-6 alkyl groups (e.g., methyl); (ii) C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and (iii) an aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl group) (e.g., thiazolylsulfonyl) C optionally substituted by 1 to 3 substituents selected from 6-14 Aryl groups (e.g., phenyl).

[0029] In yet another embodiment, R 1 is preferably an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group) or C 6-14Aryl groups, each of which may be substituted with 1 to 3 substituents selected from the following: (1) a halogen atom, (2) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), (3) optionally substituted C 6-14 An aryl group (e.g., C optionally having a substituent selected from Substituent Group A) 6-14 aryl group), (4) A heterocyclic group which may have a substituent selected from the group consisting of the substituents A and a thioxo group (the substituents are the group consisting of the substituents A, an azido group, and a mono- or di-C 1-6 Alkylamino group (alkyl is C 3-10 substituted by a substituent selected from a cycloalkyl group and a halogen atom); (5) C 3-10 cycloalkylsulfonyl groups, (6) C 1-6 alkyl-carbonyl groups, (7) an aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group), and (8) Halogenated sulfanyl groups.

[0030] R 1 is more preferably an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group or an 8- to 14-membered fused polycyclic aromatic heterocyclic group) (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)), or C 6-14 and aryl groups (eg, phenyl), each of which may be substituted with 1 to 3 substituents selected from the following: (1) a halogen atom (e.g., a fluorine atom), (2) The following: (i) a halogen atom (e.g., a fluorine atom), and (ii) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (3) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 6-14 aryl groups (e.g., phenyl); (4) The following: (i) Below: (a) a halogen atom (e.g., a fluorine atom), and (b)C 3-10 cycloalkyl groups (e.g., cyclopropyl) C optionally substituted by 1 to 3 substituents selected from 1-6 an amino group optionally mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); (ii) a halogen atom (e.g., a chlorine atom), (iii)C 1-6 alkoxy groups (e.g., methoxy), (iv) a cyano group, (v) Below: (a) an azido group, (b) Halogen atoms (e.g., fluorine atoms) and C 3-10 C optionally substituted with 1 to 3 substituents selected from cycloalkyl groups (e.g., cyclopropyl) 1-6 an amino group optionally mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); (c) a hydroxy group, and (d) halogen atoms (e.g., fluorine atoms) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl); (vi) a formyl group, (vii) a carboxy group, (viii) a carbamoyl group, (ix) C 3-10 cycloalkyl groups (e.g., cyclopropyl), and (x) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., dioxolanyl (e.g., 1,3-dioxolanyl)). an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- or 6-membered monocyclic aromatic heterocyclic group or an 8- to 14-membered fused polycyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl, pyrimidinyl, imidazolyl, pyrazolyl, tetrazolyl, benzimidazolyl (e.g., 1H-benzimidazolyl), thiazolyl) optionally substituted by 1 to 3 substituents selected from (5) The following: (i) Below: (a) a hydroxy group, (b)C 1-6 an amino group optionally mono- or disubstituted by alkyl groups (e.g., methyl); (c) a cyano group, and (d)C 6-14 aryl groups (e.g., phenyl) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl); (ii) an oxo group, (iii) a hydroxy group, (iv) a carbamoyl group, and (v) Thioxo group a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group, a 9- to 14-membered fused polycyclic non-aromatic heterocyclic group, or a 7- to 14-membered spiro heterocyclic group) (e.g., morpholinyl, dihydropyranyl (e.g., 3,6-dihydro-2H-pyranyl), tetrahydropyranyl, dihydropyridyl (e.g., 1,2-dihydropyridyl), dihydrobenzofuranyl (e.g., 2,3-dihydrobenzofuranyl), imidazoline, methyl ... Zolidinyl, pyrrolidinyl, dihydroisoxazolyl (e.g., 4,5-dihydroisoxazolyl), dihydropyrrolopyrazolyl (e.g., 5,6-dihydropyrrolo[3,4-c]pyrazolyl), piperazinyl, triazaspirononyl (e.g., 1,3,7-triazaspiro[4.4]nonyl), thiadiazaspirononyl (e.g., 7-thia-1,3-diazaspiro[4.4]nonyl), dioxide thiadiazaspirononyl (e.g., 7,7-dioxide-7-thia-1,3-diazaspiro[4.4]nonyl)), (6) C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), (7) C 1-6 alkyl-carbonyl groups (e.g., acetyl); (8) Aromatic heterocyclylsulfonyl groups (preferably 5- to 14-membered aromatic heterocyclylsulfonyl groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl groups) (e.g., thiazolylsulfonyl), and (9) Halogenated thio groups (e.g., pentafluorothio).

[0031] R 1is even more preferably an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- or 6-membered monocyclic aromatic heterocyclic group or an 8- to 14-membered fused polycyclic aromatic heterocyclic group) optionally substituted by 1 to 3 substituents selected from the following (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)). (i) Below: (a) a halogen atom (e.g., a fluorine atom), and (b) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (ii) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 6-14 aryl groups (e.g., phenyl); (iii) Below: (a) Below: (I) a halogen atom (e.g., a fluorine atom), and (II)C 3-10 cycloalkyl groups (e.g., cyclopropyl) C optionally substituted by 1 to 3 substituents selected from 1-6 an amino group optionally mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); (b) a halogen atom (e.g., a chlorine atom), (c)C 1-6 alkoxy groups (e.g., methoxy), (d) a cyano group, (e) Below: (I) an azide group, (II) Halogen atoms (e.g., fluorine atoms) and C 3-10 C optionally substituted with 1 to 3 substituents selected from cycloalkyl groups (e.g., cyclopropyl) 1-6an amino group optionally mono- or di-substituted by alkyl groups (e.g., methyl, ethyl); (III) a hydroxy group, and (IV) Halogen atoms (e.g., fluorine atoms) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl); (f) a formyl group, (g) a carboxy group, (h) a carbamoyl group, (I C 3-10 cycloalkyl groups (e.g., cyclopropyl), and (j) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., dioxolanyl (e.g., 1,3-dioxolanyl)); an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl, pyrimidinyl, pyrazolyl, thiazolyl, imidazolyl) optionally substituted by 1 to 3 substituents selected from (iv) Below: (a) Below: (I) a hydroxy group, (II)C 1-6 an amino group optionally mono- or disubstituted by alkyl groups (e.g., methyl); (III) a cyano group, and (IV)C 6-14 aryl groups (e.g., phenyl) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl); (b) an oxo group, (c) a hydroxy group, (d) a carbamoyl group, and (e) Thioxo group a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group, a 9- to 14-membered fused polycyclic non-aromatic heterocyclic group, or a 7- to 14-membered spiro heterocyclic group) (e.g., morpholinyl, dihydropyranyl (e.g., 3,6-dihydro-2H-pyranyl), tetrahydropyranyl, dihydropyridyl (e.g., 1,2-dihydropyridyl), dihydrobenzofuranyl (e.g., 2,3-dihydrobenzofuranyl), imidazoline, methyl ... Zolidinyl, pyrrolidinyl, dihydroisoxazolyl (e.g., 4,5-dihydroisoxazolyl), dihydropyrrolopyrazolyl (e.g., 5,6-dihydropyrrolo[3,4-c]pyrazolyl), piperazinyl, triazaspirononyl (e.g., 1,3,7-triazaspiro[4.4]nonyl), thiadiazaspirononyl (e.g., 7-thia-1,3-diazaspiro[4.4]nonyl), dioxide thiadiazaspirononyl (e.g., 7,7-dioxide-7-thia-1,3-diazaspiro[4.4]nonyl)), (v) C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and (vi) C 1-6 an alkyl-carbonyl group (e.g., acetyl), or (2) The following: (i) a halogen atom (e.g., a fluorine atom), (ii) C 1-6 alkyl groups (e.g., methyl); (iii) aromatic heterocyclic groups (preferably 5- to 14-membered aromatic heterocyclic groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclic groups, and 8- to 14-membered fused polycyclic aromatic heterocyclic groups) (e.g., imidazolyl, pyrazolyl, tetrazolyl, benzimidazolyl (e.g., 1H-benzimidazolyl)), (iv) C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), (v) an aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl group) (e.g., thiazolylsulfonyl), (vi) halogenated thio groups (e.g., pentafluorothio), and (vii) Below: (a) C optionally substituted with 1 to 3 amino groups 1-6 alkyl groups (e.g., methyl), and (b) oxo group a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group, or a 7- to 14-membered spiro heterocyclic group) optionally substituted by 1 to 3 substituents selected from the group consisting of imidazolidinyl, triazaspirononyl (e.g., 1,3,7-triazaspiro[4.4]nonyl), C optionally substituted by 1 to 3 substituents selected from 6-14 Aryl groups (e.g., phenyl).

[0032] R 1 is even more preferably an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- or 6-membered monocyclic aromatic heterocyclic group) optionally substituted by 1 to 3 substituents selected from the following (e.g., oxazolyl, pyridyl, pyrazolyl): (i) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 1-6 alkyl groups (e.g., methyl); (ii) Below: (a) Below: (I) a halogen atom (e.g., a fluorine atom), and (II)C 3-10 cycloalkyl groups (e.g., cyclopropyl) C optionally substituted by 1 to 3 substituents selected from 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl, ethyl), and (b) C optionally substituted with 1 to 3 amino groups 1-6 Alkyl groups (e.g., methyl) an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- or 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, pyrazolyl) optionally substituted by 1 to 3 substituents selected from (iii) Below: (a) C optionally substituted with 1 to 3 amino groups 1-6 alkyl groups (e.g., methyl), and (b) oxo group a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group, or a 7- to 14-membered spiro heterocyclic group) (e.g., imidazolidinyl, triazaspirononyl (e.g., 1,3,7-triazaspiro[4.4]nonyl)) optionally substituted by 1 to 3 substituents selected from (2) 1 to 3 Cs 1-6 C optionally substituted with an alkyl group (e.g., methyl) 6-14 Aryl groups (e.g., phenyl).

[0033] R 1 is particularly preferably C optionally substituted by 1 to 3 substituents selected from the following: 1-6 and aromatic heterocyclic groups (preferably 5- to 14-membered aromatic heterocyclic groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclic groups) (e.g., oxazolyl) optionally substituted by aromatic heterocyclic groups (preferably 5- to 14-membered aromatic heterocyclic groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclic groups) (e.g., pyridyl) optionally substituted by amino groups which may be mono- or di-substituted by alkyl groups (e.g., methyl, ethyl). (1) a halogen atom (e.g., a fluorine atom), and (2) C 3-10 Cycloalkyl groups (eg, cyclopropyl).

[0034] R 2 is a hydrogen atom or a substituent.

[0035] In one embodiment, R 2Examples of the "substituents" include those similar to the "substituents" exemplified herein.

[0036] R 2 The "substituent" in the formula (I) is preferably an optionally substituted hydrocarbon group (for example, a hydrocarbon group which may have a substituent selected from the substituent group A), more preferably an optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group).

[0037] In another embodiment, R 2 Examples of the "substituent" in the formula (I) include a halogen atom, a cyano group, a nitro group, an optionally substituted hydrocarbon group (the "hydrocarbon group" may have a substituent selected from Substituent Group A and a non-aromatic heterocyclic group having an oxo group), an optionally substituted heterocyclic group, an acyl group, an optionally substituted amino group, an optionally substituted carbamoyl group, an optionally substituted thiocarbamoyl group, an optionally substituted sulfamoyl group, an optionally substituted hydroxy group, an optionally substituted sulfanyl (SH) group, and an optionally substituted silyl group.

[0038] R 2 The "substituent" in the formula (I) is preferably an optionally substituted hydrocarbon group (for example, a hydrocarbon group which may have a substituent selected from Substituent Group A and a non-aromatic heterocyclic group having an oxo group), or an optionally substituted heterocyclic group (for example, a heterocyclic group which may have a substituent selected from Substituent Group A), and more preferably (1) optionally substituted C 1-6 C optionally having an alkyl group (for example, a substituent selected from Substituent Group A) and a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) having an oxo group 1-6 alkyl group), (2) optionally substituted C 3-10 A cycloalkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 3-10cycloalkyl groups), or (3) An optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A) is.

[0039] In one embodiment, R 2 is preferably optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group).

[0040] In another embodiment, R 2 is preferably optionally substituted C 1-6 C optionally having an alkyl group (for example, a substituent selected from Substituent Group A) and a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) having an oxo group 1-6 alkyl group), (2) optionally substituted C 3-10 A cycloalkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 3-10 cycloalkyl groups), or (3) An optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A) is.

[0041] R 2 is more preferably C optionally substituted by 1 to 3 substituents selected from the following: 1-6 It is an alkyl group (eg, methyl, ethyl). (I C 1-6 alkoxy-carbonyl groups (e.g., methoxycarbonyl), (ii) C 1-6 alkylsulfonyl groups (e.g., methylsulfonyl), (iii) a carbamoyl group, (iv) a cyano group, (v) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) optionally substituted by 1 to 3 oxo groups (e.g., pyrrolidinyl, tetrahydrofuryl, oxetanyl), and (vi) a halogen atom (e.g., a fluorine atom), (2) C optionally substituted with 1 to 3 hydroxy groups 3-10 a cycloalkyl group (e.g., cyclopentyl), or (3) A non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (for example, oxetanyl).

[0042] R 2 More preferably, C 1-6 It is an alkyl group (eg, methyl).

[0043] R 3 and R 4 are independently a hydrogen atom or a substituent, or R 3 and R 4 may combine to form an optionally substituted ring.

[0044] R 3 or R 4 Examples of the "substituents" include those similar to the "substituents" exemplified herein.

[0045] R 3 or R 4 The "substituent" in the formula (I) is preferably an optionally substituted hydrocarbon group (for example, a hydrocarbon group which may have a substituent selected from the substituent group A), more preferably an optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group).

[0046] R 3 and R 4Examples of the "ring" of the "optionally substituted ring" formed by 3-10 Cycloalkane, C 3-10 Examples include cycloalkenes and non-aromatic heterocycles (preferably 3- to 14-membered non-aromatic heterocycles).

[0047] R 3 and R 4 The "ring" of the "optionally substituted ring" formed by the formula (I) may have, at substitutable positions, 1 to 3 substituents selected from Substituent Group A. When there are a plurality of substituents, the respective substituents may be the same or different.

[0048] R 3 and R 4 are preferably independently a hydrogen atom or a substituent.

[0049] R 3 and R 4 are more preferably independently a hydrogen atom or an optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group).

[0050] In one embodiment, R 3 and R 4 are more preferably independently a hydrogen atom or C 1-6 It is an alkyl group (eg, methyl).

[0051] In another embodiment, R 3 and R 4 and more preferably, independently (1) a hydrogen atom, or (2) C 1-6 C optionally substituted by 1 to 3 substituents selected from amino groups optionally mono- or di-substituted by alkyl groups (e.g., methyl); 1-6 Alkyl groups (e.g., methyl) is.

[0052] Even more preferably, R3 and R 4 One of the atoms is a hydrogen atom, and the other is (1) a hydrogen atom, or (2) A C1-6 alkyl group (e.g., methyl) optionally substituted by 1 to 3 substituents selected from an amino group optionally mono- or di-substituted by a C1-6 alkyl group (e.g., methyl). is.

[0053] Even more preferably, R 3 and R 4 One of the groups is a hydrogen atom, and the other is a hydrogen atom or C 1-6 It is an alkyl group (eg, methyl).

[0054] R 3 and R 4 and are particularly preferably both hydrogen atoms.

[0055] R 5 and R 6 are independently a hydrogen atom or a substituent, or R 5 and R 6 may combine to form an optionally substituted ring.

[0056] In one embodiment, R 5 or R 6 Examples of the "substituents" include those similar to the "substituents" exemplified herein.

[0057] R 5 or R 6 The "substituents" of are preferably (1) an optionally substituted hydroxy group, (2) an optionally substituted hydrocarbon group (for example, a hydrocarbon group optionally having a substituent selected from Substituent Group A), (3) an optionally substituted amino group, or (4) Optionally substituted heterocyclic group (for example, a heterocyclic group optionally having a substituent selected from Substituent Group A) and more preferably, (1) a hydroxy group, (2) an optionally substituted C1-6 alkyl group (for example, a C1-6 alkyl group optionally having a substituent selected from Substituent Group A), (3) an optionally substituted C alkoxy group (for example, a C alkoxy group optionally having a substituent selected from Substituent Group A), (4) The following: ○(i) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ○(ii) optionally substituted C 1-6 an alkyl-carbonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl-carbonyl groups), and ○(iii) Optionally substituted C 1-6 an alkylsulfonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkylsulfonyl group) an amino group which may be mono- or di-substituted by a substituent selected from (5) An optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A) is.

[0058] In another embodiment, R 5 or R 6 Examples of the "substituent" include a halogen atom, a cyano group, a nitro group, an optionally substituted hydrocarbon group (the "hydrocarbon group" may be substituted with a substituent selected from the following: (1) Substituent group A, and (2) (a) C 1-6 (b) an alkyl group optionally substituted with 1 to 3 halogen atoms; 3-10 (c) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group), (d) C 1-6alkylsulfonyl groups, and (e) C 3-10 Examples of the amino group include an amino group mono- or di-substituted by a substituent selected from a cycloalkyl-carbonyl group, an optionally substituted heterocyclic group, an acyl group, an optionally substituted amino group, an optionally substituted carbamoyl group, an optionally substituted thiocarbamoyl group, an optionally substituted sulfamoyl group, an optionally substituted hydroxy group, an optionally substituted sulfanyl (SH) group, and an optionally substituted silyl group.

[0059] R 5 or R 6 The "substituents" of are preferably (1) an optionally substituted hydroxy group, (2) optionally substituted hydrocarbon groups (for example, (1) Substituent group A, and (2) (a) C alkyl groups, (b) C cycloalkyl groups optionally substituted with 1 to 3 halogen atoms, (c) non-aromatic heterocyclic groups (preferably 3 to 14-membered non-aromatic heterocyclic groups), (d) C 1-6 alkylsulfonyl groups, and (e) C 3-10 a hydrocarbon group optionally having a substituent selected from an amino group mono- or di-substituted with a substituent selected from a cycloalkyl-carbonyl group; (3) an optionally substituted amino group, (4) an optionally substituted heterocyclic group (for example, a heterocyclic group optionally having a substituent selected from Substituent Group A), or (5) Acyl group and more preferably (1) a hydroxy group, (2) optionally substituted C 1-6 Alkyl groups (e.g., (1) Substituent group A, and (2) (a) C 1-6 (b) an alkyl group optionally substituted with 1 to 3 halogen atoms; 3-10 (c) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group), (d) C 1-6 alkylsulfonyl groups, and (e) C 3-10C optionally having a substituent selected from an amino group mono- or di-substituted with a substituent selected from a cycloalkyl-carbonyl group 1-6 alkyl group), (3) optionally substituted C 1-6 an alkoxy group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkoxy groups), (4) The following: ○(i) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ○(ii) optionally substituted C 1-6 an alkyl-carbonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl-carbonyl groups), and ○(iii) Optionally substituted C 1-6 an alkylsulfonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkylsulfonyl group) an amino group which may be mono- or di-substituted by a substituent selected from (5) an optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A), (6) a carboxy group, or (7) C 1-6 a carbamoyl group which may be mono- or disubstituted by alkyl groups; is.

[0060] R 5 and R 6 Examples of the "ring" of the "optionally substituted ring" formed by 3-10 Cycloalkane, C 3-10 Examples thereof include cycloalkenes and non-aromatic heterocycles (preferably 3- to 14-membered non-aromatic heterocycles), and preferred examples thereof include C 3-10Examples include cycloalkanes and non-aromatic heterocycles (preferably 3- to 14-membered non-aromatic heterocycles).

[0061] R 5 and R 6 The "ring" of the "optionally substituted ring" formed by the formula (I) may have, at substitutable positions, 1 to 3 substituents selected from Substituent Group A. When there are a plurality of substituents, the respective substituents may be the same or different.

[0062] In one embodiment, R 5 and R 6 are preferably independently a hydrogen atom or a substituent.

[0063] R 5 and R 6 are more preferably independently (1) a hydrogen atom, (2) a hydroxy group, (3) an optionally substituted C1-6 alkyl group (for example, a C1-6 alkyl group optionally having a substituent selected from Substituent Group A), (4) an optionally substituted C alkoxy group (for example, a C alkoxy group optionally having a substituent selected from Substituent Group A), (5) The following: ○(i) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ○(ii) optionally substituted C 1-6 an alkyl-carbonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl-carbonyl groups), and ○(iii) Optionally substituted C 1-6 an alkylsulfonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkylsulfonyl group) an amino group which may be mono- or di-substituted by a substituent selected from (6) An optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A) is.

[0064] R 5 and R 6 and even more preferably, independently (1) a hydrogen atom, (2) a hydroxy group, (3) The following: (i) a hydroxy group, and ○(ii)C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl, ethyl); a C1-6 alkyl group (e.g., methyl) optionally substituted by 1 to 3 substituents selected from (4) C 1-6 alkoxy groups (e.g., methoxy), (5) The following: ○(i)C 1-6 alkyl groups (e.g., methyl, ethyl); ○(ii)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ○(iii)C 1-6 Alkyl sulfonyl groups (e.g., methyl sulfonyl an amino group which may be mono- or di-substituted by a substituent selected from (6) A non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl). is.

[0065] Even more preferably, R 5 and R 6 One of the atoms is a hydrogen atom, and the other is (1) a hydrogen atom, (2) a hydroxy group, (3) The following: (i) a hydroxy group, and ○(ii)C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl, ethyl); a C1-6 alkyl group (e.g., methyl) optionally substituted by 1 to 3 substituents selected from (4) C 1-6 alkoxy groups (e.g., methoxy), (5) The following: ○(i)C 1-6 alkyl groups (e.g., methyl, ethyl); ○(ii)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ○(iii)C 1-6 Alkylsulfonyl groups (e.g., methylsulfonyl) an amino group which may be mono- or di-substituted by a substituent selected from (6) A non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl). is.

[0066] Particularly preferably, R 5 and R 6 One of the atoms is a hydrogen atom, and the other is (1) a hydrogen atom, (2) a hydroxy group, (3) a C1-6 alkyl group (e.g., methyl) optionally substituted by an amino group, which may be mono- or disubstituted by a C1-6 alkyl group (e.g., methyl), or (4) an amino group optionally mono- or di-substituted by a C1-6 alkyl group (e.g., methyl); is.

[0067] In another embodiment, R 5 and R 6 are preferably independently (1) a hydrogen atom, (2) a hydroxy group, (3) an optionally substituted C1-6 alkyl group (for example, (1) Substituent group A, and (2) a C1-6 alkyl group optionally having a substituent selected from (a) a C1-6 alkyl group, (b) a C3-10 cycloalkyl group optionally substituted by 1 to 3 halogen atoms, (c) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group), (d) a C1-6 alkylsulfonyl group, and (e) an amino group mono- or di-substituted by a substituent selected from a C3-10 cycloalkyl-carbonyl group), (4) an optionally substituted C alkoxy group (for example, a C alkoxy group optionally having a substituent selected from Substituent Group A), (5) The following: ○(i) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ○(ii) optionally substituted C 1-6 an alkyl-carbonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl-carbonyl groups), and ○(iii) Optionally substituted C 1-6 an alkylsulfonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkylsulfonyl group) an amino group which may be mono- or di-substituted by a substituent selected from (6) an optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A), (7) a carboxy group, or (8) C 1-6 a carbamoyl group which may be mono- or disubstituted by alkyl groups; or R 5 and R 6 are combined, (1) An optionally substituted non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle) (for example, a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle) optionally having a substituent selected from Substituent Group A), or (2) optionally substituted C 3-10 Cycloalkane (e.g., C optionally having a substituent selected from Substituent Group A) 3-10 Cycloalkane) may be formed.

[0068] R 5 and R 6 are more preferably independently (1) a hydrogen atom, (2) a hydroxy group, (3) The following: (i) a hydroxy group, ○(ii) or below: (a) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 1-6 alkyl groups (e.g., methyl, ethyl); (b) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 3-13 cycloalkyl groups (e.g., cyclopropyl, cyclobutyl); (c) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., oxetanyl), ■(d)C 1-6 alkylsulfonyl groups (e.g., methylsulfonyl), ■(e)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ■(f)C 3-10 cycloalkyl-carbonyl groups (e.g., cyclopropylcarbonyl) an amino group which may be mono- or di-substituted by a substituent selected from (iii) a halogen atom (e.g., a fluorine atom), ○(iv)C 1-6 alkylsulfanyl groups (e.g., methylsulfanyl), ○(v)C 1-6 alkylsulfinyl groups (e.g., methylsulfinyl), and ○(vi)C 1-6 Alkylsulfonyl groups (e.g., methylsulfonyl) a C1-6 alkyl group (e.g., methyl) optionally substituted by 1 to 3 substituents selected from (4) C 1-6 alkoxy groups (e.g., methoxy), (5) The following: ○(i)C 1-6 alkyl groups (e.g., methyl, ethyl); ○(ii)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ○(iii)C 1-6 Alkylsulfonyl groups (e.g., methylsulfonyl) an amino group which may be mono- or di-substituted by a substituent selected from (6) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl), (7) a carboxy group, or (8) C 1-6 a carbamoyl group optionally mono- or disubstituted by an alkyl group (e.g., methyl); or R 5 and R 6 are combined, (1) a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle, more preferably a 3- to 8-membered monocyclic non-aromatic heterocycle) (e.g., tetrahydrofuran), or (2) C 3-10 Cycloalkanes (e.g., cyclopentane) may be formed.

[0069] Even more preferably, R 5 and R 6 One of the atoms is a hydrogen atom or C 1-6 an alkyl group (e.g., methyl), and the other (1) a hydrogen atom, (2) a hydroxy group, (3) The following: (i) a hydroxy group, ○(ii) or below: (a) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 1-6 alkyl groups (e.g., methyl, ethyl); (b) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 3-10 cycloalkyl groups (e.g., cyclopropyl, cyclobutyl); (c) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., oxetanyl), ■(d)C 1-6 alkylsulfonyl groups (e.g., methylsulfonyl), ■(e)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ■(f)C 3-10 cycloalkyl-carbonyl groups (e.g., cyclopropylcarbonyl) an amino group which may be mono- or di-substituted by a substituent selected from (iii) a halogen atom (e.g., a fluorine atom), ○(iv)C 1-6 alkylsulfanyl groups (e.g., methylsulfanyl), ○(v)C 1-6 alkylsulfinyl groups (e.g., methylsulfinyl), and ○(vi)C 1-6 Alkylsulfonyl groups (e.g., methylsulfonyl) a C1-6 alkyl group (e.g., methyl) optionally substituted by 1 to 3 substituents selected from (4) C 1-6 alkoxy groups (e.g., methoxy), (5) The following: ○(i)C 1-6 alkyl groups (e.g., methyl, ethyl); ○(ii)C1-6 alkyl-carbonyl groups (e.g., acetyl), and ○(iii)C 1-6 Alkylsulfonyl groups (e.g., methylsulfonyl) an amino group which may be mono- or di-substituted by a substituent selected from (6) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl), (7) a carboxy group, or (8) C 1-6 a carbamoyl group optionally mono- or disubstituted by an alkyl group (e.g., methyl); or R 5 and R 6 are combined, (1) a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle, more preferably a 3- to 8-membered monocyclic non-aromatic heterocycle) (e.g., tetrahydrofuran), or (2) C 3-10 Cycloalkanes (e.g., cyclopentane) may be formed.

[0070] Even more preferably, R 5 and R 6 One of the atoms is a hydrogen atom, and the other is (1) a hydrogen atom, (2) a hydroxy group, (3) The following: ○(i)C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl), and (ii) Hydroxy group a C1-6 alkyl group (e.g., methyl) optionally substituted by 1 to 3 substituents selected from (4) C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl); is.

[0071] Particularly preferably, R 5 and R 6 One of the atoms is a hydrogen atom, and the other is (1) a hydrogen atom, (2) a C1-6 alkyl group (e.g., methyl) optionally substituted by an amino group, which may be mono- or disubstituted by a C1-6 alkyl group (e.g., methyl), or (3) an amino group optionally mono- or di-substituted by a C1-6 alkyl group (e.g., methyl); is.

[0072] In particular, R 5 and R 6 and are particularly preferably both hydrogen atoms.

[0073] X is CR 7 R 8 , N.R. 9 , O, or S.

[0074] X is preferably CR 7 R 8 , N.R. 9 , or O.

[0075] X is more preferably CR 7 R 8 or NR 9 is.

[0076] In one embodiment, X is even more preferably CR 7 R 8 is.

[0077] In another embodiment, X is even more preferably NR 9 is.

[0078] R 7 and R 8 are independently a hydrogen atom or a substituent, or R 7 and R 8 may combine to form an optionally substituted ring.

[0079] R 7 or R 8 Examples of the "substituents" include those similar to the "substituents" exemplified herein.

[0080] In one embodiment, R 7 or R 8 The "substituents" of are preferably (1) a cyano group, or (2) Optionally substituted hydrocarbon groups (for example, hydrocarbon groups which may have a substituent selected from Substituent Group A) and more preferably (1) a cyano group, or (2) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group) is. In another embodiment, R 7 or R 8 The "substituents" of are preferably (1) a cyano group, (2) an optionally substituted hydrocarbon group (for example, a hydrocarbon group optionally having a substituent selected from Substituent Group A), or (3) an optionally substituted hydroxy group and more preferably (1) a cyano group, (2) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), or (3) Hydroxy group is.

[0081] R 7 and R 8 Examples of the "ring" of the "optionally substituted ring" formed by 3-10 Cycloalkane, C 3-10 Examples thereof include cycloalkenes and non-aromatic heterocycles (preferably 3- to 14-membered non-aromatic heterocycles), and preferred examples thereof include C 3-10Examples include cycloalkanes and non-aromatic heterocycles (preferably 3- to 14-membered non-aromatic heterocycles).

[0082] In one embodiment, R 7 and R 8 The "ring" of the "optionally substituted ring" formed by the formula (I) may have, at substitutable positions, 1 to 3 substituents selected from Substituent Group A. When there are a plurality of substituents, the respective substituents may be the same or different.

[0083] In another embodiment, R 7 and R 8 The "ring" of the "optionally substituted ring" formed by 7-16 The aryl group may have 1 to 3 substituents selected from aralkyl groups. When the number of substituents is plural, the respective substituents may be the same or different.

[0084] In one embodiment, R 7 and R 8 are preferably independently a hydrogen atom or a substituent.

[0085] R 7 and R 8 are more preferably independently (1) a hydrogen atom, (2) a cyano group, or (3) An optionally substituted C1-6 alkyl group (for example, a C1-6 alkyl group optionally having a substituent selected from Substituent Group A) is.

[0086] R7 and R8 are even more preferably independently (1) a hydrogen atom, (2) a cyano group, or (3) C1-6 alkyl groups (e.g., methyl, ethyl) is.

[0087] In another embodiment, R7 and R8 are preferably independently (1) a hydrogen atom, (2) a cyano group, (3) an optionally substituted C1-6 alkyl group (for example, a C1-6 alkyl group optionally having a substituent selected from Substituent Group A), or (4) Hydroxy group or R 7 and R 8 are combined, (1) optionally substituted C 3-10 Cycloalkane (e.g., C optionally having a substituent selected from Substituent Group A) 3-10 cycloalkane), or (2) Optionally substituted non-aromatic heterocycle (preferably 3- to 14-membered non-aromatic heterocycle) (for example, substituent groups A and C 7-16 a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle) which may have a substituent selected from an aralkyl group; may be formed.

[0088] R 7 and R 8 are more preferably independently (1) a hydrogen atom, (2) a cyano group, (3) C optionally substituted with 1 to 3 hydroxy groups 1-6 an alkyl group (e.g., methyl, ethyl), or (4) Hydroxy group or R 7 and R 8 are combined, (1) The following: (i) an oxo group, and (ii) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 3-10 a cycloalkane (e.g., cyclohexane), or (2) 1 to 3 Cs 7-15a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle, more preferably a 3- to 8-membered monocyclic non-aromatic heterocycle) (e.g., pyrrolidine, piperidine) optionally substituted with an aralkyl group (e.g., benzyl); may be formed.

[0089] R 7 and R 8 and even more preferably, independently (1) a hydrogen atom, or (2) C 1-6 Alkyl groups (e.g., methyl) is.

[0090] R 9 is a hydrogen atom or a substituent.

[0091] R 9 Examples of the "substituents" include those similar to the "substituents" exemplified herein.

[0092] In one embodiment, R 9 The "substituent" in the formula (I) is preferably an optionally substituted hydrocarbon group (for example, a hydrocarbon group which may have a substituent selected from the substituent group A), more preferably an optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group).

[0093] In another embodiment, R 9 The "substituent" in the formula (I) is preferably an optionally substituted hydrocarbon group, more preferably (1) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), (2) optionally substituted C 2-6 an alkenyl group (e.g., C optionally having a substituent selected from Substituent Group A) 2-6 alkenyl group), or (3) optionally substituted C7-16 An aralkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 7-16 aralkyl group) is.

[0094] In one embodiment, R 9 is preferably optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group).

[0095] R 9 is more preferably C optionally substituted by 1 to 3 substituents selected from the following: 1-6 It is an alkyl group (eg, methyl, ethyl). (1) Hydroxy group, and ○(2) 1 to 3 C 6-14 C optionally substituted by an aryl group (e.g., phenyl) 1-6 Alkoxy groups (e.g., methoxy).

[0096] In another embodiment, R 9 is preferably a hydrogen atom or an optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group).

[0097] R 9 is more preferably (1) a hydrogen atom, or (2) The following: (i) a hydroxy group, and ○(ii) 1 to 3 C 6-14 C optionally substituted by an aryl group (e.g., phenyl) 1-6 Alkoxy groups (e.g., methoxy) C optionally substituted by 1 to 3 substituents selected from 1-6 Alkyl groups (e.g., methyl, ethyl) is.

[0098] In yet another embodiment, R 9 is preferably (1) a hydrogen atom, (2) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), (3) optionally substituted C 2-6 an alkenyl group (e.g., C optionally having a substituent selected from Substituent Group A) 2-6 alkenyl group), or (4) optionally substituted C 7-16 An aralkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 7-16 aralkyl group) is.

[0099] R 9 is more preferably (1) a hydrogen atom, or (2) The following: (i) a hydroxy group, ○(ii) 1 to 3 C 6-14 C optionally substituted by an aryl group (e.g., phenyl) 1-6 alkoxy groups (e.g., methoxy), and ○(iii)C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl); C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, propyl, isopropyl); (3) C 2-6 an alkenyl group (e.g., allyl), or (4) 1 to 3 Cs 1-6 C optionally substituted by an alkoxy group (e.g., methoxy) 7-16 Aralkyl groups (e.g., benzyl) is.

[0100] R 9 is even more preferably (1) a hydrogen atom, or (2) C optionally substituted with 1 to 3 hydroxy groups 1-6 an alkyl group (e.g., methyl, ethyl, propyl, preferably methyl, ethyl); is.

[0101] Preferred examples of compound (1) include the following compounds: [Compound A-1] Compound (I), wherein R 1 is an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group) or C 6-14 aryl groups, each of which is optionally substituted with 1 to 3 substituents selected from: ○(1) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ○(2) Optionally substituted C 6-14 An aryl group (e.g., C optionally having a substituent selected from Substituent Group A) 6-14 aryl group), (3) an optionally substituted heterocyclic group (for example, a heterocyclic group optionally having a substituent selected from Substituent Group A (the substituent may be further substituted with a substituent selected from Substituent Group A)), ○(4)C 3-10 cycloalkylsulfonyl groups, ○(5)C 1-6 alkyl-carbonyl groups, and (6) an aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group), R 2 may be substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), R 3 and R 4 are independently a hydrogen atom or an optionally substituted C 1-6an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), R 5 and R 6 is independently (1) a hydrogen atom, (2) a hydroxy group, (3) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), (4) optionally substituted C 1-6 an alkoxy group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkoxy groups), (5) The following: ■(i) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ■(ii) Optionally substituted C 1-6 an alkyl-carbonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl-carbonyl groups), and ■ (iii) Optionally substituted C 1-6 an alkylsulfonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkylsulfonyl group) an amino group which may be mono- or di-substituted by a substituent selected from (6) An optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A) and X is CR 7 R 8 , N.R. 9 , O, R 7 and R 8 is, independently, (1) a hydrogen atom, (2) a cyano group, or (3) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group) and R 9 may be substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), Compound (I). [Compound A-2] Compound (I), wherein R 1 is an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group) or C 6-14 aryl groups, each of which is optionally substituted with 1 to 3 substituents selected from: ○(1) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ○(2) Optionally substituted C 6-14 An aryl group (e.g., C optionally having a substituent selected from Substituent Group A) 6-14 aryl group), (3) an optionally substituted heterocyclic group (for example, a heterocyclic group optionally having a substituent selected from Substituent Group A (the substituent may be further substituted with a substituent selected from Substituent Group A)), ○(4)C 3-10 cycloalkylsulfonyl groups, ○(5)C 1-6 alkyl-carbonyl groups, and (6) an aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group), R 2 may be substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6alkyl group), R 3 and R 4 are independently a hydrogen atom or an optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), R 5 and R 6 is independently (1) a hydrogen atom, (2) a hydroxy group, (3) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), (4) optionally substituted C 1-6 an alkoxy group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkoxy groups), (5) The following: ○(i) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ○(ii) optionally substituted C 1-6 an alkyl-carbonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl-carbonyl groups), and ○(iii) Optionally substituted C 1-6 an alkylsulfonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkylsulfonyl group) an amino group which may be mono- or di-substituted by a substituent selected from (6) An optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A) and X is CR 7 R 6 , N.R.9 , O, R 7 and R 8 is, independently, (1) a hydrogen atom, (2) a cyano group, or (3) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group) and R 9 is a hydrogen atom or an optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), Compound (I). [Compound A-3] Compound (I), wherein R 1 is an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group) or C 6-14 aryl groups, each of which is optionally substituted with 1 to 3 substituents selected from: ○(1) Halogen atoms, ○(2) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ○(3) Optionally substituted C 6-14 An aryl group (e.g., C optionally having a substituent selected from Substituent Group A) 6-14 aryl group), (4) A heterocyclic group which may be substituted (for example, a heterocyclic group which may have a substituent selected from the group consisting of the group A and a thioxo group (the substituents are the group A, an azido group, and a mono- or di-C 1-6 Alkylamino group (alkyl is C 3-10 substituted by a substituent selected from a cycloalkyl group and a halogen atom); ○(5)C 3-10cycloalkylsulfonyl groups, ○(6)C 1-6 alkyl-carbonyl groups, (7) Aromatic heterocyclylsulfonyl groups (preferably 5- to 14-membered aromatic heterocyclylsulfonyl groups), and (8) halogenated sulfanyl groups, R 2 teeth, (1) optionally substituted C 1-6 C optionally having an alkyl group (for example, a substituent selected from Substituent Group A) and a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) having an oxo group 1-6 alkyl group), (2) optionally substituted C 3-10 A cycloalkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 3-10 cycloalkyl groups), or (3) An optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A) and R 3 and R 4 are independently a hydrogen atom or an optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), R 5 and R 6 is independently (1) a hydrogen atom, (2) a hydroxy group, (3) optionally substituted C 1-6 Alkyl groups (e.g., (1) Substituent group A, and (2) (a) C 1-5 (b) an alkyl group optionally substituted with 1 to 3 halogen atoms; 3-10 (c) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group), (d) C 1-6 alkylsulfonyl groups, and (e) C 3-10C optionally having a substituent selected from an amino group mono- or di-substituted with a substituent selected from a cycloalkyl-carbonyl group 1-6 alkyl group), (4) optionally substituted C 1-6 an alkoxy group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkoxy groups), (5) The following: ○(i) Optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), ○(ii) optionally substituted C 1-6 an alkyl-carbonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl-carbonyl groups), and ○(iii) Optionally substituted C 1-6 an alkylsulfonyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkylsulfonyl group) an amino group which may be mono- or di-substituted by a substituent selected from (6) an optionally substituted non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) (for example, a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group) optionally having a substituent selected from Substituent Group A), (7) a carboxy group, or (8) C 1-6 a carbamoyl group optionally mono- or di-substituted by alkyl groups; or R 5 and R 6 are combined, (1) An optionally substituted non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle) (for example, a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle) optionally having a substituent selected from Substituent Group A), or (2) optionally substituted C 3-10Cycloalkane (e.g., C optionally having a substituent selected from Substituent Group A) 3-10 Cycloalkane) and X is CR 7 R 8 , N.R. 9 , O, or S; R 7 and R 8 is, independently, (1) a hydrogen atom, (2) a cyano group, (3) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), or (4) Hydroxy group or R 7 and R 8 are combined, (1) optionally substituted C 3-10 Cycloalkane (e.g., C optionally having a substituent selected from Substituent Group A) 3-10 cycloalkane), or (2) Optionally substituted non-aromatic heterocycle (preferably 3- to 14-membered non-aromatic heterocycle) (for example, substituent groups A and C 7-16 a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle) which may have a substituent selected from an aralkyl group; and R 9 teeth, (1) a hydrogen atom, (2) optionally substituted C 1-6 an alkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 1-6 alkyl group), (3) optionally substituted C 2-6 an alkenyl group (e.g., C optionally having a substituent selected from Substituent Group A) 2-6 alkenyl group), or (4) optionally substituted C 7-16An aralkyl group (e.g., C optionally having a substituent selected from Substituent Group A) 7-16 aralkyl group) That is, Compound (I). [Compound B-1] Compound (I), wherein R 1 teeth, (1) Aromatic heterocyclic groups (preferably 5- to 14-membered aromatic heterocyclic groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclic groups, and 8- to 14-membered fused polycyclic aromatic heterocyclic groups) optionally substituted by 1 to 3 substituents selected from the following (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)), ○(i) or below: (a) a halogen atom (e.g., a fluorine atom), and ■ (b) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (ii) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 6-14 aryl groups (e.g., phenyl); (iii) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 1-6 an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., ethyl); ○(iv) 1 to 3 C 1-6 a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl) optionally substituted by an alkyl group (e.g., methyl); ○(v)C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and ○(vi)C 1-6 an alkyl-carbonyl group (e.g., acetyl), or (2) The following: ○(i)C 1-6 alkyl groups (e.g., methyl); ○(ii)C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and (iii) an aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl group) (e.g., thiazolylsulfonyl); C optionally substituted by 1 to 3 substituents selected from 6-14 aryl groups (e.g., phenyl) and R 2 is C 1-6 an alkyl group (e.g., methyl), R 3 and R 4 are independently a hydrogen atom or C 1-6 an alkyl group (e.g., methyl), R 5 and R 6 is independently (1) a hydrogen atom, (2) a hydroxy group, (3) The following: (i) a hydroxy group, and ○(ii)C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl, ethyl); C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl); (4) C 1-6 alkoxy groups (e.g., methoxy), (5) The following: ○(i)C 1-6 alkyl groups (e.g., methyl, ethyl); ○(ii)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ○(iii)C 1-6 Alkylsulfonyl groups (e.g., methylsulfonyl) an amino group which may be mono- or di-substituted by a substituent selected from (6) A non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl). and X is CR 7 R 8 , N.R. 9 , or 0, R 7 and R 8 is, independently, (1) a hydrogen atom, (2) a cyano group, or (3) C 1-6 Alkyl groups (e.g., methyl, ethyl) and R 9 is the following: (1) Hydroxy group, and ○(2) 1 to 3 C 6-14 C optionally substituted by an aryl group (e.g., phenyl) 1-6 Alkoxy groups (e.g., methoxy) C optionally substituted by 1 to 3 substituents selected from 1-6 Alkyl groups (e.g., methyl, ethyl) That is, Compound (I). [Compound B-2] Compound (I), wherein R 1 teeth, (1) Aromatic heterocyclic groups (preferably 5- to 14-membered aromatic heterocyclic groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclic groups, and 8- to 14-membered fused polycyclic aromatic heterocyclic groups) optionally substituted by 1 to 3 substituents selected from the following (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)), ○(i) or below: (a) a halogen atom (e.g., a fluorine atom), and ■ (b) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (ii) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 6-14 aryl groups (e.g., phenyl); ○(iii) or below: (a) a halogen atom (e.g., a fluorine atom), and ■(b)C 3-10 cycloalkyl groups (e.g., cyclopropyl) C optionally substituted by 1 to 3 substituents selected from 1-6 an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); ○(iv) 1 to 3 C 1-5 a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl) optionally substituted by an alkyl group (e.g., methyl); ○(v)C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and ○(vi)C 1-6an alkyl-carbonyl group (e.g., acetyl), or (2) The following: ○(i)C 1-6 alkyl groups (e.g., methyl); ○(ii)C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and (iii) an aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl group) (e.g., thiazolylsulfonyl); C optionally substituted by 1 to 3 substituents selected from 6-14 aryl groups (e.g., phenyl) and R 2 is C 1-6 an alkyl group (e.g., methyl), R 3 and R 4 are independently a hydrogen atom or C 1-6 an alkyl group (e.g., methyl), R 5 and R 6 is independently (1) a hydrogen atom, (2) a hydroxy group, (3) The following: (i) a hydroxy group, and ○(ii)C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl, ethyl); C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl); (4) C 1-6 alkoxy groups (e.g., methoxy), (5) The following: ○(i)C 1-6 alkyl groups (e.g., methyl, ethyl); ○(ii)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ○(iii)C 1-6Alkylsulfonyl groups (e.g., methylsulfonyl) an amino group which may be mono- or di-substituted by a substituent selected from (6) A non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl). and X is CR 7 R 8 , N.R. 9 , O, R 7 and R 8 is, independently, (1) a hydrogen atom, (2) a cyano group, or (3) C 1-6 Alkyl groups (e.g., methyl, ethyl) and R 9 teeth, (1) a hydrogen atom, or (2) The following: (i) a hydroxy group, and ○(ii) 1 to 3 C 6-14 C optionally substituted by an aryl group (e.g., phenyl) 1-6 Alkoxy groups (e.g., methoxy) C optionally substituted by 1 to 3 substituents selected from 1-6 Alkyl groups (e.g., methyl, ethyl) That is, Compound (I). [Compound B-3] Compound (I), wherein R 1 is an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group or an 8- to 14-membered fused polycyclic aromatic heterocyclic group) (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)), or C6-14 aryl groups (e.g., phenyl), each of which is optionally substituted with 1 to 3 substituents selected from: (1) Halogen atoms (e.g., fluorine atoms), ○(2) and below: (i) a halogen atom (e.g., a fluorine atom), and ■ (ii) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (3) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 6-14 aryl groups (e.g., phenyl); ○(4) and below: ■(i) Below: (a) a halogen atom (e.g., a fluorine atom), and ■(b)C 3-10 cycloalkyl groups (e.g., cyclopropyl) C optionally substituted by 1 to 3 substituents selected from 1-6 an amino group optionally mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); ■ (ii) a halogen atom (e.g., a chlorine atom), ■(iii)C 1-6 alkoxy groups (e.g., methoxy), ■ (iv) a cyano group, ■(v) Below: ■ (a) an azido group; (b) Halogen atoms (e.g., fluorine atoms) and C 3-10 C optionally substituted with 1 to 3 substituents selected from cycloalkyl groups (e.g., cyclopropyl) 1-6 an amino group optionally mono- or di-substituted by alkyl groups (e.g., methyl, ethyl); ■ (c) a hydroxy group, and ■ (d) Halogen atoms (e.g., fluorine atoms) C optionally substituted by 1 to 3 substituents selected from 1-6alkyl groups (e.g., methyl, ethyl); ■ (vi) a formyl group, ■ (vii) a carboxy group, ■ (viii) a carbamoyl group, ■(ix)C 3-10 cycloalkyl groups (e.g., cyclopropyl), and (x) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., dioxolanyl (e.g., 1,3-dioxolanyl)) an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- or 6-membered monocyclic aromatic heterocyclic group or an 8- to 14-membered fused polycyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl, pyrimidinyl, imidazolyl, pyrazolyl, tetrazolyl, benzimidazolyl (e.g., 1H-benzimidazolyl), thiazolyl) optionally substituted by 1 to 3 substituents selected from ○(5) and below: ■(i) Below: ■ (a) hydroxy group, ■(b)C 1-6 an amino group optionally mono- or disubstituted by alkyl groups (e.g., methyl); ■ (c) a cyano group, and ■(d)C 6-14 aryl groups (e.g., phenyl) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl); ■ (ii) an oxo group, ■ (iii) a hydroxy group, (iv) a carbamoyl group, and (v) Thioxo group a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group, a 9- to 14-membered fused polycyclic non-aromatic heterocyclic group, or a 7- to 14-membered spiro heterocyclic group) (e.g., morpholinyl, dihydropyranyl (e.g., 3,6-dihydro-2H-pyranyl), tetrahydropyranyl, dihydropyridyl (e.g., 1,2-dihydropyridyl), dihydrobenzofuranyl (e.g., 2,3-dihydrobenzofuranyl), imidazoline, methyl ... Zolidinyl, pyrrolidinyl, dihydroisoxazolyl (e.g., 4,5-dihydroisoxazolyl), dihydropyrrolopyrazolyl (e.g., 5,6-dihydropyrrolo[3,4-c]pyrazolyl), piperazinyl, triazaspirononyl (e.g., 1,3,7-triazaspiro[4.4]nonyl), thiadiazaspirononyl (e.g., 7-thia-1,3-diazaspiro[4.4]nonyl), dioxide thiadiazaspirononyl (e.g., 7,7-dioxide-7-thia-1,3-diazaspiro[4.4]nonyl)), ○(6)C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), ○(7)C 1-6 alkyl-carbonyl groups (e.g., acetyl); (8) Aromatic heterocyclylsulfonyl groups (preferably 5- to 14-membered aromatic heterocyclylsulfonyl groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl groups) (e.g., thiazolylsulfonyl), and (9) halogenated thio groups (e.g., pentafluorothio); R 2 teeth, (1) The following: ○(i)C 1-6 alkoxy-carbonyl groups (e.g., methoxycarbonyl), ○(ii)C 1-6 alkylsulfonyl groups (e.g., methylsulfonyl), (iii) a carbamoyl group, (iv) a cyano group, (v) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) optionally substituted by 1 to 3 oxo groups (e.g., pyrrolidinyl, tetrahydrofuryl, oxetanyl), and (vi) Halogen atoms (e.g., fluorine atoms) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl); (2) C optionally substituted with 1 to 3 hydroxy groups 3-10 a cycloalkyl group (e.g., cyclopentyl), or (3) A non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., oxetanyl). and R 3 and R 4 is independently (1) a hydrogen atom, or (2) C 1-6 C optionally substituted by 1 to 3 substituents selected from an amino group optionally mono- or di-substituted by an alkyl group (e.g., methyl); 1-6 Alkyl groups (e.g., methyl) and R 5 and R 6 is independently (1) a hydrogen atom, (2) a hydroxy group, (3) The following: (i) a hydroxy group, ○(ii) or below: (a) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 1-6 alkyl groups (e.g., methyl, ethyl); (b) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 3-10 cycloalkyl groups (e.g., cyclopropyl, cyclobutyl); (c) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., oxetanyl), ■(d)C 1-6 alkylsulfonyl groups (e.g., methylsulfonyl), ■(e)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ■(f)C 3-10 cycloalkyl-carbonyl groups (e.g., cyclopropylcarbonyl) an amino group which may be mono- or di-substituted by a substituent selected from (iii) a halogen atom (e.g., a fluorine atom), ○(iv)C 1-6 alkylsulfanyl groups (e.g., methylsulfanyl), ○(v)C 1-6 alkylsulfinyl groups (e.g., methylsulfinyl), and ○(vi)C 1-6 Alkylsulfonyl groups (e.g., methylsulfonyl) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl); (4) C 1-6 alkoxy groups (e.g., methoxy), (5) The following: ○(i)C 1-6 alkyl groups (e.g., methyl, ethyl); ○(ii)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ○(iii)C 1-6 Alkylsulfonyl groups (e.g., methylsulfonyl) an amino group which may be mono- or di-substituted by a substituent selected from (6) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl), (7) a carboxy group, or (8) C 1-6a carbamoyl group optionally mono- or disubstituted by an alkyl group (e.g., methyl); or R 5 and R 6 are combined, (1) a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle, more preferably a 3- to 8-membered monocyclic non-aromatic heterocycle) (e.g., tetrahydrofuran), or (2) C 3-10 Cycloalkanes (e.g., cyclopentane) and X is CR 7 R 9 , N.R. 9 , O, or S; R 7 and R 8 is, independently, (1) a hydrogen atom, (2) a cyano group, (3) an alkyl group (e.g., methyl, ethyl) optionally substituted with 1 to 3 hydroxy groups, or (4) Hydroxy group or R 7 and R 8 are combined, (1) The following: (i) an oxo group, and (ii) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 3-10 a cycloalkane (e.g., cyclohexane), or (2) 1 to 3 Cs 7-16 a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle, more preferably a 3- to 8-membered monocyclic non-aromatic heterocycle) (e.g., pyrrolidine, piperidine) optionally substituted with an aralkyl group (e.g., benzyl); and R 9 teeth, (1) a hydrogen atom, or (2) The following: (i) a hydroxy group, ○(ii) 1 to 3 C 6-14 C optionally substituted by an aryl group (e.g., phenyl) 1-6 alkoxy groups (e.g., methoxy), and ○(iii)C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl); C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, propyl, isopropyl); (3) C 2-6 an alkenyl group (e.g., allyl), or (4) 1 to 3 Cs 1-6 C optionally substituted by an alkoxy group (e.g., methoxy) 7-16 Aralkyl groups (e.g., benzyl) That is, Compound (I). [Compound B-4] Compound (I), wherein R 1 teeth, (1) Aromatic heterocyclic groups (preferably 5- to 14-membered aromatic heterocyclic groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclic groups, and 8- to 14-membered fused polycyclic aromatic heterocyclic groups) optionally substituted by 1 to 3 substituents selected from the following (e.g., oxazolyl, thiazolyl, thienyl, pyrazolyl, pyridyl, imidazopyridyl (e.g., imidazo[1,5-a]pyridyl), imidazopyridazinyl (e.g., imidazo[1,2-b]pyridazinyl), pyrazolopyrimidinyl (e.g., pyrazolo[1,5-a]pyrimidinyl)), ○(i) or below: (a) a halogen atom (e.g., a fluorine atom), and ■ (b) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, isopropyl); (ii) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms)6-14 aryl groups (e.g., phenyl); ○(iii) or below: ■(a) and below: (I) a halogen atom (e.g., a fluorine atom), and ■(II)C 3-10 cycloalkyl groups (e.g., cyclopropyl) C optionally substituted by 1 to 3 substituents selected from 1-6 an amino group optionally mono- or di-substituted by alkyl groups (e.g., methyl, ethyl); ■ (b) a halogen atom (e.g., a chlorine atom); ■(c)C 1-6 alkoxy groups (e.g., methoxy), ■ (d) a cyano group; ■(e) and below: ■ (I) an azide group, (II) Halogen atoms (e.g., fluorine atoms) and C 3-10 C optionally substituted with 1 to 3 substituents selected from cycloalkyl groups (e.g., cyclopropyl) 1-6 an amino group optionally mono- or di-substituted by alkyl groups (e.g., methyl, ethyl); (III) a hydroxy group, and ■ (IV) Halogen atoms (e.g., fluorine atoms) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl); ■ (f) formyl group, ■ (g) carboxyl group, ■ (h) a carbamoyl group, ■(i)C 3-10 cycloalkyl groups (e.g., cyclopropyl), and (j) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., dioxolanyl (e.g., 1,3-dioxolanyl)) an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, thienyl, pyrimidinyl, pyrazolyl, thiazolyl, imidazolyl) optionally substituted by 1 to 3 substituents selected from ○(iv) or below: ■(a) and below: ■ (I) a hydroxy group, ■(II)C 1-6 an amino group optionally mono- or disubstituted by alkyl groups (e.g., methyl); (III) a cyano group, and ■(IV)C 6-14 aryl groups (e.g., phenyl) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl); ■ (b) an oxo group, ■ (c) hydroxy group, (d) a carbamoyl group, and ■(e) Thioxo group a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group, a 9- to 14-membered fused polycyclic non-aromatic heterocyclic group, or a 7- to 14-membered spiro heterocyclic group) (e.g., morpholinyl, dihydropyranyl (e.g., 3,6-dihydro-2H-pyranyl), tetrahydropyranyl, dihydropyridyl (e.g., 1,2-dihydropyridyl), dihydrobenzofuranyl (e.g., 2,3-dihydrobenzofuranyl), imidazoline, methyl ... Zolidinyl, pyrrolidinyl, dihydroisoxazolyl (e.g., 4,5-dihydroisoxazolyl), dihydropyrrolopyrazolyl (e.g., 5,6-dihydropyrrolo[3,4-c]pyrazolyl), piperazinyl, triazaspirononyl (e.g., 1,3,7-triazaspiro[4.4]nonyl), thiadiazaspirononyl (e.g., 7-thia-1,3-diazaspiro[4.4]nonyl), dioxide thiadiazaspirononyl (e.g., 7,7-dioxide-7-thia-1,3-diazaspiro[4.4]nonyl)), ○(v)C3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), and ○(vi)C 1-6 an alkyl-carbonyl group (e.g., acetyl), or (2) The following: (i) a halogen atom (e.g., a fluorine atom), ○(ii)C 1-6 alkyl groups (e.g., methyl); (iii) aromatic heterocyclic groups (preferably 5- to 14-membered aromatic heterocyclic groups, more preferably 5- to 6-membered monocyclic aromatic heterocyclic groups, and 8- to 14-membered fused polycyclic aromatic heterocyclic groups) (e.g., imidazolyl, pyrazolyl, tetrazolyl, benzimidazolyl (e.g., 1H-benzimidazolyl)), ○(iv)C 3-10 cycloalkylsulfonyl groups (e.g., cyclopentylsulfonyl), (v) an aromatic heterocyclylsulfonyl group (preferably a 5- to 14-membered aromatic heterocyclylsulfonyl group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclylsulfonyl group) (e.g., thiazolylsulfonyl), (vi) halogenated thio groups (e.g., pentafluorothio), and ○(vii) or below: (a) C optionally substituted with 1 to 3 amino groups 1-6 alkyl groups (e.g., methyl), and ■(b) Oxo group a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group, or a 7- to 14-membered spiro heterocyclic group) optionally substituted by 1 to 3 substituents selected from the group consisting of imidazolidinyl, triazaspirononyl (e.g., 1,3,7-triazaspiro[4.4]nonyl), C optionally substituted by 1 to 3 substituents selected from 6-14 aryl groups (e.g., phenyl) and R 2 teeth, (1) The following: ○(i)C1-6 alkoxy-carbonyl groups (e.g., methoxycarbonyl), ○(ii)C 1-6 alkylsulfonyl groups (e.g., methylsulfonyl), (iii) a carbamoyl group, (iv) a cyano group, (v) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) optionally substituted by 1 to 3 oxo groups (e.g., pyrrolidinyl, tetrahydrofuryl, oxetanyl), and (vi) Halogen atoms (e.g., fluorine atoms) C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl); (2) C optionally substituted with 1 to 3 hydroxy groups 3-10 a cycloalkyl group (e.g., cyclopentyl), or (3) A non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., oxetanyl). and R 3 and R 4 One of the atoms is a hydrogen atom, and the other is (1) a hydrogen atom, or (2) C 1-6 C optionally substituted by 1 to 3 substituents selected from an amino group optionally mono- or di-substituted by an alkyl group (e.g., methyl); 1-6 Alkyl groups (e.g., methyl) and R 5 and R 6 One of the groups is a hydrogen atom or C 1-6 an alkyl group (e.g., methyl), and the other (1) a hydrogen atom, (2) a hydroxy group, (3) C optionally substituted with 1 to 3 substituents selected from the following: 1-6 Alkyl groups (e.g., methyl) (i) a hydroxy group, ○(ii) or below: (a) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 1-6 alkyl groups (e.g., methyl, ethyl); (b) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 3-10 cycloalkyl groups (e.g., cyclopropyl, cyclobutyl); (c) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., oxetanyl), ■(d)C 1-6 alkylsulfonyl groups (e.g., methylsulfonyl), ■(e)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ■(f)C 3-10 cycloalkyl-carbonyl groups (e.g., cyclopropylcarbonyl) an amino group which may be mono- or di-substituted by a substituent selected from (iii) a halogen atom (e.g., a fluorine atom), ○(iv)C 1-6 alkylsulfanyl groups (e.g., methylsulfanyl), ○(v)C 1-6 alkylsulfinyl groups (e.g., methylsulfinyl), and ○(vi)C 1-6 alkylsulfonyl groups (e.g., methylsulfonyl), (4) C 1-6 alkoxy groups (e.g., methoxy), (5) The following: ○(i)C 1-6 alkyl groups (e.g., methyl, ethyl); ○(ii)C 1-6 alkyl-carbonyl groups (e.g., acetyl), and ○(iii)C 1-6 Alkylsulfonyl groups (e.g., methylsulfonyl) an amino group which may be mono- or di-substituted by a substituent selected from (6) a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group) (e.g., morpholinyl), (7) a carboxy group, or (8) C 1-6 a carbamoyl group optionally mono- or disubstituted by an alkyl group (e.g., methyl); or R 5 and R 6 are combined, (1) a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle, more preferably a 3- to 8-membered monocyclic non-aromatic heterocycle) (e.g., tetrahydrofuran), or (2) C 3-10 Cycloalkanes (e.g., cyclopentane) and X is CR 7 R 8 , N.R. 9 , O, or S; R 7 and R 8 is, independently, (1) a hydrogen atom, (2) a cyano group, (3) C optionally substituted with 1 to 3 hydroxy groups 1-6 an alkyl group (e.g., methyl, ethyl), or (4) Hydroxy group or R 7 and R 8 are combined, (1) The following: (i) an oxo group, and (ii) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 3-10 a cycloalkane (e.g., cyclohexane), or (2) 1 to 3 Cs 7-16a non-aromatic heterocycle (preferably a 3- to 14-membered non-aromatic heterocycle, more preferably a 3- to 8-membered monocyclic non-aromatic heterocycle) (e.g., pyrrolidine, piperidine) optionally substituted with an aralkyl group (e.g., benzyl); and R 9 teeth, (1) a hydrogen atom, or (2) The following: (i) a hydroxy group, ○(ii) 1 to 3 C 6-14 C optionally substituted by an aryl group (e.g., phenyl) 1-6 alkoxy groups (e.g., methoxy), and ○(iii)C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl); C optionally substituted by 1 to 3 substituents selected from 1-6 alkyl groups (e.g., methyl, ethyl, propyl, isopropyl); (3) C 2-6 an alkenyl group (e.g., allyl), or (4) 1 to 3 Cs 1-6 C optionally substituted by an alkoxy group (e.g., methoxy) 7-16 Aralkyl groups (e.g., benzyl) That is, Compound (I). [Compound C-1] Compound (I), wherein R 1 teeth, (1) An aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) optionally substituted by 1 to 3 substituents selected from the following (e.g., oxazolyl, pyridyl, pyrazolyl): (i) C optionally substituted with 1 to 3 halogen atoms (e.g., fluorine atoms) 1-6 alkyl groups (e.g., methyl); ○(ii) or below: ■(a) and below: (I) a halogen atom (e.g., a fluorine atom), and ■(II)C 3-10 cycloalkyl groups (e.g., cyclopropyl) C optionally substituted by 1 to 3 substituents selected from 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl, ethyl), and (b) C optionally substituted with 1 to 3 amino groups 1-6 Alkyl groups (e.g., methyl) an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- or 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl, pyrazolyl) optionally substituted by 1 to 3 substituents selected from ○(iii) or below: (a) C optionally substituted with 1 to 3 amino groups 1-6 alkyl groups (e.g., methyl), and ■(b) Oxo group a non-aromatic heterocyclic group (preferably a 3- to 14-membered non-aromatic heterocyclic group, more preferably a 3- to 8-membered monocyclic non-aromatic heterocyclic group, or a 7- to 14-membered spiro heterocyclic group) (e.g., imidazolidinyl, triazaspirononyl (e.g., 1,3,7-triazaspiro[4.4]nonyl)) optionally substituted by 1 to 3 substituents selected from (2) 1 to 3 Cs 1-6 C optionally substituted with an alkyl group (e.g., methyl) 6-14 aryl groups (e.g., phenyl) and R 2 is C 1-6 an alkyl group (e.g., methyl), R 3 and R 4 One of the groups is a hydrogen atom, and the other is a hydrogen atom or C 1-6 an alkyl group (e.g., methyl), R 5 and R 6 One of the atoms is a hydrogen atom, and the other is (1) a hydrogen atom, (2) a hydroxy group, (3) The following: ○(i)C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl), and (ii) Hydroxy group C optionally substituted by 1 to 3 substituents selected from 1-6 an alkyl group (e.g., methyl), or (4) C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl); and X is CR 7 R 9 , N.R. 9 , or 0, R 7 and R 8 is, independently, (1) a hydrogen atom, or (2) C 1-6 Alkyl groups (e.g., methyl) and R 9 teeth, (1) a hydrogen atom, or (2) C optionally substituted with 1 to 3 hydroxy groups 1-6 Alkyl groups (e.g., methyl, ethyl, propyl) That is, Compound (I). [Compound D-1] Compound (I), wherein R 1 is C optionally substituted by 1 to 3 halogen atoms (e.g., fluorine atoms); 1-6 an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., oxazolyl) optionally substituted by an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., ethyl); R 2 is C 1-6 an alkyl group (e.g., methyl), R 3 and R 4 are both hydrogen atoms, R 5 and R 6 One of the atoms is a hydrogen atom, and the other is (1) a hydrogen atom, (2) a hydroxy group, (3) C 1-6 C optionally substituted by an amino group which may be mono- or disubstituted by an alkyl group (e.g., methyl); 1-6 an alkyl group (e.g., methyl), or (4) C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl); and X is CR 7 R 8 and R 7 and R 8 is, independently, (1) a hydrogen atom, or (2) C 1-6 Alkyl groups (e.g., methyl) That is, Compound (I). [Compound D-2] Compound (I), wherein R 1 C optionally substituted with 1 to 3 substituents selected from the following: 1-6 an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., oxazolyl) optionally substituted by an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); (1) Halogen atoms (e.g., fluorine atoms), and ○(2)C3-10 cycloalkyl groups (e.g., cyclopropyl); R 2 is C 1-6 an alkyl group (e.g., methyl), R 3 and R 4 are both hydrogen atoms, R 5 and R 6 One of the atoms is a hydrogen atom, and the other is (1) a hydrogen atom, (2) C 1-6 C optionally substituted by an amino group which may be mono- or disubstituted by an alkyl group (e.g., methyl); 1-6 an alkyl group (e.g., methyl), or (3) C 1-6 an amino group which may be mono- or disubstituted by alkyl groups (e.g., methyl); and X is CR 7 R 8 or NR 9 and R 7 and R 8 is, independently, (1) a hydrogen atom, or (2) C 1-6 Alkyl groups (e.g., methyl) and R 9 teeth, (1) a hydrogen atom, or (2) C optionally substituted with 1 to 3 hydroxy groups 1-6 Alkyl groups (e.g., methyl, ethyl) That is, Compound (I). [Compound E-1] Compound (I), wherein R 1 is C optionally substituted by 1 to 3 halogen atoms (e.g., fluorine atoms); 1-6an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., oxazolyl) optionally substituted by an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); R 2 is C 1-6 an alkyl group (e.g., methyl), R 3 and R 4 are both hydrogen atoms, R 5 and R 6 are both hydrogen atoms, X is CR 7 R 8 or NR 9 and R 7 and R 8 is, independently, (1) a hydrogen atom, or (2) C 1-6 Alkyl groups (e.g., methyl) and R 9 teeth, (1) a hydrogen atom, or (2) C optionally substituted with 1 to 3 hydroxy groups 1-6 Alkyl groups (e.g., methyl, ethyl) That is, Compound (I). [Compound F-1] Compound (I), wherein R 1 is C optionally substituted by 1 to 3 halogen atoms (e.g., fluorine atoms); 1-6an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., oxazolyl) optionally substituted by an aromatic heterocyclic group (preferably a 5- to 14-membered aromatic heterocyclic group, more preferably a 5- to 6-membered monocyclic aromatic heterocyclic group) (e.g., pyridyl) optionally substituted by an amino group which may be mono- or di-substituted by an alkyl group (e.g., methyl, ethyl); R 2 is C 1-6 an alkyl group (e.g., methyl), R 3 and R 4 are both hydrogen atoms, R 5 and R 6 are both hydrogen atoms, X is NR 9 and R 9 teeth, (1) a hydrogen atom, or (2) C optionally substituted with 1 to 3 hydroxy groups 1-6 Alkyl groups (e.g., methyl, ethyl) That is, Compound (I). [Compound G-1] N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide or a salt thereof, or N-(1-methyl-3-(2-oxoimidazolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide or a salt thereof. [Compound H-1] N-(1-methyl-3-((3S)-3-methyl-2-oxopyrrolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide or a salt thereof.

[0102] In one embodiment, the present disclosure provides a compound of formula (III) having the following structure [Compound 2]: or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof, wherein: R1 and R2 are independently H, optionally substituted by hydroxyl, 1-6 alkyl, R3 is H, OH, -OC 1-3 alkyl, or CH2NR6R7, R4 is optionally halogenated C 1-6 Alkyl groups (e.g., CF3), optionally halogenated C 3-10 a cycloalkyl group, an optionally substituted non-aromatic heterocyclic group, an optionally substituted aromatic heterocyclic group, or an optionally substituted C 6-14 is an aryl group, R5 is C 1-6 alkyl, optionally halo-substituted C 3-10 a cycloalkyl group or a non-aromatic heterocyclic group, R6 and R7 are independently H, C 1-6 Alkyl, and C 3-10 cycloalkyl groups, X is N or C; n is 0, 1, or 2; wherein when X is N, R2 is absent.

[0103] The present disclosure further provides compounds of formula III: 2.1 X is C and at least one of R1 and R2 is C 1-3 Compound 2 is an alkyl. 2.2 Compound 2, wherein X is C and at least one of R1 and R2 is H. 2.3 X is C, R1 is H, and R2 is C 1-3 Compound 2 is an alkyl. 2.4 X is C and R1 and R2 are both C 1-3 Compound 2 is an alkyl. 2.5 Compound 2, where X is C and R1 and R2 are both H. 2.6 Compound 2, where X is N. 2.7 Compound 2.6, where R1 is H. 2.8 R1 is C 1-3 Compound 2.6, which is an alkyl. 2.9 Compound 2.6 or 2.8, where R1 is methyl or propyl. 2.10 C where R1 is substituted with hydroxyl 1-6 Compound 2.6, which is an alkyl. 2.11 Compound 2.6 or 2.10, wherein R1 is hydroxyethyl or hydroxypropyl (eg, 2-hydroxyethyl or 2-hydroxypropyl). 2.12 Compound 2 or any of 2.1-2.11, wherein R3 is H. 2.13 Compound 2 or any of 2.1-2.11, wherein R3 is OH. 2.14 Any of compounds 2 or 2.1 or 2.11, wherein R3 is CH2NR6R7 and at least one of R6 and R7 is H. 2.15 R3 is CH2NR6R7, and at least one of R6 and R7 is C 1-6 Any of compounds 2 or 2.1-2.11, wherein: 2.16 R3 is CH2NR6R7, and at least one of R6 and R7 is C 3-10 Any of compounds 2 or 2.1-2.11, which is a cycloalkyl group (eg, cyclopropyl). 2.17 R3 is CH2NR6R7, R6 is H, and R7 is C 1-6Any of compounds 2 or 2.1-2.11, which is alkyl (eg, methyl). 2.18 R3 is CH2NR6R7, and R6 and R7 are both C 1-6 Any of compounds 2 or 2.1-2.11, which is alkyl (eg, methyl). 2.19 R4 is halogenated C 1-6 Any of compounds 2 or 2.1-2.18, which is an alkyl group. 2.20 Compound 2 or any of 2.1-2.19, wherein R4 is CF3. 2.21 R4 is optionally halogenated C 3-10 Any of compounds 2 or 2.1-2.18, which is a cycloalkyl group (eg, cyclopropyl). 2.22 R5, C 1-6 Any of compounds 2 or 2.1-2.21, wherein: 2.23 Any of the preceding compounds wherein R5 is methyl. 2.24 Compound 2 or any of 2.1-2.21, wherein R5 is a non-aromatic heterocyclic group. 2.25 Compound 2 or any of 2.1 to 2.21 or 2.24, wherein R5 is a 3- to 14-membered non-aromatic heterocyclic group. 2.26 Compound 2 or any of 2.1-2.21 or 2.24-2.25, wherein R5 is a 4-membered non-aromatic heterocyclic group. 2.27 Compound 2 or any of 2.1-2.21 or 2.24-2.26, wherein R5 is oxetanyl. 2.28 The compound of formula III has the following structure: TIFF0007813733000004.tif43128TIFF0007813733000005.tif217119TIFF0007813733000006.tif57128, or any of the preceding compounds having one of the following stereoisomers, solvates, tautomers, or pharmaceutically acceptable salts thereof. 2.29 Any of the preceding compounds, wherein the compound of formula III is selected from: N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, 2-(2-((2,2-difluoroethyl)amino)pyridin-4-yl)-N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-1,3-oxazole-4-carboxamide, N-(3-((3S,4S)-4-hydroxy-3-methyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(1-methyl-3-(2-oxoimidazolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(1-methyl-3-((3S)-3-methyl-2-oxopyrrolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, 2-(2-((cyclopropylmethyl)amino)pyridin-4-yl)-N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3,3-dimethyl-4-((methylamino)methyl)-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3,3-dimethyl-4-((methylamino)methyl)-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3-isopropyl-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((dimethylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3-(2-hydroxypropyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((dimethylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((cyclopropylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, and N-(3-(3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-(oxetan-3-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.30 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000007.tif38128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.31 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000008.tif22128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.32 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000009.tif32128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.33 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000010.tif28128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.34 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000011.tif31128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.35 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000012.tif36128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.36 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000013.tif42128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.37 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000014.tif46128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.38 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000015.tif40128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.39 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000016.tif38128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.40 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000017.tif53128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.41 The compound of formula III has the following structure: Compound 2.28, having TIFF0007813733000018.tif34128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.42 The compound of formula III has the following structure: Compound 2.28 having one of the following structures: TIFF0007813733000019.tif97128, or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.43 The compound of formula III has the following structure: Compound 2.42, having TIFF0007813733000020.tif49128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.44 The compound of formula III has the following structure: Compound 2.42, having TIFF0007813733000021.tif49128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof. 2.45 The compound of formula III has the following structure: Compound 2.42, having TIFF0007813733000022.tif53128 or a stereoisomer, solvate, tautomer, or pharmaceutically acceptable salt thereof.

[0104] In a further aspect, the present disclosure provides a method for producing a medicament for a medicament comprising: a pharmaceutically effective amount of an IRAK4 inhibitor of the present disclosure, i.e., a compound of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later); a solvent system comprising one or more solvents; Antioxidants and There is further provided a topical composition, "Composition 1," comprising:

[0105] The present disclosure further provides the following compositions: 1.1 Composition 1, wherein the IRAK4 inhibitor is selected from the following: N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, 2-(2-((2,2-difluoroethyl)amino)pyridin-4-yl)-N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-1,3-oxazole-4-carboxamide, N-(3-((3S,4S)-4-hydroxy-3-methyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(1-methyl-3-(2-oxoimidazolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(1-methyl-3-((3S)-3-methyl-2-oxopyrrolidin-1-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, 2-(2-((cyclopropylmethyl)amino)pyridin-4-yl)-N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3,3-dimethyl-4-((methylamino)methyl)-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3,3-dimethyl-4-((methylamino)methyl)-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3-isopropyl-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((dimethylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3-(2-hydroxypropyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((dimethylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((cyclopropylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, and N-(3-(3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-(oxetan-3-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, or a stereoisomer, tautomer, or pharmaceutically acceptable salt thereof. 1.2 The preceding composition, wherein the solvent system comprises one or more solvents selected from polyethers, polyethylene glycols (e.g., PEG 400), polyether alcohols (e.g., diethylene glycol monoethyl ether; Transcutol® P), ethers, and alcohols. 1.3 Any of the preceding compositions wherein the solvent system comprises one or more solvents selected from polyethylene glycol having a molecular weight of about 300 to about 600, polyether alcohols having a molecular weight of less than 200 daltons (e.g., diethylene glycol monoethyl ether, Transcutol® P), alcohols (e.g., benzyl alcohol or phenoxyethanol), and ethers (e.g., dimethyl isosorbide). 1.4 Any of the preceding compositions wherein the solvent system comprises polyethylene glycol (e.g., PEG 400) and a polyether alcohol. 1.5 Any of the preceding compositions wherein the solvent system comprises PEG 400 and diethylene glycol monoethyl ether (Transcutol® P). 1.6 Composition 1.5, wherein the solvent system further comprises one or more preservatives. 1.7 Composition 1.6, wherein the preservative is present in an amount from about 0.01% to about 20% by weight of the composition, or from about 0.1% to about 10% by weight of the composition, or from about 0.5% to about 5% by weight of the composition, or from about 1% to about 3% by weight of the composition, or about 2% by weight of the composition. 1.8 Composition 1.6, wherein the preservative is an alcohol selected from, for example, benzyl alcohol and phenoxyethanol. 1.9 Any of the preceding compositions, wherein the solvent system is present in an amount of from about 50% to about 90% by weight of the composition, or from about 75% to about 90% by weight of the composition, or from about 80% to about 90% by weight of the composition, or from about 85% to about 90% by weight of the composition, or from about 55% to about 65% by weight of the composition, or from about 55% to about 60% by weight of the composition. 1.10 Any of the preceding compositions, wherein the solvent system is present in an amount of about 80% to about 90% by weight of the composition, or about 50% to about 65% by weight of the composition, or about 60%, or about 65% by weight of the composition. 1.11 Any of the preceding compositions, wherein the solvent system comprises PEG 400 in an amount from about 20% to about 70% by weight of the composition, or from about 35% to about 70% by weight of the composition, or from about 35% to about 50% by weight of the composition, or from about 40% to about 45% by weight of the composition, or from about 55% to about 65% by weight of the composition, or about 40%, about 45%, about 50%, about 55%, or about 60% by weight of the composition. 1.12 Any of the preceding compositions wherein the solvent system comprises diethylene glycol monoethyl ether (Transcutol® P) in an amount between about 10% and about 45% by weight of the composition, or between about 10% and about 20% by weight of the composition, or between about 20% and about 30% by weight of the composition, or about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, or about 45% by weight of the composition. 1.13 Any of the preceding compositions wherein the antioxidant is selected from one or more of butylated hydroxytoluene (BHT), sodium metabisulfite, ascorbic acid, propyl gallate, and / or alpha tocopherol (vitamin E). 1.14 Any of the preceding compositions wherein the antioxidant is present in an amount of about 0.001% to about 1% by weight, based on the total weight of the composition. 1.15 Any of the preceding compositions wherein the antioxidant comprises or consists of butylated hydroxytoluene in an amount from about 0.01% to about 1% by weight, e.g., about 0.2% by weight, or about 0.1% by weight, based on the total weight of the composition. 1.16 Any of the preceding compositions, wherein the composition further comprises a surfactant. 1.17 Composition 1.16, wherein the non-solvent is water, a silicone oil (e.g., dimethicone 350), or a mixture thereof. 1.18 Composition 1.17, wherein water is present in an amount from about 5% to about 30% by weight of the composition, or from about 5% to about 15% by weight of the composition, or from about 15% to about 25% by weight of the composition, or about 10%, or about 15%, or about 20% by weight of the composition. 1.19 Composition 1.17, wherein the silicone oil is Dimethicone 350 and is present in an amount from about 0.01% to about 2% by weight of the composition, or from about 0.1% to about 1.5% by weight of the composition, or from about 0.5% to about 1% by weight of the composition, or about 0.75% by weight of the composition. 1.20 Any of the preceding compositions, wherein the composition further comprises a gelling agent. 1.21 Any of the preceding compositions, wherein the composition further comprises a gelling agent. 1.22 Composition 1.20 or 1.21, wherein the gelling agent is a polymer. 1.23 Composition 1.20 or 1.21, wherein the gelling agent comprises one or more of crosslinked polyacrylic acid and nonionic cellulose ether. 1.24 Composition 1.20 or 1.21, wherein the gelling agent comprises one or more of a Carbopol polymer and hydroxypropyl cellulose. 1.25 Composition 1.20 or 1.21, wherein the gelling agent comprises one or more of Carbopol 980 NF and HPC HF. 1.26 Any of the preceding compositions 1.20-1.25, wherein the gelling agent is present in an amount from 0.01% to about 5% by weight of the composition, or from about 0.1% to about 3% by weight of the composition, or from about 0.5% to about 2% by weight of the composition, or from about 0.75% to about 1.25% by weight of the composition, or about 1% by weight of the composition. 1.27 Any of the preceding compositions further comprising a skin conditioning agent. 1.28 Composition 1.27 wherein the skin conditioning agent is selected from diisopropyl adipate and silicone oil. 1.29 Composition 1.28 wherein the silicone oil is Dimethicone 350. 1.30 Any of the preceding compositions 1.27-1.29, wherein the skin conditioning agent is present in an amount from 0.1% to about 15% by weight of the composition, or from about 0.1% to about 5% by weight of the composition, or from about 0.1% to about 2% by weight of the composition, or from about 5% to about 15% by weight of the composition, or about 1% by weight of the composition, or about 10% by weight of the composition. 1.31 Any of the preceding compositions further comprising an emollient. 1.32 Composition 1.30 wherein the emollient is a triglyceride, e.g., a medium chain triglyceride. 1.33 Composition 1.30 or 1.31 wherein the emollient is Crodamol GTCC. 1.34 Any of the preceding compositions 1.31-1.33, wherein the emollient is present in an amount from 0.1% to about 15% by weight of the composition, or from about 0.1% to about 5% by weight of the composition, or from about 0.1% to about 2% by weight of the composition, or from about 5% to about 15% by weight of the composition, or about 1% by weight of the composition, or about 10% by weight of the composition. 1.35 Any of the preceding compositions further comprising a viscosity improver. 1.36 Viscosity improver contains one or more C 14 -C 30 Composition 1.35 selected from fatty alcohols, cellulose, acrylate polymers or crosspolymers, or carbomers. 1.37 Composition 1.35, wherein the viscosity enhancer is selected from hydroxypropyl cellulose, hydroxymethyl cellulose, hydroxypropyl methylcellulose (e.g., Benecel E4M), poloxamer (Pluronic PF127), carbomer (e.g., Carbomer 980, Carbomer 1342, and Carbomer 940), more specifically hydroxypropyl cellulose (e.g., hydroxypropyl cellulose Klucel® EF, GF, MF, and / or HF having a molecular weight of 850,000 to 1,150,000 Daltons), Pluronic PF127, Carbomer 980, and / or Carbomer 1342 (Pemulen® TR-1, TR-2, and / or Carbopol® ETD 2020). 1.38 Composition 1.35 wherein the viscosity enhancer is cetostearyl alcohol. 1.39 Any of the preceding compositions 1.35-1.38, wherein the viscosity enhancer is present in an amount from 0.1% to about 15% by weight of the composition, or from about 1% to about 10% by weight of the composition, or from about 3% to about 7% by weight of the composition, or about 5% by weight of the composition, or from about 1% to about 5% by weight of the composition, or about 1% by weight of the composition, or about 2% by weight of the composition, or about 3% by weight of the composition, or about 4% by weight of the composition, or about 5% by weight of the composition. 1.40 Any of the preceding compositions further comprising a surfactant. 1.41 Composition 1.40, wherein the surfactant is selected from one or more of polyoxyethylene fatty ethers, nonoxynol, polysorbate, polyoxyethylene alcohols, polyoxyethylene fatty acid esters, sodium lauryl sulfate, and sorbitan monostearate. 1.42 Composition 1.40 or 1.41, wherein the surfactant is selected from Brij S2 and Brij S20. 1.43 Any of the preceding compositions 1.40-1.42, wherein the surfactant is present in an amount from 0.1% to about 15% by weight of the composition, or from about 1% to about 5% by weight of the composition, or from about 1% to about 4% by weight of the composition, or about 1%, about 2%, about 3%, about 4%, about 5%, about 7%, or about 10% by weight of the composition. 1.44 Any of the preceding compositions further comprising an additional excipient. 1.45 Additional excipients include alcohol (e.g., C 1-20 Composition 1.44, selected from alkanols (e.g., oleyl alcohol, cetyl alcohol, octyldodecanol, cetostearyl alcohol, benzyl alcohol), saturated or unsaturated fatty acid esters, saturated or unsaturated fatty acid esters, polyoxythylene fatty ethers, polyoxythylene fatty acid esters, diethylene glycol monoethyl ether, 1,3-dimethyl-2-imidazolidinone, and / or dimethyl isosorbide. 1.46 Composition 1.44, wherein the additional excipient is selected from oleyl alcohol, cetyl alcohol, octyldodecanol, cetostearyl alcohol, mineral oil, benzyl alcohol, isopropyl myristate, diisopropyl adipate, ethylhexyl hydroxystearate, steareth-2 (Brij S2), steareth-20 (Brij S20), glyceryl stearate, stearic acid, magnesium stearate, diethylene glycol monoethyl ether, 1,3-dimethyl-2-imidazolidinone, and / or dimethyl isosorbide. 1.47 Composition 1.44, wherein the additional excipient is selected from one or more of propylene glycol, oleyl alcohol, diisopropyl adipate, and isopropyl myristate. 1.48 Composition 1.44, wherein the additional excipient comprises propylene glycol. 1.49 Any of the preceding compositions 1.44-1.48, wherein the additional excipient is present in an amount from 0.1% to about 20% by weight of the composition, or from about 1% to about 15% by weight of the composition, or from about 5% to about 15% by weight of the composition, or about 10% by weight of the composition. 1.50 Any of the preceding compositions wherein the composition is in the form of a cream, lotion, foam, aqueous gel, non-aqueous gel, spray, or ointment (e.g., a polyethylene glycol-based ointment). 1.51 Any of the preceding compositions wherein the composition is an aqueous gel. 1.52 Any of the preceding compositions wherein the composition is a non-aqueous gel. 1.53 Any of the preceding compositions wherein the composition is a cream. 1.54 Any of the preceding compositions wherein the composition is an ointment (e.g., a polyethylene glycol-based ointment). 1.55 Any of the preceding compositions, wherein the composition has an apparent pH of about 3.5 to about 7.5, about 4 to about 7, about 4.5 to about 6.5, or about 5 to about 6.5, or about 5.5 to 6.5, or about 6. 1.56 Any of the preceding compositions, wherein the composition is applied to the patient's skin three times a day, twice a day, once a day, every other day, once a week, or once a month. 1.57 Any of the preceding compositions, wherein the composition is applied to the patient's skin twice daily. 1.58 Any of the preceding compositions, wherein the composition is applied to the patient's skin three or more times daily. 1.59 Any of the preceding compositions, wherein the composition is administered to a patient suffering from a dermatological condition characterized by inflammation. 1.60 Composition 1.59, wherein the dermatological condition is selected from rosacea, psoriasis, atopic dermatitis, hidradenitis suppurativa, seborrheic dermatitis, contact dermatitis, urticaria, dermatitis herpetiformis, nummular eczema, lichen planus, pityriasis rosea, cutaneous lupus, acne, cancer of the skin (e.g., cutaneous T-cell lymphoma), and miliaria. 1.61 Composition 1.59 wherein the dermatological disorder is rosacea. 1.62 Composition 1.59 wherein the rosacea is papulopustular rosacea. 1.63 Composition 1.59 wherein the dermatological disorder is psoriasis. 1.64 Composition 1.59, wherein the dermatological disorder is atopic dermatitis. 1.65 Composition 1.59 wherein the dermatological disorder is hidradenitis suppurativa. 1.66 Composition 1.59 wherein the dermatological disorder is psoriasis. 1.67 Any of the preceding compositions wherein the skin is mammalian skin (e.g., human skin). 1.68 Any of the preceding compositions, wherein the topical composition is an aqueous gel, the solvent system comprises PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is from about 0.7 to about 1.1, e.g., from about 0.8 to about 1.0, e.g., about 0.9. 1.69 Any of the preceding compositions, wherein the topical composition is a non-aqueous gel, the solvent system comprises PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is from about 2.2 to about 2.6, e.g., from about 2.3 to about 2.5, e.g., about 2.4. 1.70 Any of the preceding compositions, wherein the topical composition is a cream, the solvent system comprises PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is from about 2.6 to about 3.2, e.g., from about 2.7 to about 3.1, e.g., about 2.9. 1.71 Any of the preceding compositions, wherein the topical composition is an ointment, the solvent system comprises PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is from about 3.5 to about 4.5, e.g., from about 3.8 to about 4.2, e.g., about 4.

[0106] The IRAK4 inhibitors described herein can be prepared, for example, according to the methods disclosed in US Pat. No. 9,890,145 and US Pat. No. 9,321,757, which are incorporated by reference in their entireties.

[0107] The definition of each substituent used herein is detailed below. Unless otherwise specified, each substituent has the following definition.

[0108] As used herein, examples of a "halogen atom" include fluorine, chlorine, bromine, and iodine.

[0109] In this specification, "C 1-6 Examples of "alkyl groups" include methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, pentyl, isopentyl, neopentyl, 1-ethylpropyl, hexyl, isohexyl, 1,1-dimethylbutyl, 2,2-dimethylbutyl, 3,3-dimethylbutyl, and 2-ethylbutyl.

[0110] As used herein, "optionally halogenated C 1-6 Examples of the "alkyl group" include C alkyl groups which may have 1 to 7, preferably 1 to 5, halogen atoms. 1-6 Specific examples thereof include alkyl groups, such as methyl, chloromethyl, difluoromethyl, trichloromethyl, trifluoromethyl, ethyl, 2-bromoethyl, 2,2,2-trifluoroethyl, tetrafluoroethyl, pentafluoroethyl, propyl, 2,2-difluoropropyl, 3,3,3-trifluoropropyl, isopropyl, butyl, 4,4,4-trifluorobutyl, isobutyl, sec-butyl, tert-butyl, pentyl, isopentyl, neopentyl, 5,5,5-trifluoropentyl, hexyl, and 6,6,6-trifluorohexyl.

[0111] In this specification, "C 2-6 Examples of "alkenyl groups" include ethenyl, 1-propenyl, 2-propenyl, 2-methyl-1-propenyl, 1-butenyl, 2-butenyl, 3-butenyl, 3-methyl-2-butenyl, 1-pentenyl, 2-pentenyl, 3-pentenyl, 4-pentenyl, 4-methyl-3-pentenyl, 1-hexenyl, 3-hexenyl, and 5-hexenyl.

[0112] In this specification, "C 2-6Examples of "alkynyl groups" include ethynyl, 1-propynyl, 2-propynyl, 1-butynyl, 2-butynyl, 3-butynyl, 1-pentynyl, 2-pentynyl, 3-pentynyl, 4-pentynyl, 1-hexynyl, 2-hexynyl, 3-hexynyl, 4-hexynyl, 5-hexynyl, and 4-methyl-2-pentynyl.

[0113] In this specification, "C 3-10 Examples of "cycloalkyl groups" include cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl, cyclooctyl, bicyclo[2.2.1]heptyl, bicyclo[2.2.2]octyl, bicyclo[3.2.1]octyl, and adamantyl.

[0114] As used herein, "optionally halogenated C 3-10 Examples of the "cycloalkyl group" include C alkyl groups which may have 1 to 7, preferably 1 to 5, halogen atoms. 3-10 Specific examples of cycloalkyl groups include cyclopropyl, 2,2-difluorocyclopropyl, 2,3-difluorocyclopropyl, cyclobutyl, difluorocyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl, and cyclooctyl.

[0115] In this specification, "C 3-10 Examples of "cycloalkenyl groups" include cyclopropenyl, cyclobutenyl, cyclopentenyl, cyclohexenyl, cycloheptenyl, and cyclooctenyl.

[0116] In this specification, "C 6-14 Examples of "aryl groups" include phenyl, 1-naphthyl, 2-naphthyl, 1-anthryl, 2-anthryl, and 9-anthryl.

[0117] In this specification, "C 7-16 Examples of the "aralkyl group" include benzyl, phenethyl, naphthylmethyl, and phenylpropyl.

[0118] In this specification, "C 1-6 Examples of "alkoxy groups" include methoxy, ethoxy, propoxy, isopropoxy, butoxy, isobutoxy, sec-butoxy, tert-butoxy, pentyloxy, and hexyloxy.

[0119] As used herein, "optionally halogenated C 1-6 Examples of the "alkoxy group" include C alkoxy groups optionally having 1 to 7, preferably 1 to 5, halogen atoms. 1-6 Specific examples of alkoxy groups include methoxy, difluoromethoxy, trifluoromethoxy, ethoxy, 2,2,2-trifluoroethoxy, propoxy, isopropoxy, butoxy, 4,4,4-trifluorobutoxy, isobutoxy, sec-butoxy, pentyloxy, and hexyloxy.

[0120] In this specification, "C 3-10 Examples of the "cycloalkyloxy group" include cyclopropyloxy, cyclobutyloxy, cyclopentyloxy, cyclohexyloxy, cycloheptyloxy, and cyclooctyloxy.

[0121] In this specification, "C 1-6 Examples of the "alkylthio group" include methylthio, ethylthio, propylthio, isopropylthio, butylthio, sec-butylthio, tert-butylthio, pentylthio, and hexylthio.

[0122] As used herein, "optionally halogenated C 1-6 Examples of the alkylthio group include C alkylthio groups optionally having 1 to 7, preferably 1 to 5, halogen atoms. 1-6 Specific examples of alkylthio groups include methylthio, difluoromethylthio, trifluoromethylthio, ethylthio, propylthio, isopropylthio, butylthio, 4,4,4-trifluorobutylthio, pentylthio, and hexylthio.

[0123] In this specification, "C 1-6 Examples of "alkyl-carbonyl groups" include acetyl, propanoyl, butanoyl, 2-methylpropanoyl, pentanoyl, 3-methylbutanoyl, 2-methylbutanoyl, 2,2-dimethylpropanoyl, hexanoyl, and heptanoyl.

[0124] As used herein, "optionally halogenated C 1-6 Examples of the "alkyl-carbonyl group" include C alkyl-carbonyl groups which may have 1 to 7, preferably 1 to 5, halogen atoms. 1-6 Alkyl-carbonyl groups include, for example, acetyl, chloroacetyl, trifluoroacetyl, trichloroacetyl, propanoyl, butanoyl, pentanoyl, and hexanoyl.

[0125] In this specification, "C 1-6 Examples of "alkoxy-carbonyl groups" include methoxycarbonyl, ethoxycarbonyl, propoxycarbonyl, isopropoxycarbonyl, butoxycarbonyl, isobutoxycarbonyl, sec-butoxycarbonyl, tert-butoxycarbonyl, pentyloxycarbonyl, and hexyloxycarbonyl.

[0126] In this specification, "C 6-14 Examples of the "aryl-carbonyl group" include benzoyl, 1-naphthoyl, and 2-naphthoyl.

[0127] In this specification, "C 7-16 Examples of "aralkyl-carbonyl groups" include phenylacetyl and phenylpropionyl.

[0128] In the present specification, examples of the "5- to 14-membered aromatic heterocyclylcarbonyl group" include nicotinoyl, isonicotinoyl, thenoyl, and furoyl.

[0129] In the present specification, examples of the "3- to 14-membered non-aromatic heterocyclylcarbonyl group" include morpholinylcarbonyl, piperidinylcarbonyl, and pyrrolidinylcarbonyl.

[0130] As used herein, "mono- or di-C 1-6 Examples of the "alkyl-carbamoyl group" include methylcarbamoyl, ethylcarbamoyl, dimethylcarbamoyl, diethylcarbamoyl, and N-ethyl-N-methylcarbamoyl.

[0131] As used herein, "mono- or di-C 7-16 Examples of the "aralkyl-carbamoyl group" include benzylcarbamoyl and phenethylcarbamoyl.

[0132] In this specification, "C 1-6 Examples of the "alkylsulfonyl group" include methylsulfonyl, ethylsulfonyl, propylsulfonyl, isopropylsulfonyl, butylsulfonyl, sec-butylsulfonyl, and tert-butylsulfonyl.

[0133] In the present specification, "optionally halogenated" 1-6 Examples of the alkylsulfonyl group include C alkylsulfonyl groups optionally having 1 to 7, preferably 1 to 5, halogen atoms. 1-6 Specific examples thereof include alkylsulfonyl groups, such as methylsulfonyl, difluoromethylsulfonyl, trifluoromethylsulfonyl, ethylsulfonyl, propylsulfonyl, isopropylsulfonyl, butylsulfonyl, 4,4,4-trifluorobutylsulfonyl, pentylsulfonyl, and hexylsulfonyl.

[0134] In this specification, "C 6-14 Examples of the "arylsulfonyl group" include phenylsulfonyl, 1-naphthylsulfonyl, and 2-naphthylsulfonyl.

[0135] In this specification, examples of the "substituent" include a halogen atom, a cyano group, a nitro group, an optionally substituted hydrocarbon group, an optionally substituted heterocyclic group, an acyl group, an optionally substituted amino group, an optionally substituted carbamoyl group, an optionally substituted thiocarbamoyl group, an optionally substituted sulfamoyl group, an optionally substituted hydroxy group, an optionally substituted sulfanyl (SH) group, and an optionally substituted silyl group.

[0136] In the present specification, examples of the "hydrocarbon group" (including the "hydrocarbon group" of the "optionally substituted hydrocarbon group") include C 1-6 Alkyl group, C 2-6 Alkenyl group, C 2-6 Alkynyl group, C 3-10 Cycloalkyl groups, C 3-40 Cycloalkenyl group, C 6-14 Aryl groups, and C 7-16 Examples include aralkyl groups.

[0137] In the present specification, examples of the "optionally substituted hydrocarbon group" include hydrocarbon groups which may have a substituent selected from the following Substituent Group A.

[0138] [Substituent group A] (1) a halogen atom, (2) a nitro group, (3) a cyano group, (4) an oxo group, (5) a hydroxy group, (6) Optionally halogenated C 1-6 alkoxy groups, (7) C 6-14 aryloxy groups (e.g., phenoxy, naphthoxy); (8) C 7-16 aralkyloxy groups (e.g., benzyloxy), (9) 5- to 14-membered aromatic heterocyclyloxy groups (e.g., pyridyloxy), (10) 3- to 14-membered non-aromatic heterocyclyloxy groups (e.g., morpholinyloxy, piperidinyloxy), (11)C 1-6 alkyl-carbonyloxy groups (e.g., acetoxy, propanoyloxy); (12)C 6-14 arylcarbonyloxy groups (e.g., benzoyloxy, naphthoyloxy, 2-naphthoyloxy); (13)C 1-6 alkoxy-carbonyloxy groups (e.g., methoxycarbonyloxy, ethoxycarbonyloxy, propoxycarbonyloxy, butoxycarbonyloxy); (14) Mono- or di-C 1-6 alkyl-carbamoyloxy groups (e.g., methylcarbamoyloxy, ethylcarbamoyloxy, dimethylcarbamoyloxy, diethylcarbamoyloxy); (15)C 6-14 aryl-carbamoyloxy groups (e.g., phenylcarbamoyloxy, naphthylcarbamoyloxy); (16) 5- to 14-membered aromatic heterocyclylcarbonyloxy groups (e.g., nicotinoyloxy), (17) 3- to 14-membered non-aromatic heterocyclylcarbonyloxy groups (e.g., morpholinylcarbonyloxy, piperidinylcarbonyloxy), (18) Optionally halogenated C 1-6 alkylsulfonyloxy groups (e.g., methylsulfonyloxy, trifluoromethylsulfonyloxy); (19)C 1-6 C optionally substituted by alkyl groups 6-14 arylsulfonyloxy groups (e.g., phenylsulfonyloxy, toluenesulfonyloxy); (20) Optionally halogenated C 1-6 alkylthio groups, (21) a 5- to 14-membered aromatic heterocyclic group, (22) a 3- to 14-membered non-aromatic heterocyclic group, (23) a formyl group, (24) a carboxy group, (25) Optionally halogenated C 1-6 alkyl-carbonyl groups, (26)C 6-14 aryl-carbonyl groups, (27) a 5- to 14-membered aromatic heterocyclylcarbonyl group, (28) a 3- to 14-membered non-aromatic heterocyclylcarbonyl group, (29)C 1-6 alkoxy-carbonyl groups, (30)C 6-14 aryloxy-carbonyl groups (e.g., phenyloxycarbonyl, 1-naphthyloxycarbonyl, 2-naphthyloxycarbonyl); (31)C 7-16 aralkyloxy-carbonyl groups (e.g., benzyloxycarbonyl, phenethyloxycarbonyl), (32) a carbamoyl group, (33) a thiocarbamoyl group, (34) Mono- or di-C 1-6 alkyl-carbamoyl groups, (35)C 6-14 aryl-carbamoyl groups (e.g., phenylcarbamoyl); (36) 5- to 14-membered aromatic heterocyclylcarbamoyl groups (e.g., pyridylcarbamoyl, thienylcarbamoyl), (37) 3- to 14-membered non-aromatic heterocyclylcarbamoyl groups (e.g., morpholinylcarbamoyl, piperidinylcarbamoyl), (38) Optionally halogenated C 1-6 alkylsulfonyl groups, (39)C 6-14 arylsulfonyl groups, (40) 5- to 14-membered aromatic heterocyclylsulfonyl groups (e.g., pyridylsulfonyl, thienylsulfonyl), (41) Optionally halogenated C 1-6 alkylsulfinyl groups, (42)C 6-14 arylsulfinyl groups (e.g., phenylsulfinyl, 1-naphthylsulfinyl, 2-naphthylsulfinyl); (43) 5- to 14-membered aromatic heterocyclylsulfinyl groups (e.g., pyridylsulfinyl, thienylsulfinyl), (44) amino group, (45) Mono- or di-C 1-6 alkylamino groups (e.g., methylamino, ethylamino, propylamino, isopropylamino, butylamino, dimethylamino, diethylamino, dipropylamino, dibutylamino, N-ethyl-N-methylamino); (46) Mono- or di-C 6-14 arylamino groups (e.g., phenylamino); (47) 5- to 14-membered aromatic heterocyclylamino groups (e.g., pyridylamino), (48)C 7-16 aralkylamino groups (e.g., benzylamino), (49) formylamino group, (50)C 1-6 alkyl-carbonylamino groups (e.g., acetylamino, propanoylamino, butanoylamino); (51)(C 1-6 Alkyl)(C 1-6 alkyl-carbonyl)amino groups (e.g., N-acetyl-N-methylamino), (52)C 6-14 aryl-carbonylamino groups (e.g., phenylcarbonylamino, naphthylcarbonylamino); (53)C 1-6 alkoxycarbonylamino groups (e.g., methoxycarbonylamino, ethoxycarbonylamino, propoxycarbonylamino, butoxycarbonylamino, tert-butoxycarbonylamino), (54)C 7-16 aralkyloxy-carbonylamino groups (e.g., benzyloxycarbonylamino), (55)C 1-6 alkylsulfonylamino groups (e.g., methylsulfonylamino, ethylsulfonylamino); (56)C 1-6 C optionally substituted by alkyl groups 6-14arylsulfonylamino groups (e.g., phenylsulfonylamino, toluenesulfonylamino); (57) Optionally halogenated C 1-6 alkyl groups, (58)C 2-6 alkenyl groups, (59)C 2-6 alkynyl groups, (60)C 3-10 cycloalkyl groups, (61)C 3-10 cycloalkenyl groups, and (62)C 6-14 Aryl groups.

[0139] The number of the above-mentioned substituents in the "optionally substituted hydrocarbon group" is, for example, 1 to 5, preferably 1 to 3. When the number of substituents is two or more, the respective substituents may be the same or different.

[0140] In this specification, examples of the "heterocyclic group" (including the "heterocyclic group" of the "optionally substituted heterocyclic group") include (i) an aromatic heterocyclic group, (ii) a non-aromatic heterocyclic group, and (iii) a 7- to 10-membered bridged heterocyclic group, each of which contains, as ring-constituting atoms other than carbon atoms, 1 to 4 heteroatoms selected from a nitrogen atom, a sulfur atom, and an oxygen atom.

[0141] In this specification, examples of the "aromatic heterocyclic group" (including "5- to 14-membered aromatic heterocyclic group") include 5- to 14-membered (preferably 5- to 10-membered) aromatic heterocyclic groups containing, as ring-constituting atoms other than carbon atoms, 1 to 4 heteroatoms selected from nitrogen atoms, sulfur atoms, and oxygen atoms.

[0142] Preferred examples of the "aromatic heterocyclic group" include 5- or 6-membered monocyclic aromatic heterocyclic groups such as thienyl, furyl, pyrrolyl, imidazolyl, pyrazolyl, thiazolyl, isothiazolyl, oxazolyl, isoxazolyl, pyridyl, pyrazinyl, pyrimidinyl, pyridazinyl, 1,2,4-oxadiazolyl, 1,3,4-oxadiazolyl, 1,2,4-thiadiazolyl, 1,3,4-thiadiazolyl, triazolyl, tetrazolyl, and triazinyl; Benzothiophenyl, benzofuranyl, benzimidazolyl, benzoxazolyl, benzisoxazolyl, benzothiazolyl, benzisothiazolyl, benzotriazolyl, imidazopyridinyl, thienopyridinyl, furopyridinyl, pyrrolopyridinyl, pyrazolopyridinyl, oxazolopyridinyl, thiazolopyridinyl, imidazopyrazinyl, imidazopyrimidinyl, imidazopyrimidinyl, thienopyrimidinyl, furopyrimidinyl, pyrrolopyrimidinyl, pyrazolopyrimidinyl, oxazolopyriminyl and 8- to 14-membered fused polycyclic (preferably bicyclic or tricyclic) aromatic heterocyclic groups such as cinnolinyl, thiazolopyrimidinyl, pyrazolotriazinyl, naphtho[2,3-b]thienyl, phenoxathiinyl, indolyl, isoindolyl, 1H-indazolyl, purinyl, isoquinolyl, quinolyl, phthalazinyl, naphthyridinyl, quinoxalinyl, quinazolinyl, cinnolinyl, carbazolyl, β-carbolinyl, phenanthridinyl, acridinyl, phenazinyl, phenothiazinyl, and phenoxazinyl.

[0143] In the present specification, examples of the "non-aromatic heterocyclic group" (including "3- to 14-membered non-aromatic heterocyclic group") include 3- to 14-membered (preferably 4- to 10-membered) non-aromatic heterocyclic groups containing, as ring-constituting atoms other than carbon atoms, 1 to 4 heteroatoms selected from nitrogen atoms, sulfur atoms, and oxygen atoms.

[0144] Preferred examples of the "non-aromatic heterocyclic group" include aziridinyl, oxiranyl, thiiranyl, azetidinyl, oxetanyl, thietanyl, tetrahydrothienyl, tetrahydrofuranyl, pyrrolinyl, pyrrolidinyl, imidazolinyl, imidazolidinyl, oxazolinyl, oxazolidinyl, pyrazolinyl, pyrazolidinyl, thiazolinyl, thiazolidinyl, tetrahydroisothiazolyl, tetrahydrooxazolyl, tetrahydrofuran ... 3- to 8-membered monocyclic non-aromatic heterocyclic groups such as isoxazolyl, piperidinyl, piperazinyl, tetrahydropyridinyl, dihydropyridinyl, dihydrothiopyranyl, tetrahydropyrimidinyl, tetrahydropyridazinyl, dihydropyranyl, tetrahydropyranyl, tetrahydrothiopyranyl, morpholinyl, thiomorpholinyl, azepanyl, diazepanyl, azepinyl, oxepanyl, azocanyl, and diazocanyl; Dihydrobenzofuranyl, dihydrobenzimidazolyl, dihydrobenzoxazolyl, dihydrobenzothiazolyl, dihydrobenzisothiazolyl, dihydronaphtho[2,3-b]thienyl, tetrahydroisoquinolyl, tetrahydroquinolyl, 4H-quinolidinyl, indolinyl, isoindolinyl, tetrahydrothieno[2,3-c]pyridinyl, tetrahydrobenzazepinyl, tetrahydroquinoxalinyl, tetrahydrophenanthridinyl, hexa Examples thereof include 9- to 14-membered fused polycyclic (preferably bicyclic or tricyclic) non-aromatic heterocyclic groups such as hydrophenothiazinyl, hexahydrophenoxazinyl, tetrahydrophthalazinyl, tetrahydronaphthyridinyl, tetrahydroquinazolinyl, tetrahydrocinnolinyl, tetrahydrocarbazolyl, tetrahydro-β-carbolinyl, tetrahydroacridinyl, tetrahydrophenazinyl, tetrahydrothioxanthenyl, and octahydroisoquinolyl.

[0145] In the present specification, preferred examples of the "7- to 10-membered bridged heterocyclic group" include quinuclidinyl and 7-azabicyclo[2.2.1]heptanyl.

[0146] In the present specification, examples of the "nitrogen-containing heterocyclic group" include a "heterocyclic group" containing at least one nitrogen atom as a ring-constituting atom.

[0147] In the present specification, examples of the "optionally substituted heterocyclic group" include a heterocyclic group which may have a substituent selected from the above-mentioned Substituent Group A.

[0148] The number of substituents in the "optionally substituted heterocyclic group" is, for example, 1 to 3. When the number of substituents is two or more, the respective substituents may be the same or different.

[0149] In the present specification, examples of the "acyl group" include a formyl group, a carboxy group, a carbamoyl group, a thiocarbamoyl group, a sulfino group, a sulfo group, a sulfamoyl group, and a phosphono group, each of which is "a halogen atom, an optionally halogenated C 1-6 C optionally having 1 to 3 substituents selected from an alkoxy group, a hydroxy group, a nitro group, a cyano group, an amino group, and a carbamoyl group; 1-6 Alkyl group, C 2-6 Alkenyl group, C 3-10 Cycloalkyl groups, C 3-10 Cycloalkenyl group, C 6-14 Aryl group, C 7-16 It may have one or two substituents selected from an aralkyl group, a 5- to 14-membered aromatic heterocyclic group, and a 3- to 14-membered non-aromatic heterocyclic group.

[0150] Examples of "acyl groups" also include hydrocarbon-sulfonyl groups, heterocyclylsulfonyl groups, hydrocarbon-sulfinyl groups, and heterocyclylsulfinyl groups.

[0151] Here, the term "hydrocarbon-sulfonyl group" refers to a sulfonyl group having a hydrocarbon group bonded thereto, the term "heterocyclylsulfonyl group" refers to a sulfonyl group having a heterocyclic group bonded thereto, the term "hydrocarbon-sulfinyl group" refers to a sulfinyl group having a hydrocarbon group bonded thereto, and the term "heterocyclylsulfinyl group" refers to a sulfinyl group having a heterocyclic group bonded thereto.

[0152] Preferred examples of the "acyl group" include a formyl group, a carboxy group, and C 1-6 Alkyl-carbonyl group, C 2-6 Alkenyl-carbonyl groups (e.g., crotonoyl), C 3-10 Cycloalkyl-carbonyl groups (e.g., cyclobutanecarbonyl, cyclopentanecarbonyl, cyclohexanecarbonyl, cycloheptanecarbonyl), C 3-10 Cycloalkenyl-carbonyl groups (e.g., 2-cyclohexenecarbonyl), C 6-14 Aryl-carbonyl group, C 7-16 Aralkyl-carbonyl group, 5- to 14-membered aromatic heterocyclylcarbonyl group, 3- to 14-membered non-aromatic heterocyclylcarbonyl group, C 1-6 Alkoxy-carbonyl group, C 6-14 Aryloxy-carbonyl groups (e.g., phenyloxycarbonyl, naphthyloxycarbonyl), C 7-16 Aralkyloxy-carbonyl group (e.g., benzyloxycarbonyl, phenethyloxycarbonyl), carbamoyl group, mono- or di-C 1-6 Alkyl-carbamoyl group, mono- or di-C 2-6 Alkenyl-carbamoyl groups (e.g., diallylcarbamoyl), mono- or di-C 3-10 Cycloalkyl-carbamoyl groups (e.g., cyclopropylcarbamoyl), mono- or di-C 6-14 Aryl-carbamoyl groups (e.g., phenylcarbamoyl), mono- or di-C 7-16 Aralkyl-carbamoyl group, 5- to 14-membered aromatic heterocyclylcarbamoyl group (e.g., pyridylcarbamoyl), thiocarbamoyl group, mono- or di-C 1-6Alkyl-thiocarbamoyl groups (e.g., methylthiocarbamoyl, N-ethyl-N-methylthiocarbamoyl), mono- or di-C 2-6 Alkenyl-thiocarbamoyl groups (e.g., diallylthiocarbamoyl), mono- or di-C 3-10 Cycloalkyl-thiocarbamoyl groups (e.g., cyclopropylthiocarbamoyl, cyclohexylthiocarbamoyl), mono- or di-C 6-14 Aryl-thiocarbamoyl groups (e.g., phenylthiocarbamoyl), mono- or di-C 7-16 Aralkyl-thiocarbamoyl groups (e.g., benzylthiocarbamoyl, phenethylthiocarbamoyl), 5- to 14-membered aromatic heterocyclylthiocarbamoyl groups (e.g., pyridylthiocarbamoyl), sulfino groups, C 1-6 Alkyl sulfinyl group (e.g., methyl sulfinyl, ethyl sulfinyl), sulfo group, C 1-6 Alkylsulfonyl group, C 6-14 Arylsulfonyl group, phosphono group, and mono- or di-C 1-6 Examples include alkylphosphono groups (for example, dimethylphosphono, diethylphosphono, diisopropylphosphono, dibutylphosphono).

[0153] In the present specification, examples of the "optionally substituted amino group" include "amino groups each of which may have 1 to 3 substituents selected from Substituent group A, C 1-6 Alkyl group, C 2-6 Alkenyl group, C 3-10 Cycloalkyl groups, C 6-14 Aryl group, C 7-16 Aralkyl group, C 1-6 Alkyl-carbonyl group, C 6-14 Aryl-carbonyl group, C 7-16 Aralkyl-carbonyl group, 5- to 14-membered aromatic heterocyclylcarbonyl group, 3- to 14-membered non-aromatic heterocyclylcarbonyl group, C 1-6 Alkoxy-carbonyl group, 5- to 14-membered aromatic heterocyclic group, carbamoyl group, mono- or di-C 1-6 Alkyl-carbamoyl group, mono- or di-C 7-16Aralkyl-carbamoyl group, C 1-6 Alkylsulfonyl group, and C 6-14 and an amino group optionally having one or two substituents selected from arylsulfonyl groups.

[0154] Preferred examples of the optionally substituted amino group include an amino group, a mono- or di-(optionally halogenated C 1-6 alkyl)amino groups (e.g., methylamino, trifluoromethylamino, dimethylamino, ethylamino, diethylamino, propylamino, dibutylamino), mono- or di-C 2-6 Alkenylamino groups (e.g., diallylamino), mono- or di-C 3-10 Cycloalkylamino groups (e.g., cyclopropylamino, cyclohexylamino), mono- or di-C 6-14 Arylamino groups (e.g., phenylamino), mono- or di-C 7-16 Aralkylamino groups (e.g., benzylamino, dibenzylamino), mono- or di-(optionally halogenated C 1-6 alkyl)-carbonylamino group (e.g., acetylamino, propionylamino), mono- or di-C 6-14 Aryl-carbonylamino groups (e.g., benzoylamino), mono- or di-C 7-16 Aralkyl-carbonylamino group (e.g., benzylcarbonylamino), mono- or di-5- to 14-membered aromatic heterocyclic carbonylamino group (e.g., nicotinoylamino, isonicotinoylamino), mono- or di-3- to 14-membered non-aromatic heterocyclic carbonylamino group (e.g., piperidinylcarbonylamino), mono- or di-C 1-6 Alkoxy-carbonylamino group (e.g., tert-butoxycarbonylamino), 5- to 14-membered aromatic heterocyclic amino group (e.g., pyridylamino), carbamoylamino group, (mono- or di-C 1-6 alkyl-carbamoyl)amino groups (e.g., methylcarbamoylamino), (mono- or di-C 7-16 aralkyl-carbamoyl)amino group (e.g., benzylcarbamoylamino), C 1-6Alkyl sulfonylamino groups (e.g., methyl sulfonyl amino, ethyl sulfonyl amino), C 6-14 Arylsulfonylamino groups (e.g., phenylsulfonylamino), (C 1-6 Alkyl)(C 1-6 alkyl-carbonyl)amino groups (e.g., N-acetyl-N-methylamino), and (C 1-6 Alkyl)(C 6-14 and aryl-carbonyl)amino groups (for example, N-benzoyl-N-methylamino).

[0155] In the present specification, examples of the "optionally substituted carbamoyl group" include "a carbamoyl group which optionally has 1 to 3 substituents selected from Substituent group A, C 1-6 Alkyl group, C 2-6 Alkenyl group, C 3-10 Cycloalkyl groups, C 6-14 Aryl group, C 7-16 Aralkyl group, C 1-6 Alkyl-carbonyl group, C 6-14 Aryl-carbonyl group, C 7-16 Aralkyl-carbonyl group, 5- to 14-membered aromatic heterocyclylcarbonyl group, 3- to 14-membered non-aromatic heterocyclylcarbonyl group, C 1-6 Alkoxy-carbonyl group, 5- to 14-membered aromatic heterocyclic group, carbamoyl group, mono- or di-C 1-6 Alkyl-carbamoyl group, and mono- or di-C 7-16 and carbamoyl groups which may have one or two substituents selected from aralkyl-carbamoyl groups.

[0156] Preferred examples of the optionally substituted carbamoyl group include mono- or di-C 1-6 Alkyl-carbamoyl group, mono- or di-C 2-6 Alkenyl-carbamoyl groups (e.g., diallylcarbamoyl), mono- or di-C 3-10 Cycloalkyl-carbamoyl groups (e.g., cyclopropylcarbamoyl, cyclohexylcarbamoyl), mono- or di-C 6-14Aryl-carbamoyl groups (e.g., phenylcarbamoyl), mono- or di-C 7-16 Aralkyl-carbamoyl group, mono- or di-C 1-6 Alkyl-carbamoyl-carbamoyl groups (e.g., acetylcarbamoyl, propionylcarbamoyl), mono- or di-C 6-14 Examples include carbonyl-carbamoyl groups (for example, benzoylcarbamoyl) and 5- to 14-membered aromatic heterocyclylcarbamoyl groups (for example, pyridylcarbamoyl).

[0157] In the present specification, examples of the "optionally substituted thiocarbamoyl group" include "C 1-6 Alkyl group, C 2-6 Alkenyl group, C 3-10 Cycloalkyl groups, C 6-14 Aryl group, C 7-16 Aralkyl group, C 1-6 Alkyl-carbonyl group, C 6-14 Aryl-carbonyl group, C 7-16 Aralkyl-carbonyl group, 5- to 14-membered aromatic heterocyclylcarbonyl group, 3- to 14-membered non-aromatic heterocyclylcarbonyl group, C 1-6 Alkoxy-carbonyl group, 5- to 14-membered aromatic heterocyclic group, carbamoyl group, mono- or di-C 1-6 Alkyl-carbamoyl group, and mono- or di-C 7-16 and a thiocarbamoyl group optionally having one or two substituents selected from an aralkyl-carbamoyl group.

[0158] Preferred examples of the optionally substituted thiocarbamoyl group include a thiocarbamoyl group, a mono- or alkyl-thiocarbamoyl group (e.g., methylthiocarbamoyl, ethylthiocarbamoyl, dimethylthiocarbamoyl, diethylthiocarbamoyl, N-ethyl-N-methylthiocarbamoyl), a mono- or di-C 2-6 Alkenyl-thiocarbamoyl groups (e.g., diallylthiocarbamoyl), mono- or di-C 3-10Cycloalkyl-thiocarbamoyl groups (e.g., cyclopropylthiocarbamoyl, cyclohexylthiocarbamoyl), mono- or di-C 6-14 Aryl-thiocarbamoyl groups (e.g., phenylthiocarbamoyl), mono- or di-C 7-16 Aralkyl-thiocarbamoyl groups (e.g., benzylthiocarbamoyl, phenylthiocarbamoyl), mono- or di-C 1-6 Alkyl-carbonyl-thiocarbamoyl groups (e.g., acetylthiocarbamoyl, propionylthiocarbamoyl), mono- or di-C 6-14 Examples thereof include aryl-carbonyl-thiocarbamoyl groups (for example, benzoylthiocarbamoyl) and 5- to 14-membered aromatic heterocyclylthiocarbamoyl groups (for example, pyridylthiocarbamoyl).

[0159] In the present specification, examples of the "optionally substituted sulfamoyl group" include "a sulfamoyl group which optionally has 1 to 3 substituents selected from Substituent group A, C 1-6 Alkyl group, C 2-6 Alkenyl group, C 3-10 Cycloalkyl groups, C 6-14 Aryl group, C 7-16 Aralkyl group, C 1-6 Alkyl-carbonyl group, C 6-14 Aryl-carbonyl group, C 7-16 Aralkyl-carbonyl group, 5- to 14-membered aromatic heterocyclylcarbonyl group, 3- to 14-membered non-aromatic heterocyclylcarbonyl group, C 1-6 Alkoxy-carbonyl group, 5- to 14-membered aromatic heterocyclic group, carbamoyl group, mono- or di-C 1-6 Alkyl-carbamoyl group, and mono- or di-C 7-16 and a sulfamoyl group which may have one or two substituents selected from an aralkyl-carbamoyl group.

[0160] Preferred examples of the optionally substituted sulfamoyl group include a sulfamoyl group, a mono- or di-C 1-6Alkyl-sulfamoyl groups (e.g., methylsulfamoyl, ethylsulfamoyl, dimethylsulfamoyl, diethylsulfamoyl, N-ethyl-N-methylsulfamoyl), mono- or di-C 2-6 Alkenyl-sulfamoyl group (e.g., diallylsulfamoyl), mono- or di-C 3-10 Cycloalkyl-sulfamoyl groups (e.g., cyclopropylsulfamoyl, cyclohexylsulfamoyl), mono- or di-C 6-14 Aryl-sulfamoyl groups (e.g., phenylsulfamoyl), mono- or di-C 7-16 Aralkyl-sulfamoyl groups (e.g., benzylsulfamoyl, phenethylsulfamoyl), mono- or alkyl-carbonyl-sulfamoyl groups (e.g., acetylsulfamoyl, propionylsulfamoyl), mono- or di-C 6-14 Examples thereof include aryl-carbonyl-sulfamoyl groups (for example, benzoylsulfamoyl) and 5- to 14-membered aromatic heterocyclylsulfamoyl groups (for example, pyridylsulfamoyl).

[0161] In the present specification, examples of the "optionally substituted hydroxy group" include "a hydroxy group which may have 1 to 3 substituents selected from Substituent group A, each of which may have 1 to 3 substituents selected from Substituent group A, C 1-6 Alkyl group, C 2-6 Alkenyl group, C 3-10 Cycloalkyl groups, C 6-14 Aryl group, C 7-16 Aralkyl group, C 1-6 Alkyl-carbonyl group, C 6-14 Aryl-carbonyl group, C 7-16 Aralkyl-carbonyl group, 5- to 14-membered aromatic heterocyclylcarbonyl group, 3- to 14-membered non-aromatic heterocyclylcarbonyl group, C 1-6 Alkoxy-carbonyl group, 5- to 14-membered aromatic heterocyclic group, carbamoyl group, mono- or di-C 1-6 Alkyl-carbamoyl group, mono- or di-C 7-16 Aralkyl-carbamoyl group, C 1-6 Alkylsulfonyl group, and C 6-14and arylsulfonyl groups.

[0162] Preferred examples of the optionally substituted hydroxy group include a hydroxy group, C 1-6 Alkoxy group, C 2-6 Alkenyloxy groups (e.g., allyloxy, 2-butenyloxy, 2-pentenyloxy, 3-hexenyloxy), C 3-10 cycloalkyloxy groups (e.g., cyclohexyloxy), C 6-14 Aryloxy groups (e.g., phenoxy, naphthyloxy), C 7-16 Aralkyloxy groups (e.g., benzyloxy, phenethyloxy), C 1-6 Alkyl-carbonyloxy groups (e.g., acetyloxy, propionyloxy, butyryloxy, isobutyryloxy, pivaloyloxy), C 6-14 Aryl-carbonyloxy groups (e.g., benzoyloxy), C 7-16 Aralkyl-carbonyloxy groups (e.g., benzylcarbonyloxy), 5- to 14-membered aromatic heterocyclylcarbonyloxy groups (e.g., nicotinoyloxy), 3- to 14-membered non-aromatic heterocyclylcarbonyloxy groups (e.g., piperidinylcarbonyloxy), C 1-6 Alkoxy-carbonyloxy groups (e.g., tert-butoxycarbonyloxy), 5- to 14-membered aromatic heterocyclyloxy groups (e.g., pyridyloxy), C 1-6 Alkyl-carbamoyloxy groups (e.g., methylcarbamoyloxy), C 7-16 Aralkyl-carbamoyloxy groups (e.g., benzylcarbamoyloxy), C 1-6 Alkyl sulfonyloxy groups (e.g., methyl sulfonyloxy, ethyl sulfonyloxy), and C 6-14 Arylsulfonyloxy groups (for example, phenylsulfonyloxy) are included.

[0163] In the present specification, examples of the "optionally substituted sulfanyl group" include "C1-6 Alkyl group, C 2-6 Alkenyl group, C 3-10 Cycloalkyl groups, C 6-14 Aryl group, C 7-16 Aralkyl group, C 1-6 Alkyl-carbonyl group, C 6-14 Examples thereof include a sulfanyl group and a halogenated sulfanyl group which may have a substituent selected from an aryl-carbonyl group and a 5- to 14-membered aromatic heterocyclic group.

[0164] Preferred examples of the optionally substituted sulfanyl group include a sulfanyl (—SH) group, C 1-6 Alkylthio group, C 2-6 Alkenylthio groups (e.g., allylthio, 2-butenylthio, 2-pentenylthio, 3-hexenylthio), C 3-10 cycloalkylthio groups (e.g., cyclohexylthio), C 6-14 Alkylthio groups (e.g., phenylthio, naphthylthio), C 7-16 Aralkylthio groups (e.g., benzylthio, phenethylthio), C 1-6 Alkylcarbonylthio groups (e.g., acetylthio, propionylthio, butyrylthio, isobutyrylthio, pivaloylthio), C 6-14 Examples include aryl-carbonylthio groups (eg, benzoylthio), 5- to 14-membered aromatic heterocyclylthio groups (eg, pyridylthio), and halogenated thio groups (eg, pentafluorothio).

[0165] In the present specification, examples of the "optionally substituted silyl group" include "C 1-6 Alkyl group, C 2-6 Alkenyl group, C 3-10 Cycloalkyl groups, C 6-14 Aryl groups, and C 7-16 Examples of the silyl group include a silyl group which may have 1 to 3 substituents selected from aralkyl groups.

[0166] Examples of optionally substituted silyl groups include tri-C1-6 Examples include alkylsilyl groups (for example, trimethylsilyl, tert-butyl(dimethyl)silyl).

[0167] In this specification, "C 1-6 Examples of the "alkylene group" include -CH-, -(CH)-, -(CH)-, -(CH)-, -(CH)-, -(CH)-, -CH(CH)-, -C(CH)-, -CH(C2H5)-, -CH(C3H7)-, -CH(CH(CH))-, -(CH(CH))-, -CH-CH(CH)-, -CH(CH)-CH-, -CH-CH-C(CH)-, -C(CH)-CH-CH-, -CH-CH-CH-C(CH)-, and -C(CH)-CH-CH-CH-CH-.

[0168] In this specification, "C 2-6 Examples of the "alkenylene group" include -CH=CH-, -CH2-CH=CH-, -CH=CH-CH2-, -C(CH3)2-CH=CH-, -CH=CH-C(CH3)2-, -CH2-CH=CH-CH2-, -CH2-CH2-CH=CH-, -CH=CH-CH2-CH2-, -CH=CH-CH2-CH2-, -CH=CH-CH=CH-, -CH=CH-CH2-CH2-CH2-, and -CH2-CH2-CH2-CH=CH-.

[0169] In this specification, "C 2-6 Examples of the "alkynylene group" include -C≡C-, -CH2-C≡C-, -C≡C-CH2-, -C(CH3)2-C≡C-, -C≡CC(CH3)2-, -CH2-C≡C-CH2-, -CH2-CH2-C≡C-, -C≡C-CH2-CH2-, -C≡CC≡C-, -C≡C-CH2-CH2-, and -CH2-CH2-CH2-C≡C-.

[0170] In the present specification, examples of the "hydrocarbon ring" include C 6-14 Aromatic hydrocarbon ring, C 3-10 Cycloalkanes and C 3-10 Cycloalkenes are examples.

[0171] In this specification, "C 6-44 Examples of the "aromatic hydrocarbon ring" include benzene and naphthalene.

[0172] In this specification, "C 3-10 Examples of "cycloalkanes" include cyclopropane, cyclobutane, cyclopentane, cyclohexane, cycloheptane, and cyclooctane.

[0173] In this specification, "C 3-10 Examples of "cycloalkenes" include cyclopropene, cyclobutene, cyclopentene, cyclohexene, cycloheptene, and cyclooctene.

[0174] In the present specification, examples of the "heterocycle" include an aromatic heterocycle and a non-aromatic heterocycle, each of which contains, as atoms constituting the ring, in addition to carbon atoms, 1 to 4 heteroatoms selected from a nitrogen atom, a sulfur atom, and an oxygen atom.

[0175] In the present specification, examples of the "aromatic heterocycle" include 5- to 14-membered (preferably 5- to 10-membered) aromatic heterocycles containing 1 to 4 heteroatoms selected from nitrogen, sulfur, and oxygen atoms as ring-constituting atoms other than carbon. Preferred examples of the "aromatic heterocycle" include 5- or 6-membered monocyclic aromatic heterocycles such as thiophene, furan, pyrrole, imidazole, pyrazole, thiazole, isothiazole, oxazole, isoxazole, pyridine, pyrazine, pyrimidine, pyridazine, 1,2,4-oxadiazole, 1,3,4-oxadiazole, 1,2,4-thiadiazole, 1,3,4-thiadiazole, triazole, tetrazole, and triazine; Benzothiophene, benzofuran, benzimidazole, benzoxazole, benzisoxazole, benzothiazole, benzisothiazole, benzotriazole, imidazopyridine, thienopyridine, furopyridine, pyrrolopyridine, pyrazolopyridine, oxazolopyridine, thiazolopyridine, imidazopyrazine, imidazopyrimidine, thienopyrimidine, furopyrimidine, pyrrolopyrimidine, pyrazolopyrimidine, oxazolopyrimidine, thiazolopyrimidine, pyrazo Examples of aromatic heterocycles include 8- to 14-membered fused polycyclic (preferably bicyclic or tricyclic) aromatic heterocycles such as pyridopyrimidine, pyrazolopyrimidine, pyrazolotriazine, naphtho[2,3-b]thiophene, phenoxathiin, indole, isoindole, 1H-indazole, purine, isoquinoline, quinoline, phthalazine, naphthyridine, quinoxaline, quinazoline, cinnoline, carbazole, β-carboline, phenanthridine, acridine, phenazine, phenothiazine, and phenoxathiin.

[0176] In the present specification, examples of the "non-aromatic heterocycle" include 3- to 14-membered (preferably 4- to 10-membered) non-aromatic heterocycles containing, as ring-constituting atoms other than carbon, 1 to 4 heteroatoms selected from a nitrogen atom, a sulfur atom, and an oxygen atom. Preferred examples of the "non-aromatic heterocycle" include 3- to 8-membered non-aromatic heterocycles such as aziridine, oxirane, thiirane, azetidine, oxetane, thietane, tetrahydrothiophene, tetrahydrofuran, pyrroline, pyrrolidine, imidazoline, imidazolidine, oxazoline, oxazolidine, pyrazoline, pyrazolidine, thiazoline, thiazolidine, tetrahydroisothiazole, tetrahydrooxazole, tetrahydroisoxazole, piperidine, piperazine, tetrahydropyridine, dihydropyridine, dihydrothiopyran, tetrahydropyrimidine, tetrahydropyridazine, dihydropyran, tetrahydropyran, tetrahydrothiopyran, morpholine, thiomorpholine, azepanine, diazepane, azepine, azocane, diazocane, and oxepane; Examples of the heterocyclic ring include 9- to 14-membered fused polycyclic (preferably bicyclic or tricyclic) non-aromatic heterocycles such as dihydrobenzofuran, dihydrobenzimidazole, dihydrobenzoxazole, dihydrobenzothiazole, dihydrobenzisothiazole, dihydronaphtho[2,3-b]thiophene, tetrahydroisoquinoline, tetrahydroquinoline, 4H-quinolizine, indoline, isoindoline, tetrahydrothieno[2,3-c]pyridine, tetrahydrobenzazepine, tetrahydroquinoxaline, tetrahydrophenanthridine, hexahydrophenothiazine, hexahydrophenoxazine, tetrahydrophthalazine, tetrahydronaphthyridine, tetrahydroquinazoline, tetrahydrocinnoline, tetrahydrocarbazole, tetrahydro-β-carboline, tetrahydroacridine, tetrahydrophenazine, tetrahydrothioxanthene, and octahydroisoquinoline.

[0177] In the present specification, examples of the "nitrogen-containing heterocycle" include a "heterocycle" containing at least one nitrogen atom as a ring-constituting atom.

[0178] In one embodiment, preferred examples of the "non-aromatic heterocyclic group" include the above-mentioned "3- to 8-membered monocyclic non-aromatic heterocyclic group" and "9- to 14-membered fused polycyclic (preferably bicyclic or tricyclic) non-aromatic heterocyclic group", as well as 7- to 14-membered spiroheterocyclic groups such as triazaspirononyl (e.g., 1,3,7-triazaspiro[4.4]nonyl), thiadiazaspirononyl (e.g., 7-thia-1,3-diazaspiro[4.4]nonyl), and dioxidethiadiazaspirononyl (e.g., 7,7-dioxide-7-thia-1,3-diazaspiro[4.4]nonyl).

[0179] As used herein, a "topical composition" refers to a formulation of an invention compound with a medium generally accepted in the art, including all dermatologically acceptable carriers, diluents, or excipients therefor, for delivering a biologically active compound to mammalian skin, e.g., human skin.

[0180] "Stereoisomers" refer to compounds composed of the same atoms joined by the same bonds, but which have different three-dimensional structures and are not interchangeable. The present invention contemplates various stereoisomers and mixtures thereof, and includes "enantiomers," which refer to two stereoisomers whose molecules are non-superimposable mirror images of one another.

[0181] "Solvate" refers to a form of a compound complexed with solvent molecules.

[0182] "Tautomers" refer to two molecules that are structural isomers that readily interconvert.

[0183] "Pharmaceutically acceptable salts" include both acid and base addition salts.

[0184] "Pharmaceutically acceptable acid addition salts" are salts that retain the biological effectiveness and properties of the free base, even if they are not biologically or otherwise undesirable, and include those salts formed with inorganic acids such as, but not limited to, hydrochloric acid, hydrobromic acid, sulfuric acid, nitric acid, phosphoric acid, and the like, as well as, but not limited to, acetic acid, 2,2-dichloroacetic acid, adipic acid, alginic acid, ascorbic acid, aspartic acid, benzenesulfonic acid, benzoic acid, 4-acetamidobenzoic acid, camphoric acid, camphor-10-sulfonic acid, capric acid, caproic acid, caprylic acid, carbonic acid, cinnamic acid, citric acid, cyclamic acid, dodecylsulfonic acid, ethane-1,2-disulfonic acid, ethanesulfonic acid, 2-hydroxyethanesulfonic acid, formic acid, fumaric acid, galactaric acid, gentisic acid, glucoheptonic acid, gluconic acid, and the like. It refers to salts formed with organic acids such as guar, guar, guar- ...

[0185] "Pharmaceutically acceptable base addition salts" refer to salts that retain the biological effectiveness and properties of the free acids, even if they are not biologically or otherwise undesirable. These salts are prepared from the addition of an inorganic or organic base to the free acid. Salts derived from inorganic bases include, but are not limited to, sodium, potassium, lithium, ammonium, calcium, magnesium, iron, zinc, copper, manganese, aluminum salts, and the like. Preferred inorganic salts are ammonium, sodium, potassium, calcium, and magnesium salts. Salts derived from organic bases include, but are not limited to, salts of primary, secondary, and tertiary amines, substituted amines including naturally occurring substituted amines, cyclic amines, and basic ion exchange resins such as ammonia, isopropylamine, trimethylamine, diethylamine, triethylamine, tripropylamine, diethanolamine, ethanolamine, deanol, 2-dimethylaminoethanol, 2-diethylaminoethanol, dicyclohexylamine, lysine, arginine, histidine, caffeine, procaine, hydrabamine, choline, betaine, benethamine, benzathine, ethylenediamine, glucosamine, methylglucamine, theobromine, triethanolamine, tromethamine, purine, piperazine, piperidine, N-ethylperidine, and polyamine resins. Particularly preferred organic bases are isopropylamine, diethylamine, ethanolamine, trimethylamine, dicyclohexylamine, choline, and caffeine.

[0186] The compounds of the invention, or their pharmaceutically acceptable salts, may contain one or more asymmetric centers and thus give rise to enantiomers, diastereomers, and other stereoisomeric forms that can be defined in terms of absolute stereochemistry as (R)- or (S)- for amino acids, or as (D)- or (L)-. The present invention is meant to encompass all such possible isomers, as well as their racemic and optically pure forms. Optically active (+)- and (−), (R)- and (S)-, or (D)- and (L)-isomers can be prepared using chiral synthons or chiral reagents or resolved using conventional techniques, such as chromatography and fractional crystallization. Conventional techniques for the preparation / isolation of individual enantiomers include chiral synthesis from suitable optically pure precursors or resolution of the racemate (or racemate of a salt or derivative) using, for example, chiral high-pressure liquid chromatography (HPLC).

[0187] The chemical naming protocol and structure diagrams used herein are a modification of the IUPAC naming system, using the ChemDraw Version 10 software naming program (CambridgeSoft). In the chemical structure diagrams, all bonds are identified except for some carbon atoms, which are assumed to be bonded to enough hydrogen atoms to complete the valence.

[0188] "Dermatologically acceptable excipients" include, but are not limited to, any adjuvant, carrier, vehicle, excipient, lubricant, sweetener, diluent, preservative, dye / colorant, flavor enhancer, surfactant, wetting agent, dispersing agent, suspending agent, stabilizer, isotonic agent, solvent, or emulsifier, including those approved by the U.S. Food and Drug Administration as acceptable for dermatological use in humans or domestic animals, or those known or suitable for use in dermatological compositions.

[0189] "Optionally / may" or "optionally / may" means that the subsequently described circumstance event may or may not occur, and that the description includes cases where the event or circumstance occurs and cases where it does not. When a functional group is described as "optionally substituted," and thus a substituent on the functional group is also "optionally substituted," etc., for purposes of the present invention, such repetition is limited to five times, and preferably such repetition is limited to two times.

[0190] Treatment of dermatological disorders In one embodiment, the present disclosure provides a method for treating a dermatological disorder [Method 1], the method comprising topically administering to a subject in need thereof a topical composition described in Composition 1 or any of 1.1-1.71 above.

[0191] The present disclosure provides additional embodiments of Method 1 as follows. 1.1 Method 1, wherein the IRAK4 inhibitor is a dual IRAK4 / TrkA inhibitor. 1.2 Any of the preceding methods wherein the IRAK4 inhibitor is a compound described as Compound 1 or later, or Compound 2 or later. 1.3 Any of the preceding methods, wherein the dermatological disorder is an inflammatory dermatological disorder. 1.4 The preceding methods, wherein the inflammatory dermatological disorder is rosacea, psoriasis, atopic dermatitis, hidradenitis suppurativa, seborrheic dermatitis, contact dermatitis, urticaria, dermatitis herpetiformis, nummular eczema, lichen planus, pityriasis rosea, cutaneous lupus, acne, cancer of the skin (e.g., cutaneous T-cell lymphoma), or miliaria. 1.5 Any of methods 1 or 1.3-1.4, wherein the inflammatory dermatological disorder is rosacea. 1.6 The preceding method, wherein the rosacea is papulopustular rosacea. 1.7 Method 1 or 1.1-1.4, wherein the inflammatory dermatological disorder is psoriasis. 1.8 Method 1 or 1.1-1.4, wherein the inflammatory dermatological disorder is atopic dermatitis. 1.9 Method 1 or 1.1-1.4, wherein the inflammatory dermatological disorder is hidradenitis suppurativa. 1.10 Method 1 or 1.1-1.4, wherein the inflammatory dermatological disorder is cutaneous lupus. 1.11 Method 1 or 1.1-1.4, wherein the inflammatory dermatological disorder is acne. 1.12 Methods 1 or 1.1-1.4, wherein the inflammatory dermatological disorder is a cancer of the skin (e.g., cutaneous T-cell lymphoma). 1.13 Any of the preceding methods in which the subject is a human.

[0192] Another embodiment provides a method [Method 2] for reducing inflammation in mammalian skin, the method comprising topically administering to mammalian skin an effective amount of a topical composition described in any of Compositions 1 or 1.1-1.71 above to a subject in need thereof.

[0193] The present disclosure provides additional embodiments of Method 2 as follows. 2.1 Method 2, wherein the IRAK4 inhibitor is a dual IRAK4 / TrkA inhibitor. 2.2 Any of the preceding methods wherein the IRAK4 inhibitor is a compound described as Compound 1 or later, or Compound 2 or later. 2.3 Any of the preceding methods wherein the subject is suffering from a dermatological disorder. 2.4 Method 2.3, wherein the dermatological disorder is an inflammatory dermatological disorder. 2.5 The preceding methods, wherein the inflammatory dermatological disorder is rosacea, psoriasis, atopic dermatitis, hidradenitis suppurativa, seborrheic dermatitis, contact dermatitis, urticaria, dermatitis herpetiformis, nummular eczema, lichen planus, pityriasis rosea, cutaneous lupus, acne, cancer of the skin (e.g., cutaneous T-cell lymphoma), or miliaria. 2.6 Any of methods 2.3-2.5, wherein the inflammatory dermatological disorder is rosacea. 2.7 The preceding method, in which the rosacea is papulopustular rosacea. 2.8 Any of methods 2.3-2.5, wherein the inflammatory dermatological disorder is psoriasis. 2.9 Any of methods 2.3-2.5, wherein the inflammatory dermatological disorder is atopic dermatitis. 2.10 Any of methods 2.3-2.5, wherein the inflammatory dermatological disorder is hidradenitis suppurativa. 2.11 Any of methods 2.3-2.5, wherein the inflammatory dermatological disorder is cutaneous lupus. 2.12 Any of methods 2.3-2.5, wherein the inflammatory dermatological disorder is acne. 2.13 Any of methods 2.3-2.5, wherein the inflammatory dermatological disorder is a cancer of the skin (e.g., cutaneous T-cell lymphoma). 2.14 Any of the preceding methods in which the subject is a human. 2.15 Any of the preceding methods, wherein the mammalian skin is human skin.

[0194] A further embodiment provides a method [Method 3] for reducing inflammation and vascular dysfunction in mammalian skin, the method comprising topically administering to mammalian skin a therapeutically effective amount of a topical composition described in any of Compositions 1 or 1.1-1.71 above to a subject in need thereof.

[0195] The present disclosure provides additional embodiments of Method 3 as follows. 3.1 Method 3, wherein the IRAK4 inhibitor is a dual IRAK4 / TrkA inhibitor. 3.2 Any of the preceding methods wherein the IRAK4 inhibitor is a compound described as Compound 1 or later, or Compound 2 or later. 3.3 Any of the preceding methods wherein the subject is suffering from a dermatological disorder. 3.4 Method 3.3, wherein the dermatological disorder is an inflammatory dermatological disorder. 3.5 The preceding methods wherein the inflammatory dermatological disorder is rosacea, psoriasis, atopic dermatitis, hidradenitis suppurativa, seborrheic dermatitis, contact dermatitis, urticaria, dermatitis herpetiformis, nummular eczema, lichen planus, pityriasis rosea, cutaneous lupus, acne, cancer of the skin (e.g., cutaneous T-cell lymphoma), or miliaria. 3.6 Any of methods 3.3-3.5, wherein the inflammatory dermatological disorder is rosacea. 3.7 The preceding method, in which the rosacea is papulopustular rosacea. 3.8 Any of methods 3.3-3.5, wherein the inflammatory dermatological disorder is psoriasis. 3.9 Any of methods 3.3-3.5, wherein the inflammatory dermatological disorder is atopic dermatitis. 3.10 Any of Methods 3.3-3.5, wherein the inflammatory dermatological disorder is hidradenitis suppurativa. 3.11 Any of Methods 3.3-3.5, wherein the inflammatory dermatological disorder is cutaneous lupus. 3.12 Any of methods 3.3-3.5, wherein the inflammatory dermatological disorder is acne. 3.13 Any of methods 3.3-3.5, wherein the inflammatory dermatological disorder is a cancer of the skin (e.g., cutaneous T-cell lymphoma). 3.14 Any of the preceding methods in which the subject is a human. 3.15 Any of the preceding methods, wherein the mammalian skin is human skin.

[0196] As used herein, "inflammatory dermatological disorder" refers to disorders involving skin inflammation, including, for example, rosacea, psoriasis, atopic dermatitis, hidradenitis suppurativa, seborrheic dermatitis, contact dermatitis, urticaria, dermatitis herpetiformis, nummular eczema, lichen planus, pityriasis rosea, cutaneous lupus, acne, skin cancer (e.g., cutaneous T-cell lymphoma), and miliaria. Skin inflammation is typically characterized by redness / flushing, pain, pustules, heat, and / or swelling.

[0197] "Lesioned skin" refers to areas on the skin with active rosacea, such as areas of erythematotelangiectatic rosacea (e.g., with erythematous or visible blood vessels) or areas of papulopustular rosacea (e.g., skin with swollen, red, pimple-like bumps).

[0198] "Mammal" or "mammalian" includes both humans and domestic animals, such as laboratory animals and household pets (e.g., cats, dogs, pigs, cows, sheep, goats, horses, rabbits), and non-domestic animals, such as wildlife.

[0199] A "therapeutically effective amount" refers to an amount of a compound of the invention that, when administered to a mammal, preferably a human, is sufficient to achieve treatment of the desired disease or condition in a mammal, preferably a human, having the disease or condition. The amount of a compound of the invention that corresponds to a "therapeutically effective amount" will vary depending on the compound, the disease or condition and its severity, the mode of administration, and the age of the mammal being treated, but can be routinely determined by one of ordinary skill in the art given their knowledge and this disclosure. Preferably, for purposes of the present invention, a "therapeutically effective amount" is an amount of a compound of the invention that is sufficient to inhibit skin inflammation.

[0200] As used herein, "treating" or "treatment" encompasses the treatment of a disease or condition of interest in a mammal, preferably a human; (i) preventing a disease or condition from occurring in a mammal; (ii) inhibiting a disease or condition in a mammal, i.e., preventing its occurrence; (iii) alleviating a disease or condition in a mammal, i.e., causing regression of the disease or condition; or (iv) alleviating the symptoms of a disease or condition in a mammal, i.e., alleviating the symptoms without addressing the underlying disease or condition. Includes:

[0201] As used herein, the terms "disease," "disorder," and "condition" may be used interchangeably or may differ in that a particular illness or condition may not have a known causative agent (and thus the etiology has not yet been elucidated), and therefore is not yet recognized as a disease, but only as an undesirable state or syndrome, with more or less specific sets of symptoms identified by clinicians.

[0202] "Reducing inflammation locally" refers to a decrease or reduction in local inflammation at the site of topical administration of a pharmaceutical composition. Administering a topical composition described herein may reduce inflammation at the site on the body where the pharmaceutical composition is topically administered. Reduction of local inflammation may be evidenced by reduced redness, reduced swelling, loss of pain or irritation, reduced heat sensation, and / or reduced expression of one or more inflammatory markers, such as interleukin-6 (IL-6), CC motif chemokine ligand 3 (CCL3, or MIP-1α).

[0203] As used herein, the term "about" means ±20% of the indicated range, value, or structure, unless otherwise indicated.

[0204] Any suitable amount of a compound of Formula I, II (e.g., Compound 1 onward), or III (e.g., Compound 2 onward) can be used in the dermatological compositions of the present disclosure, provided that the amount effectively reduces local inflammation and / or vascular dysfunction and maintains stability in the composition over an extended period of time. Preferably, the stability extends over an extended period of time, e.g., up to about 3 years, up to 1 year, or up to about 6 months, that is typical for the manufacture, packaging, shipping, and / or storage of dermatologically acceptable compositions. The compound of Formula I, II (e.g., Compound 1 onward), or III (e.g., Compound 2 onward) can be present in solution, partially in solution with undissolved portions, or completely in undissolved suspension.

[0205] In some embodiments, the IRAK4 inhibitor of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) is present in the topical composition of the present disclosure at a concentration of about 0.005% to about 20% by weight, e.g., about 0.005% to about 15% by weight, or about 0.005% to about 10% by weight, or about 0.005% to about 5% by weight. In some embodiments, the IRAK4 inhibitor of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) is present in the topical composition at a concentration of about 0.01% to about 5% by weight, or about 0.1% to about 5% by weight, about 0.1% to about 1% by weight, about 1% to about 2% by weight, about 2% to about 3% by weight, about 3% to about 4% by weight, or about 4% to about 5% by weight. In some embodiments, the IRAK4 inhibitor of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) is present in the topical composition at a concentration of about 0.1%, 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, 0.7%, 0.8%, 0.9%, or 1% by weight, or about 1.5%, 2%, 2.5%, 3%, 3.5%, 4%, 4.5%, or about 5% by weight, or 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, 12%, 135, 14%, or 15% by weight.

[0206] In some embodiments, the therapeutically effective dosage should be from about 0.0001 mg to about 1000 mg per day. In some embodiments, the therapeutically effective dosage may be from about 0.001 to 50 mg of active ingredient (a compound of Formula I described herein) per kilogram of body weight per day, delivered locally as described herein. In some embodiments, the compound of formula I is administered in a dosage of up to 1500 mg / day, e.g., 1200 mg / day, 900 mg / day, 850 mg / day, 800 mg / day, 750 mg / day, 700 mg / day, 650 mg / day, 600 mg / day, 550 mg / day, 500 mg / day, 450 mg / day, 400 mg / day, 350 mg / day, 300 mg / day, 250 mg / day, 200 mg / day, 150 mg / day, 1000 mg / day, 50 mg / day, 25 mg / day, 10 mg / day, or 9, 8, 7, 6, 5, 4, 3, 2, 1, 0.75, 0.5, 0.25, 0.10, 0.05, or 0.01 mg / day.

[0207] In certain embodiments, the pharmaceutical compositions described herein further comprise one or more additional dermatologically acceptable excipients, which may be one or more solvents that solubilize and / or stabilize the active ingredient (e.g., an IRAK4 inhibitor) contained therein, and may include viscosity enhancers, pH adjusters, film formers, etc. Non-limiting examples of suitable additional excipients include alcohols such as alkanols having 1 to 20 carbon atoms, e.g., oleyl alcohol, cetyl alcohol, octyldodecanol, cetostearyl alcohol, benzyl alcohol, butylene glycol, diethylene glycol, glycofurol, glycerides, glycerin, glycerol, phenethyl alcohol, polypropylene glycol, polyvinyl alcohol, phenoxyethanol, and phenol; amides such as N-butyl-N-dodecylacetamide, crotamiton, N,N-dimethylformamide, N,N-dimethylacetamide, N-methylformamide, and urea; amino acids such as L-α-amino acids and water-soluble proteins; azones and azone-like compounds such as azacycloalkanes; almond oil, amyl butyrate, apixazone, sorbitol ... Essential oils such as cotton kernel oil, avocado oil, camphor, castor oil, 1-carvone, coconut oil, corn oil, cottonseed oil, eugenol, menthol, anise oil, clove oil, orange oil, peanut oil, peppermint oil, rose oil, safflower oil, sesame oil, shark liver oil (squalene), soybean oil, sunflower oil, and walnut oil; vitamins and herbs such as aloe, allantoin, black walnut extract, chamomile extract, panthenol, papaya, tocopherol, and vitamin A palmitate; waxes such as candelilla wax, carnuba wax, ceresin wax, beeswax, lanolin wax, jojoba oil, and petrolatum; mixtures such as primary esters of fractionated vegetable oil fatty acids with glycerin or propylene glycol, and interesterified medium-chain triglyceride oils;Amyl caproate, butyl acetate, caprylic acid, cetyl esters, diethyl sebacate, dioctyl malate, elaidic acid, ethyl caprylate, ethyl glycol palmitostearate, glyceryl beheate, glucose glutamate, isobutyl acetate, laureth-4, lauric acid, malic acid, methyl caprylate, mineral oil, myristic acid, oleic acid, palmitic acid, PEG fatty acid esters, polyoxyethylene sorbitan monooleate, polypropylene glycol, propylene glycol, sucrose distearate, salicylic acid, sodium citrate, stearic acid, soap, and fatty acids and fatty acid esters such as caproic, caprylic, capric, and lauric triglycerides; macrocylic compounds such as butylated hydroxyanisole, cyclopentadecanolide, and cyclodextrin; dialkyl phosphates, ditetradecyl phosphate, lecithin, sorbitan monooleate ... Phospholipids and phosphates such as cysteine, 2-pyrrolidone derivatives such as alkylpyrrolidone-5-carboxylic acid esters, pyroglutamic acid esters, N-methylpyrrolidone, dioxane derivatives and dioxolane derivatives; sulfoxides such as dimethyl sulfoxide and decylmethyl sulfoxide; acids such as alginic acid, sorbic acid, and succinic acid; cyclic amines; imidazolinones; imidazoles; ketones such as acetone, dimethicone, methyl ethyl ketone, and pentanedione; lanolin derivatives such as lanolin alcohol, PEG16 lanolin, and acetylated lanolin; oxazolines; oxazolindinones; proline esters; pyrroles, urethanes;and nonoxynol, polysorbate, polyoxyethylene alcohol, polyoxyethylene fatty acid ester, sodium lauryl sulfate, and sorbitan monostearate, saturated or unsaturated fatty acid ester, saturated or unsaturated fatty acid ester, polyoxythylene fatty ether, polyoxythylene fatty acid ester, diethylene glycol monoethyl ether, 1,3-dimethyl-2-imidazolidinone, and / or dimethyl isosorbide, PEG 200, ethanol, glycerol, Transcutol P (diethylene glycol monoethyl ether), propylene glycol, 1,3-dimethyl-2-imidazolidinone (DMI), sodium metabisulfite, butylated hydroxytoluene (BHT), benzyl alcohol, sodium benzoate, isopropyl myristate, diisopropyl adipate, crodamol OHS (ethylhexyl hydroxystearate), mineral oil, Betadex, TWEEN 20 (polyoxyethylene (20) stearyl ether), silicones (e.g., dimethicone, cylcomethicone, etc.), steareth-2 (Brij S2), steareth-20 (Brij S20), glyceryl stearate, stearic acid, magnesium stearate, diethylene glycol monoethyl ether, 1,3-dimethyl-2-imidazolidinone, but are not limited to these;

[0208] In some embodiments, the dermatological compositions of the present disclosure comprise a solvent system comprising one or more solvents for the IRAK4 inhibitors of the present disclosure. In some embodiments, the solvent system comprises one or more solvents selected from polyethers, polyethylene glycols (e.g., PEG 400), polyether alcohols (e.g., diethylene glycol monoethyl ether; Transcutol® P), ethers, and alcohols; e.g., PEG 400 and diethylene glycol monoethyl ether (Transcutol® P). Additional solvents include polyethers, lower polyhydroxy alcohols, ethanol, propylene glycol, isosorbide dimethyl ether, di(ethylene glycol) ethyl ether, mineral oil; light mineral oil; glycols such as glycerol behenate and polyethylene glycol (PEG), and mixtures thereof. In some embodiments, the solvent may be selected from glycerin, polyethylene glycol, propylene glycol, and mixtures thereof. Suitable polyethylene glycols (PEG) include all grades of PEG having a molecular weight of 300 to about 8000. In some embodiments, the solvent is selected from Transcutol P and polyethylene glycol of molecular weight from about 300 to about 600, or 300 to about 500, or about 400 daltons.

[0209] Further examples of useful solvents include dialkylated mono- or poly-alkylene glycols, including 1,2-dimethoxymethane, diglyme, triglyme, tetraglyme, polyethylene glycol-350-dimethyl ether, polyethylene glycol-550-dimethyl ether, polyethylene glycol-750-dimethyl ether, where 350, 550, and 750 refer to the approximate average molecular weight of the polyethylene glycol.

[0210] In some preferred embodiments, the topical composition comprises a mixture of PEG 400 and Transcutol® P. In some embodiments, PEG 400 is present in the composition in an amount of about 20% to about 70% by weight of the composition, or about 35% to about 70% by weight of the composition, or about 35% to about 50% by weight of the composition, or about 40% to about 45% by weight of the composition, or about 55% to about 65% by weight of the composition, or about 40%, about 45%, about 50%, about 55%, or about 60% by weight of the composition. In some embodiments, diethylene glycol monoethyl ether (Transcutol® P) is present in an amount of about 10% to about 45% by weight of the composition, or about 10% to about 20% by weight of the composition, or about 20% to about 30% by weight of the composition, or about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, or about 45% by weight of the composition.

[0211] In some embodiments, the topical composition is an aqueous gel and the w / w ratio of PEG 400 / Transcutol® P is about 0.7 to about 1.1, e.g., about 0.8 to about 1.0, e.g., about 0.9.

[0212] In some embodiments, the topical composition is a non-aqueous gel, and the w / w ratio of PEG 400 / Transcutol® P is about 2.2 to about 2.6, e.g., about 2.3 to about 2.5, e.g., about 2.4.

[0213] In some embodiments, the topical composition is a cream and the w / w ratio of PEG 400 / Transcutol® P is about 2.6 to about 3.2, such as about 2.7 to about 3.1, e.g., about 2.9.

[0214] In some embodiments, the topical composition is an ointment and the w / w ratio of PEG 400 / Transcutol® P is about 3.5 to about 4.5, e.g., about 3.8 to about 4.2, e.g., about 4.

[0215] A more detailed description of certain suitable excipients is provided below. As will be understood, components of the pharmaceutical formulations described herein may have multiple functions. For example, a given substance may act as both a viscosity-increasing agent and an emulsifier.

[0216] The skin (particularly the stratum corneum) provides a physical barrier against the harmful effects of the external environment and, in so doing, interferes with the absorption or transdermal delivery of topical therapeutic drugs. Therefore, suitable dermatologically acceptable excipients may include one or more penetration enhancers (or permeation enhancers), which are substances that promote the diffusion of therapeutic drugs (e.g., IRAK4 inhibitors described herein) through the skin barrier. They typically act by reducing the impedance or resistance of the skin, allowing for improved penetration of therapeutic drugs. Specifically, substances that disrupt the normal structure of the stratum corneum can disrupt the lipid organization between cells, thus reducing its effectiveness as a barrier. These substances can include any lipid substance that will partition into stratum corneum lipids, causing a direct effect, or any substance that will affect proteins, causing an indirect disruption of lipid structure. Furthermore, solvents such as ethanol can remove lipids from the stratum corneum, thus disrupting its lipid organization and disrupting its barrier function.

[0217] The topical compositions described herein typically contain one or more carriers, preferably having a vapor pressure of 23.8 mm Hg or greater at 25° C. Preferred concentration ranges of a single carrier or total combination of carriers can be from about 0.1% to about 10%, more preferably from about 10% to about 50%, and more specifically from about 50% to about 95% by weight of the dermatological composition. Non-limiting examples of solvents include water (e.g., deionized water) and lower alcohols, including ethanol, 2-propanol, and n-propanol.

[0218] The dermatological compositions of the invention may contain one or more hydrophilic cosolvents that are miscible with water and / or low-chain alcohols and preferably have a vapor pressure less than that of water (approximately 23.8 mm Hg) at 25°C. The carrier typically has a vapor pressure equal to or greater than that of the hydrophilic cosolvent, concentrating the compound of Formula I, II (e.g., Compound 1 and subsequent), or III (e.g., Compound 2 and subsequent) on the skin. The hydrophilic cosolvent may be a glycol, specifically propylene glycol. Specifically, the propylene glycol may be from the class of polyethylene glycols, specifically those in the molecular weight range of 200 to 20,000. Preferably, the solvent will be part of the glycol ether class. More specifically, the hydrophilic cosolvent of the invention will be diethylene glycol monoethyl ether (Transquitol). As used herein, "diethylene glycol monoethyl ether" ("DGME") or "Transquitol" refers to 2-(2-ethoxyethoxy)ethanol {CAS No. 001893} or ethyoxydiglycol. Another preferred co-solvent is 1,3-dimethyl-2-imidazolidinone (DMI).

[0219] The topical compositions described herein may also contain one or more "humectants" used to provide a moisturizing benefit. Preferably, the moisturizer remains stable in the composition. Any suitable concentration of a single moisturizer or combination of moisturizers may be used, provided that the resulting concentration provides the desired moisturizing benefit. Typically, the suitable amount of moisturizer will depend on the particular moisturizer or moisturizers used. A preferred concentration range for a single moisturizer or a total combination of moisturizers may be from about 0.1% to about 70% by weight of the dermatological composition, more preferably from about 5.0% to about 30% by weight, more specifically from about 10% to about 25% by weight, or from about 10% to about 20% by weight of the dermatological composition, or from about 10% to about 15% by weight of the dermatological composition, for example, about 10% by weight, or about 11% by weight, or about 12% by weight, or about 13% by weight, or about 14% by weight, or about 15% by weight of the dermatological composition. Non-limiting examples for use herein include glycerin, polyhydric alcohols, and silicone oils. More preferably, the moisturizing agent is glycerin, propylene glycol, and / or cyclomethicone. Specifically, the filler will be glycerin and / or cyclomethicone.

[0220] In certain embodiments, the pharmaceutical composition includes a viscosity-enhancing agent and / or an emulsifying agent. Gelling agents are used to increase the viscosity of the final composition. Emulsifiers are substances that stabilize emulsions. Viscosity-enhancing agents may also act as emulsifying agents. Typically, the concentration and combination of viscosity-enhancing agents will depend on the physical stability of the finished product. A preferred concentration range for the viscosity-enhancing agent may be from about 0.01% to about 20% by weight of the dermatological composition, more preferably from about 0.1% to about 10% by weight, and more specifically from about 0.5% to about 5% by weight. Non-limiting examples of viscosity-increasing agents for use herein include members of the cellulose, acrylate polymer, and acrylate crosspolymer classes, such as hydroxypropyl cellulose, hydroxymethyl cellulose, hydroxypropyl methylcellulose (e.g., Benecel E4M), Pluronic PF127 polymer, carbomers (e.g., Carbomer 980, Carbomer 1342, and Carbomer 940), more specifically hydroxypropyl cellulose (e.g., hydroxypropyl cellulose Klucel® EF, GF, MF, and / or HF having a molecular weight of 850,000 to 1,150,000 daltons), Pluronic PF127, Carbomer 980, and / or Carbomer 1342 (Pemulen® TR-1, TR-2, and / or Carbopol® ETD 2020). Examples of emulsifiers for use herein include polysorbates, laureth-4, and potassium cetyl sulfate.

[0221] The topical compositions described herein may contain one or more antioxidants, radical scavengers, and / or stabilizers, with preferred concentrations ranging from about 0.001% to about 0.1%, more preferably from about 0.1% to about 5% by weight of the dermatological composition. Examples of suitable antioxidants include amino acids such as glycine, histidine, tyrosine, trytophan, and derivatives thereof; imidazoles such as urocanic acid and derivatives thereof; peptides such as D,L-carnosine, D-carnosine, L-carnosine, and derivatives thereof, such as anserine; carotenoids; carotenes such as α-carotone, β-carotene, lycopene, and derivatives thereof; chlorogenic acid and derivatives thereof; lipoic acid and derivatives thereof, such as dihydrlipoic acid; acid), aurothioglycose, propylthiouracil, and other thiols, such as thioredoxin, glutathione, cysteine, cystamine, and glycosyl, N-acetyl, methyl, ethyl, propyl, amyl, butyl, lauryl, palmitoyl, oleyl, α-linoleyl, cholesteryl, and glyceryl esters, and their salts; dilauryl thiodipropionate, distearyl thiodipropionate, thiodipropionic acid, and their derivatives, such as esters, ethers, peptides, lipids, nucleotides, nucleosides, and salts; sulfoximine compounds, such as buthionine sulfoximine, phosphatidylcholine ... cysteine ​​sulfoximine, buthionine sulfone, penta-, hexa-, hepta-thionine sulfoximine, unsaturated fatty acids and derivatives thereof, for example, α-linolenic acid, linoleic acid, oleic acid, folic acid and derivatives thereof, ubiquinone and ubiquinol and derivatives thereof, vitamin C and derivatives thereof, for example, ascorbyl palmitate, magnesium ascorbyl phosphate, ascorbyl acetate, tocopheral and derivatives thereof, for example, vitamin E acetate, vitamin A and derivatives thereof, for example, vitamin A palmitate, vitamin B and derivatives thereof, coniferyl benzoate of benzoin resin, rutinic acidAntioxidants include, but are not limited to, alpha-glycosyl rutin, ferulic acid, furfurylidene glucitol, carnosine, butylated hydroxytoluene, trihydroxybutyrophenone, uric acid and its derivatives, mannose and its derivatives, superoxide dismutase, zinc and its derivatives, e.g., zinc oxide, zinc sulfate, selenium and its derivatives, e.g., selenium methionine, stilbene and its derivatives, e.g., stilbene oxide, trans-stilbene oxide, etc. In certain exemplary embodiments, the one or more antioxidants may include vitamin B, nordihydroguaiaretic acid, butylated hydroxyanisole (BHA), butylated hydroxytoluene (BHT), propyl gallate, erythorbic acid, sodium erythorbate, ascorbyl palmitate and ascorbyl stearate, butylated hydroxyanisole, and gallic acid esters, and in some embodiments, the one or more antioxidants may include BHT. In some embodiments, the antioxidant is selected from one or more of butylated hydroxytoluene, sodium metabisulfite, butylated hydroxyanisole, ascorbyl palmitate, citric acid, vitamin E, vitamin E acetate, vitamin E-TPGS, ascorbic acid, tocophersolan, and propyl gallate. More specifically, the antioxidant can be metabisulfite, butylated hydroxyanisole, vitamin E, ascorbic acid, and / or propyl gallate.

[0222] The topical compositions described herein may also contain preservatives that exhibit antibacterial and / or antifungal properties. Preservatives may be present in any of the gel, cream ointment, and other dermatological compositions of the present invention to minimize bacterial and / or fungal growth over the shelf life. Preservatives include glycerin, esters of parahydroxybenzoic acid such as methyl-, ethyl-, propyl, and butyl-paraben, sodium benzoate, sorbic acid and its salts such as potassium sorbate, benzoic acid and its salts as sodium benzoate, diazolidinyl urea, alcohols having 2 to 20 carbon atoms including aliphatic alcohols such as ethanol, alcohols containing saturated, unsaturated, or aromatic rings such as benzyl alcohol or phenoxyethanol, chlorobutanol, phenolic compounds such as phenol, cresols such as m-cresol, or quaternary compounds such as benzalkonium chloride and benzethonium chloride, mercury-containing substances such as merfen and thiomerosal, stabilized chlorine dioxide, butylated hydroxytoluene (BHT), butylated hydroxyanisole, tocopherol, propyl gallate, disodium EDTA, vitamin E TPGS, and derivatives thereof, and mixtures thereof. A preferred concentration range of the preservative in the dermatological composition of the present invention may be from about 0.001% to about 20% by weight of the composition, or from about 0.01% to about 10% by weight of the composition, or from about 0.1% to about 5% by weight of the composition, or from about 1% to about 3% by weight of the composition, or about 2% by weight of the composition.

[0223] The topical compositions described herein may optionally contain one or more chelating agents. As used herein, the term "chelating agent" or "chelator" refers to a skin benefit agent capable of removing metal ions from a system by forming a complex such that the metal ions cannot readily participate in or catalyze chemical reactions. Chelating agents for use herein are preferably formulated at a concentration ranging from about 0.001% to about 10% by weight of the dermatological composition, more preferably from about 0.05% to about 5.0% by weight. Non-limiting examples for use herein include EDTA, disodium edeate, dipotassium edetate, cyclodextrin, trisodium edetate, tetrasodium edetate, citric acid, sodium citrate, gluconic acid, and potassium gluconate. Specifically, the chelating agent may be EDTA, disodium edetate, dipotassium edate, trisodium edetate, or potassium gluconate.

[0224] The dermatological compositions of the present disclosure may have a neutral to slightly acidic pH to allow for comfortable application to a subject's skin, particularly taking into account the disease state or condition the subject is suffering from. For example, in various embodiments, the pH of the cream may be about 2.5 to about 7.0, preferably about 4.0 to about 7.0, and more preferably about 5.0 to about 6.5 at room temperature. In other embodiments, the pH of such creams may be about 5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 6.0, 6.1, 6.2, 6.3, 6.4, or 6.5 at room temperature. Any component or combination of components known and useful in the art can be used to achieve the appropriate pH, such as, for example, pH adjusters including, but not limited to, lactic acid, citric acid, sodium citrate, glycolic acid, succinic acid, phosphoric acid, monosodium phosphate, disodium phosphate, oxalic acid, dl-malic acid, calcium carbonate, sodium hydroxide, magnesium hydroxide, sodium carbonate, sodium bicarbonate, and ammonium bicarbonate. In certain embodiments, the pH adjuster comprises a citrate buffer or a phosphate buffer. In some embodiments, the pH adjuster comprises an alkali or alkaline earth hydroxide, such as sodium hydroxide or magnesium hydroxide. In various embodiments, the total buffer capacity can be about 0 mM to about 600 mM, about 0 mM to about 600 mM, about 5 mM to about 600 mM, about 5 mM to about 400 mM, about 5 mM to about 300 mM, about 5 mM to about 200 mM, about 200 mM to about 400 mM, about 0 mM, about 100 mM, about 200 mM, about 300 mM, about 400 mM, about 500 mM, or 600 mM.In some embodiments, the cream contains about 0.05%, about 0.1%, about 0.15%, about 0.16%, about 0.17%, about 0.18%, about 0.19%, about 0.2%, about 0.21%, about 0.22%, about 0.23%, about 0.24%, about 0.25%, about 0.26%, about 0.27%, about 0.28%, about 0.29%, about 0.3%, about 0.31%, about 0.32%, about 0.33%, about 0.34%, about 0.35%, about 0.36%, about 0.37%, about 0.38%, about 0.39%, about 0.40%, about 0.41%, about 0.42%, about 0.43%, about 0.44%, about 0.45%, about 0.46%, about 0.47%, about 0.48%, about 0.49%, about 0.50%, about 0.51%, about 0.52%, about 0.53%, about 0.54%, about 0.55%, about 0.56%, about 0.57%, about 0.58%, about 0.59%, about 100%, about 100%, about 100% by weight of PEG-40 ... Each pH adjuster is included in an amount of about 0.32%, about 0.33%, about 0.34%, about 0.35%, about 0.36%, about 0.37%, about 0.38%, about 0.39%, about 0.4%, about 0.45%, about 0.5%, about 0.55%, about 0.6%, about 0.65%, about 0.7%, about 0.75%, about 0.8%, about 0.85%, about 0.9%, about 0.95%, or about 1%.

[0225] The topical compositions described herein may include one or more commonly used compatible cosmetically acceptable adjuvants, such as colorants, fragrances, emollients, and botanicals, such as aloe, chamomile, witch hazel, and the like.

[0226] Alternatively, other pharmaceutical delivery systems can be used for the pharmaceutical compositions of the invention. Liposomes and emulsions are well-known examples of delivery vehicles that can be used to deliver active compounds or prodrugs. Certain organic solvents, such as dimethyl sulfoxide (DMSO), can also be used.

[0227] The topical compositions described herein may be provided in any cosmetically suitable form, preferably as a lotion, cream, gel (aqueous or non-aqueous), or ointment, as well as a sprayable liquid form (e.g., a spray comprising an IRAK4 inhibitor in a base, vehicle, or carrier that dries in a cosmetically acceptable manner without the greasy appearance of a lotion or ointment when applied to the skin).

[0228] In the treatment of inflammatory dermatological disorders such as rosacea, a topical composition comprising a compound of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) is preferably administered directly to the affected area of ​​the skin (e.g., rosacea lesion) of a person in need thereof. When such a composition is used (e.g., when a dermatological composition comprising a compound of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) and a dermatologically acceptable excipient is placed on the skin of a person in need thereof), the compound of Formula I, II (e.g., Compound 1 or later), or III (e.g., Compound 2 or later) is in continuous contact with the patient's skin, thereby achieving penetration and treatment.

[0229] When administering the pharmaceutical compositions of the invention topically, the human skin to be treated may optionally be pretreated (such as by washing the skin with soap and water or by washing the skin with an alcohol-based cleanser) prior to administration of the dermatological compositions of the invention.

[0230] The pharmaceutical compositions of the invention may, if desired, be presented in a pack or dispenser device, which may contain one or more unit dosage forms containing the active compound. The topical compositions described herein may also be provided in a patch having the topical composition on one side of the patch that directly contacts the skin. A dermatologically acceptable adhesive may be used to attach the patch to the skin for an extended period of time.

[0231] The following examples can be used by one skilled in the art to determine the effectiveness of compounds of the invention in treating humans with dermatological conditions characterized by inflammation. [Example]

[0232] Example 1 - Saturation solubility of Compound 1 and Compound 2 in selected excipients A series of formulations were made to test the solubility of two IRAK4 inhibitors according to the present disclosure. The formulations were made into various systems suitable for topical application (cream, PEG ointment, aqueous gel, and non-aqueous gel).

[0233] Initially, the saturated solubility of both Compound 1 and Compound 2 was evaluated in a range of 20 excipients suitable for topical application to determine solvents and non-solvents for further formulation development work. The results are shown in Table 1 and summarized as follows:

[0234] Regarding Compound 1: *The following solvents were identified for Compound 1 (solubility greater than 0.2% w / w): benzyl alcohol (1.436% w / w), phenoxyethanol (0.442% w / w), Transcutol P (0.276% w / w), SR dimethyl isosorbide (0.267% w / w), PEG 400 (0.203% w / w). *Relatively low solubility of Compound 1 was observed in IPP (0.141% w / w), ethanol (0.072% w / w), propylene glycol (0.030% w / w), and isopropanol (0.017% w / w). *T - Minimal solubility of Compound 1 was evident in deionized water at both pH values ​​evaluated, with slightly higher solubility (0.009% w / w) observed at pH 7 compared to pH 4 (BLOQ). *T - Minimal solubility of Compound 1 (≤0.009% w / w) was observed in the remaining excipients tested, namely, propylene glycol dicaprylate, mineral oil, castor oil, butyl stereate, oleyl alcohol, IPM, Miglyol 810, glycerin, and diisopropyl adipate.

[0235] Regarding compound 2: *The following solvents were identified for T-Compound 2 (solubility greater than 2% w / w): Transcutol P (4.795% w / w), benzyl alcohol (4.795% w / w), PEG 400 (2.830% w / w), phenoxyethanol (2.650% w / w), and SR dimethyl isosorbide (2.613% w / w). *Lower solubility of Compound 2 was observed in propylene glycol (0.426% w / w), ethanol (0.193% w / w), isopropanol (0.159% w / w), IPP (1.141% w / w), ethanol (0.072% w / w), castor oil (0.064% w / w), and diisopropyl adipate (0.050% w / w). *Compound 2 was found to be insoluble in deionized water (regardless of pH). *Minimal solubility of Compound 2 (≤0.013% w / w) was observed in propylene glycol dicaprylate, IPP, mineral oil, butyl stearate, oleyl alcohol, Miglyol 810, and glycerin.

[0236] Table 1. Saturation solubility (% w / w) of Compound 1 and Compound 2 in excipients suitable for topical application determined by HPLC (mean value of n = 2-3 (range)). TIFF0007813733000023.tif181139

[0237] In summary, various solvents and non-solvents for both Compound 1 and Compound 2 were identified, and pH was found to have no significant effect on the aqueous solubility of these compounds. Compound 2 generally exhibited higher solubility in most of the excipients tested compared to Compound 1. The only exceptions were IPP (0.141% w / w of Compound 1 vs. the BLOQ of Compound 2) and deionized water pH 7 (0.009% w / w of Compound 1 vs. the BLOQ of Compound 2).

[0238] Example 2 - Excipient Compatibility Based on the results of Example 1 and the forced degradation experiments, various excipients and binary systems were selected for short-term Compound 1 screening. For example, systems with and without BHT were evaluated to further confirm the antioxidant requirement. Additionally, due to the limited aqueous solubility of Compounds 1 and 2, binary systems consisting of PEG 400 and water were evaluated. These binary systems were also pH adjusted (pH 5, 6, and 7, reflecting a typical range for topical formulations) to determine any effect that pH may have on the stability of these compounds.

[0239] The excipients tested were PEG 400, Transcutol® P, 50:50 v / v ethanol:Transcutol® P, PEG 400 + 0.1% BHT, 80:20 v / v PEG 400:water, benzyl alcohol, Super Refined™ Arlasolve™ DMI (SR DMI), 80:20 v / v Transcutol® P:glycerol, 80:20 v / v Transcutol® P:glycerol + 0.1% BHT, 80:20 v / v Transcutol® P:propylene glycol, 80:20 v / v Transcutol® P:propylene glycol + 0.1% BHT, 80:20 v / v PEG 400:water + 0.1% BHT pH 5, and 80:20 v / v PEG 400:water + 0.1% BHT. pH 6, 80:20 v / v PEG 400:water + 0.1% BHT pH 5, 80:20 v / v Transcutol® P:isopropanol, 80:20 v / v Transcutol® P:isopropanol + 0.1% BHT. The percentage recovery and peak purity (% area) of Compound 1 and Compound 2 were assessed at T=0 and after 2 and 4 weeks of storage at 40 and 50°C. The results are summarized below. A decrease in peak purity of Compound 1, and a corresponding decrease in drug recovery, was observed in PEG 400 and 80:20 v / v PEG 400:water after 4 weeks at 50°C (91.33% area and 66.87% area for Compound 1 peak purity, respectively). A slight decrease in peak purity and drug recovery after storage at 50°C in PEG 400 was also observed for T-Compound 2 (96.58% area for Compound 2 peak purity). The inclusion of BHT was observed to improve the stability of both compounds in PEG 400, with no / slight decrease in peak purity and drug recovery of Compound 1 / Compound 2 reported for PEG 400 + 0.1% BHT. A gradual decrease in peak purity and recovery of compounds 1 and 2 was observed over the storage period of SR DMI (21.62% area for compound 1 and 36.35% area for compound 2 after 4 weeks at 50°C). The effect of pH on the stability of both T-Compound 1 and T-Compound 2 in an aqueous-based system containing PEG 400, water, and BHT was also evaluated, but no difference between the stability of the compounds over a 4-week storage period was observed (presumably due to the stabilizing effect of BHT). The peak purity of Compounds 1 and 2 remained consistent across the remaining excipients and binary systems tested over a T=4 week storage period, indicating their suitability for incorporation into drug-containing formulations. While slight variations in recovery values ​​were observed over the study period, it is important to note that the extraction procedure used was generic and therefore not optimized.

[0240] In summary, both Compound 1 and Compound 2 demonstrated chemical stability in the majority of excipients and binary systems tested, allowing for the identification of suitable excipients for incorporation into topical formulations and confirming the need for the inclusion of an antioxidant (such as BHT).

[0241] Example 3 - Solvent System (Saturated Solubility) To demonstrate the types of formulations that are feasible and to understand the achievable drug concentrations, the saturation solubilities of Compounds 1 and 2 were determined in solvent systems including aqueous gels (SSA1-SSA9), creams (SSC1-SSC2), non-aqueous gels (SSNA1-SSNA5), and PEG ointments (SSPO1-SSPO2, SSPO4). The compositions of the solvent systems are shown in Table 2.

[0242] Table 2. Composition (% w / w) of solvent systems developed for IRAK4 inhibitors TIFF0007813733000024.tif89147TIFF0007813733000025.tif89156

[0243] Aqueous gel solvent system Various aqueous gel solvent systems (SSA1–SSA5) were designed with different amounts of PEG 400 (32.90–69.90% w / w; solvent for the drug) and Transcutol P (0–45% w / w; solvent for the drug and penetration enhancer). Because Compound 1 and Compound 2 have limited or no solubility in water, low levels of water (10–20% w / w) were included in these solvent systems. All aqueous gel solvent systems contained BHT (an antioxidant to mitigate oxidative degradation as observed in previous experiments) and benzyl alcohol (a solvent for the drug and a preservative). Glycerol (a humectant) was additionally included in SSA4, and propylene glycol (an alternative penetration enhancer) was included in SSA5 and SSA6. The results can be summarized as follows:

[0244] Regarding Compound 1: The saturated solubility of compound 1 in aqueous solvent systems ranged from 0.14% w / w (SSA6; 10% water, 0% Transcutol P) to 0.38% w / w (SSA3; 10% water, 45% w / w Transcutol P). It was observed that the saturated solubility of compound 1 decreased with increasing water content (compare SSA3 and SSA9) and increased with increasing Transcutol P content (compare SSA1, SSA2, and SSA3). The saturated solubility of compound 1 in systems containing propylene glycol was observed to be in the range of 0.14% to 0.20% w / w.

[0245] Regarding compound 2: Across aqueous solvent systems, compound 2 showed higher solubility than compound 1, following a similar trend. Systems with low Transcutol P (SSA1-15%, SSA4-15%, and SSA6-0%) resulted in the lowest solubility of compound 2, at 0.34% w / w (SSA1) and 0.26% w / w (SSA4 and SSA6). · Inclusion of propylene glycol (SSA5 and SSA6) and glycerol (SAA4) at the expense of Transcutol P decreased solubility (as seen for compound 1).

[0246] Non-aqueous gel solvent system Various non-aqueous gel solvent systems (SSNA1-SSNA5) were designed with different amounts of PEG 400 (54.90-69.90% w / w; solvent for the drug) and Transcutol P (0-45% w / w; solvent for the drug and penetration enhancer). All non-aqueous gel solvent systems contained BHT (an antioxidant to mitigate oxidative degradation as observed in previous experiments). Benzyl alcohol (solvent for the drug and preservative) was also included in SSNA3, glycerol (a humectant) was included in SSNA2-SSNA4, and propylene glycol (an alternative penetration enhancer) was included in SSNA3. The results can be summarized as follows:

[0247] Regarding Compound 1: The saturated solubility of compound 1 in non-aqueous solvent systems ranged from 0.13% w / w (SSNA3) to 0.24% w / w (SSNA1). Glycerol was included in both SSNA2 and SSNA3, and propylene glycol was included in SSNA3 at the expense of Transcutol P, which resulted in lower solubility of Compound 1.

[0248] Regarding compound 2: The saturated solubility of compound 2 in non-aqueous systems was observed to be much greater than that of compound 1. The solubilities ranged from 3.39% w / w (SSNA3) to 5.26% w / w (SSNA1). Similar to the solubility pattern of compound 1 in non-aqueous solvent systems, a similar trend was observed for compound 2. The introduction of propylene glycol and glycerol at the expense of Transcutol P had a negative effect on solubility. The inclusion of ethanol increased the saturated solubility of compound 2 (SSNA1; 5.26% w / w) compared to a system without ethanol but with higher levels of Transcutol P and lower levels of PEG 400 (SSNA5; 4.52% w / w).

[0249] Cream solvent-based Two solvent systems (SSC1-SSC2) suitable for use in emulsion-based cream formulations were designed, with and without Transcutol P and containing low amounts of water (25-30%). The solvent systems represent the aqueous phase of the emulsion, and therefore the components do not add up to 100%. The results can be summarized as follows: Low saturated solubilities of both Compound 1 and Compound 2 were observed in SSC1 and SSC2, i.e., 0.07-0.08% w / w for Compound 1 and 0.04% w / w for T-3774394. The inclusion of Transcutol P (SSC1) did not affect the solubility of Compound 1 and Compound 2, and both the SSC1 and SSC2 solvent systems analyzed showed nearly identical results. SSC2 contained a higher PEG 400 level (solvent for the drug) and a lower water level (non-solvent for the drug).

[0250] PEG ointment solvent system PEG ointment solvent systems (SSPO1-SSPO2 and SSPO4) were designed with different amounts of PEG 400 (52.90-59.90% w / w; solvent for the drug) and Transcutol P (0-15% w / w; solvent for the drug and penetration enhancer). Propylene glycol (an alternative penetration enhancer) was included in SSPO4. A 10% level of water was included in SSPO2 and SSPO4, while no water was included in SSPO1. The results can be summarized as follows:

[0251] Although the saturated solubility of Compound 2 was found to be low (less than 0.3% w / w) in PEG ointment solvent systems containing either water and / or propylene glycol, Compound 2 was found to be highly soluble (5.08% w / w) in the PEG ointment solvent system (SSPO1).

[0252] Table 3. Saturation solubility (% w / w) of Compound 1 and Compound 2 in solvent systems as determined by HPLC. TIFF0007813733000026.tif216128

[0253] Example 4 - Short-term stability of solvent systems The short-term stability (where feasible, concentrations reflecting the maximum excipient to drug ratio (worst case) rather than the maximum solubility level) of six solvent systems (SSA1, SSA2, SSA3, SSC1, SSNA1, and SSPO1) containing 0.1% w / w Compound 1 and Compound 2 was determined, and the content and purity of Compound 1 and Compound 2 was assessed at T=0, and after T=2 and 4 weeks of storage at 40 and 50°C. The results can be summarized as follows:

[0254] For Compound 1: At T=0, peak purities of 99.94-99.95% area were reported for Compound 1 in all solvent systems evaluated. By the end of the stability testing period, peak purity for Compound 1 remained consistent with T=0, with the highest, albeit still minimal, peak purity reductions (approximately 1% area) reported for SSNA1 and SSPO1 after 4 weeks of storage at 50°C. The consistent peak purities indicate that the Compound 1 solvent systems were chemically stable over the evaluated period. Minor variations in Compound 1 recovery (95.95-98.67%) were observed throughout the testing period, which is likely related to a non-optimized extraction procedure.

[0255] For Compound 2: At T=0, peak purities of 99.88-99.92% area were reported for Compound 2 in all solvent systems evaluated. After 4 weeks of storage, no significant deviations from the T=0 results were observed, and minimal Compound 2 peak purity loss (approximately 1% area) was reported at 50 °C for SSC1, confirming the chemical stability of the Compound 2 solvent systems over the evaluation period. For Compound 1, minimal variation in Compound 2 recovery (98.38-101.78%) was observed.

[0256] Example 5 - Additional Formulations A further selection of formulation types (aqueous and non-aqueous gels, creams, and PEG ointments) were prepared. All formulations contained Compound 1 or Compound 2 at 80% saturated solubility in the relevant solvent system. Aqueous gel and cream formulations were the primary focus for Compound 1 (shown in Table 4), and non-aqueous formulations were the primary focus for Compound 2 (shown in Table 5).

[0257] Table 4. Composition of Compound 1 aqueous gel and cream formulations (% w / w) TIFF0007813733000027.tif147134

[0258] Table 5. Compositions (% w / w) of Active Compound 2 cream, non-aqueous gel, and aqueous gel formulations TIFF0007813733000028.tif174147

[0259] The formulations were subjected to macroscopic and accelerated stability evaluation (centrifugation at high speed until phase separation was observed), and the results can be summarized as follows:

[0260] Aqueous gel formulation (compound 1) Aqueous gel formulations were then based on solvent systems with the highest saturated solubility of Compound 1 and containing 25-45% Transcutol P (SSA2, SSA3, and SSA9). The following polymers were investigated at a 1% level: Carbopol 980 NF and Carbopol 974 NF. Development activities are summarized below. All active aqueous gels (AG1–AG6) were observed to be injectable with low to medium viscosity, thus suggesting that the type of polymer (at the 1.0% level) did not make a significant difference in the visual viscosity of the gels. The gels containing Carbopol 980 NF (AG1, AG3, and AG5) appeared clear, whereas the gels containing Carbopol 974 NF (AG2, AG4, and AG6) appeared slightly cloudy. Aqueous gel formulations were successfully developed with Compound 1 concentrations ranging from 0.23% w / w to 0.30% w / w.

[0261] Cream formulation (Compound 1 and Compound 2) Cream formulations for both Compound 1 and Compound 2 utilized two previously evaluated cream solvent systems (SSC1 and SSC2) and different oil phases (cetyl alcohol, liquid paraffin, Brij S2, and Brij S20 in CR3; stearic acid, Cetomacrogol 1000, Span 60, and diamethicone 350 CST in CR4). Low concentrations of both Compound 1 and Compound 2 (up to 0.06% w / w) were achievable in the cream formulations, while development work demonstrated indications of formulation stability and desirable aesthetic properties. Furthermore, the cream solvent system (SSC1) was observed to perform well in the sRICA efficacy assay (see Example 17 below, specifically for Compound 1). Results are summarized below. The active cream formulations of Compound 1 (CR3 and CR4) were non-pourable, viscous, white in appearance, and smooth upon application. CR3 and CR4 were observed to phase separate after centrifugation for 8 and 10 minutes, respectively. Both active cream formulations of Compound 2 (CR3 and CR4) were non-pourable, viscous, white in appearance, and smooth upon application. No phase separation of CR3 and CR4 was observed after 10 minutes of centrifugation. The different compositions of the creams did not significantly affect the macroscopic characteristics of the creams. However, the choice of Compound 1 or Compound 2 did not affect the accelerated stability of the creams, and the cream formulation with Compound 2 appeared more stable under accelerated stability testing (centrifugation).

[0262] Non-aqueous gel formulation (compound 2) Active gel formulations were prepared using non-aqueous gel solvent systems containing 25-45% Transcutol P, which had the highest saturated solubility of Compound 2 (SSNA1, SSNA4, and SSNA5). HPC-HF, a cellulose-based polymer, was used as the gelling agent (at a level of 1%). The results are summarized below. All active non-aqueous gel formulations of Compound 2 (NAG1, NAG3, and NAG4) were injectable, clear, and had the inherent slightly sticky feel of HPC, with NAG1 appearing more viscous than NAG3 / 4. The viscosity of the non-aqueous gel is an inherent feature of the gelling agent (HPC-HF) used in these formulations. Non-aqueous gel formulations were successfully developed with compound 2 concentrations ranging from 3.62% w / w to 4.20% w / w.

[0263] PEG ointment formulation (compound 2) PEG ointment formulations were prepared for Compound 2 using three previously evaluated PEG ointment solvent systems, namely, SSPO1, SSPO2, and SSPO4. Different high molecular weight PEGs were evaluated; PO1 and PO4 formulations contained PEG 3550, while PO2 and PO4 formulations contained PEG 4000. To improve the cosmetic properties of the developed formulations, dimethicone 350 cst (a skin conditioner) was additionally included in PO2. The results are summarized below. All active PEG ointment formulations of compound 2 (PO1–PO4) exhibited the same physical characteristics: off-white, opaque, and viscous, suggesting that the different compositions (different solvent systems and polymeric PEG) did not significantly affect the macroscopic characteristics of the ointments. No phase separation was observed for any of the ointments after 16 minutes of centrifugation. The major difference between the developed ointments was that the anhydrous SSPO1-based formulations (PO1 and PO2) had a Compound 2 loading of 4.06% w / w, while the aqueous SSPO2 (PO3) and SSPO4 (PO4)-based formulations had API loadings of 0.23% w / w and 0.16% w / w, respectively.

[0264] Example 6 - Additional excipients and solvent systems The saturation solubility of both Compound 1 and Compound 2 was evaluated in 16 additional excipients / systems suitable for topical application, and the results are shown in Table 6 below.

[0265] (Table 6) TIFF0007813733000029.tif19690

[0266] These data are summarized below. Compound 1 was found to be relatively insoluble across all excipients evaluated with the highest saturated solubility observed for Labrasol (a surfactant) at 0.099% w / w. Numerous excipients (dimethicone 350 cst and 20 cst, octyldodecanol, Crodamol GTCC, rinse water, Myrj S40 0.6% w / v in water, Tween 80 5% w / v in water, Brij S20 4% w / v in water, Brij L23 1% w / v in water, Poloxamer 407 1% w / v in water, Brij O10 1% w / v in water, and Cetomacrogol 1000 8% w / v in water) were identified as nonsolvents for Compound 2 (at or near the LOQ). Limited solubility of Compound 2 was reported for isostearic acid and hexylene glycol (greater than 0.098% w / w). In comparison, high saturated solubilities of Compound 2 were observed in Labrasol and dipropylene glycol (3.445% w / w and 1.287% w / w, respectively). The inclusion of various surfactants did not appear to increase the water solubility of any of the APIs.

[0267] Example 7 - Additional Solvent Systems The following additional solvent systems were prepared based on those described in the previous examples, with different levels and types of surfactants, penetration enhancers, and skin conditioners. The focus for Compound 1 was on aqueous systems (aqueous gels and creams) with lower drug loading, while the focus for Compound 2 was on anhydrous gel systems, as well as creams and ointments, allowing for higher drug loading. The compositions are shown in Table 7 below.

[0268] Table 7. Composition of additional solvent systems (% w / w) TIFF0007813733000030.tif135147TIFF0007813733000031.tif124128

[0269] The results of the saturation solubility studies of the formulations in Table 7 are summarized below.

[0270] Aqueous gel solvent system (A10-A14): Regarding Compound 1: The solubility of compound 1 decreased as the level of Transcutol P was reduced while maintaining a water content of 10% w / w (SSA10; 45% w / w - SSA11; 25% w / w). The inclusion of propylene glycol (SSA12), dipropylene glycol (SSA13), and PEG 300 (SSA14) while reducing the content of water and PEG 400 increased the solubility of compound 1. These three solvent systems yielded saturated solubilities of compound 1 ranging from 0.25% w / w to 0.30% w / w, which was slightly lower than both SSA10 (0.36% w / w) and SSA11 (0.31% w / w).

[0271] Regarding compound 2: Compound 2 showed slightly better solubility in these systems (SSA12, SSA13, and SSA14), resulting in solubilities of 0.68% w / w to 0.76% w / w.

[0272] In summary, the aqueous gel solvent systems of Table 7 followed similar trends as observed for the solvent systems prepared in previous examples, whereby relatively low solubilities were observed for both Compound 1 (up to 0.36% w / w) and Compound 2 (up to 0.76% w / w). As previously observed, the inclusion of water reduced the solubility of both APIs.

[0273] Non-aqueous gel solvent systems (SSNA6, SSNA7, SSNA9) The solubility of Compound 1 and Compound 2 in the non-aqueous compositions of Table 7 was also evaluated. SSNA6 and SSNA7 contained two different skin conditioners (glycerol and diisopropyl adipate), and SSNA9 contained a penetration enhancer (oleyl alcohol) while maintaining a Transcutol P level of 25% w / w. The results are summarized below. For Compound 1, as seen in the previous examples, the non-aqueous gel solvent systems were found to have low API solubility, 0.21% w / w (SSNA6) and 0.19% w / w (SSNA7). For Compound 2, as seen in the previous examples, the non-aqueous gel solvent system proved to have a higher API loading capacity than Compound 1. The solubility ranged from 2.63% w / w (SSNA9) to 4.24% w / w (SNA7). Inclusion of low MW PEG (300, included at the sponsor's request) in SSA14 did not appear to improve drug solubility.

[0274] These data show that non-aqueous gels can be formulated with either Compound 1 or Compound 2, although the systems evaluated had low API loadings for Compound 1 and higher loadings for Compound 2, depending on the target concentration.

[0275] Cream solvent system (SSC3, SSC4, SSC5, SSC6, SSC8) To mitigate chemical and physical stability issues (phase separation), a solvent system was designed using SSC1 as the base, with the water level maintained at 30% w / w. A solvent system containing 20% ​​w / w water and no benzyl alcohol was also evaluated (SSC8).

[0276] The results are summarized below. Various surfactants, Brij S20 (SSC3) and Tween 80 (SSC4), and the skin conditioner dimethicone 350 cst (SSC6), were included to assess their effect on the solubility of both Compound 1 and Compound 2. In all of these systems, Compound 1 resulted in a solubility of 0.15% w / w or less, and Compound 2 resulted in a solubility of 0.11% w / w or less (SSC3 and SSC8 only).

[0277] Evaluation of different excipient levels, as well as the inclusion of other excipients such as surfactants and skin conditioners, did not significantly affect the solubility of either Compound 1 or Compound 2.

[0278] Example 8 - Additional Solvent Systems A selection of formulation types (cream, PEG ointment, aqueous and non-aqueous gel) were prepared, with aqueous gel and cream formulations being the primary focus for Compound 1 (shown in Table 8, 45), and non-aqueous formulations being the focus for Compound 2 (shown in Table 9, 46).

[0279] Table 8. Composition of additional solvent systems for Compound 1 (% w / w) TIFF0007813733000032.tif150156

[0280] Table 9. Composition of additional solvent systems for Compound 2 (% w / w) TIFF0007813733000033.tif137128

[0281] Aqueous gel formulation Aqueous gels were prepared with 1% w / w of gelling agent (Carbopol 980NF). A single formulation (AG10) containing 0.75% w / w of Carbopol 980NF was also prepared.

[0282] Compound 1: AG1, AG9, AG10, and AG11 all incorporated BHT because the antioxidant was shown to increase the stability of the API in this excipient during pre-formulation studies. Benzyl alcohol was included in only two of the formulations (AG1 and AG11). Formulations were designed maintaining a water level of 10% w / w for AG1, AG7, AG8, and AG11, and then the water content was reduced to 5% w / w in both AG9 and AG10 to assess the impact on drug solubility and formulation physical stability.

[0283] Aqueous gel formulations were successfully prepared with the desired organoleptic properties (low viscosity). These formulations were evaluated for short-term stability as described below.

[0284] Non-aqueous gel formulation A series of non-aqueous gel formulations were designed containing various additional components, a summary of which is provided below. Similar to the non-aqueous gel formulations of the previous examples, HPC-HF was again used in these formulations at 1% w / w. NAG3 and 5 were designed to evaluate the antioxidant BHT and the humectant glycerol. NAG6 replaced glycerol with dipropylene glycol, and NAG7 contained benzyl alcohol, BHT, and propylene glycol.

[0285] Non-aqueous gels were prepared using the solvent systems with the highest API loadings for both Compound 1 and Compound 2 and evaluated for short-term stability (see below).

[0286] Cream formulation A single cream formulation based on the SSC8 solvent system was prepared to evaluate the surfactants evaluated in the previous example. This cream formulation was prepared with both Compound 1 and Compound 2 and evaluated for short-term stability as discussed below.

[0287] PEG ointment preparation A single ointment formulation (PO5) containing PEG 3350 and IPM (isopropyl myristate; a skin conditioner and penetration enhancer) was prepared using the solvent system SSPO1. This formulation evaluated the addition of lower molecular weight PEG 3350. PEG 400 had previously been prepared in formulation PO2 along with IPM and SSPO1 (Table 2). This PEG ointment formulation was prepared with both Compound 1 and Compound 2 and evaluated for short-term stability as discussed below.

[0288] Example 9 - Short-term stability of additional solvent systems The short-term stability of the formulations prepared in Example 8 was determined and both the active and placebo formulations were evaluated at T=0, T=2 weeks, and T=4 weeks (at 25°C and 40°C) for the following parameters: API content and purity (Section 8.6.1), · Macroscopic observation (Section 8.6.2), Microscopy (Section 8.6.3), · Apparent pH (Section 8.6.4).

[0289] Aliquots of all formulations were also used in the sRICA efficacy evaluation discussed in Example 17 below.

[0290] The content and purity of both Compound 1 and Compound 2 formulations in Tables 8 and 9 are summarized below in Tables 10-13.

[0291] Table 10: Percent recovery of Compound 1 at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C TIFF0007813733000034.tif85147

[0292] Table 11: Percent recovery of Compound 2 at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C TIFF0007813733000035.tif61151

[0293] Table 12: Peak purity percentage (% area) of Compound 1 at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C TIFF0007813733000036.tif71150 * A putative contamination peak at TR 12.3 min (0.79% a / a) was detected in only n = 1 replicate. ** A putative contamination peak at TR 24.5 min (approximately 4.50–4.90% a / a) was detected in n = 3 replicates throughout the stability testing period.

[0294] Table 13: Peak purity percentage (% area) of Compound 2 at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C TIFF0007813733000037.tif57151

[0295] The results can be summarized as follows:

[0296] Regarding Compound 1: For all formulations, the recoveries observed during the 4-week stability study did not deviate by more than 3% from the T=0 results. At T=0, the percentage recovery of T-compound 1 in all formulations was 97%-103%; after 4 weeks at 40°C, the percentage recovery remained consistent in the range of 96%-105%, with no significant decrease in recovery observed. No significant changes in recovery were observed, although a slight trend toward a decrease in recovery was observed for all formulations containing Compound 1. The largest change in recovery was observed for AG11, with a 2.48% decrease between T = 0 (99.86%) and T = 4 weeks (40°C; 97.38%). Note that for CR5, slight variations in the percentage recovery of compound 1 were observed, but no consistent trend was observed. The recovery at T=0 was 102.39%, while at T=4 weeks, 40°C, the recovery increased to 104.45%. A plausible explanation for this is the variation in recovery efficiency from the more complex matrix system (emulsion), leading to more variable data. Peak purity remained fairly consistent over the 4-week stability study for all formulations at all conditions. For AG7, there was a very slight decrease after storage at 40°C for T=4 weeks, with purity dropping from 99.93% area to 99.50% area. Note that for NAG3 and PO5, purity of approximately 95% area was observed at each time point (including T=0), suggesting sample contamination (no significant change in the area of ​​the contaminating peak was observed over the stability study period at both storage conditions).

[0297] Regarding compound 2: Formulations containing Compound 2 were observed to have more variable recovery percentages compared to Compound 1 formulation (CR5), which had a maximum change of 7.84% between T=0 and T=4 weeks at 40°C. At T=0, the percentage recovery of compound 2 in all formulations was between 97% and 103%, and after 4 weeks at 40°C, the percentage recovery ranged from 96% to 106%. A decreasing trend in recovery was observed for all formulations except CR5, with recovery declining by an average of 3.5% at the end of the 4-week period. However, there was no clear effect of temperature, suggesting that such differences could be due to analytical variation. Recovery rates proved to be slightly variable, but the purity of compound 2 remained consistent throughout the 4-week period across all conditions for all formulations.

[0298] These data suggest that chemical stability of both Compound 1 and Compound 2 was achieved at 25 and 40°C in multiple formulations where purity remained consistent. The inclusion of BHT in the formulation did not significantly affect the recovery or purity of either API over the course of the stability evaluation. For example, both NAG3 (with BHT) and NAG5 (without BHT) had very similar recovery and purity at the end of 4 weeks at 40°C (NAG3 - recovery: 97.98% a / a, purity: 99.78%; NAG5 - recovery: 97.20% a / a, purity: 99.82%).

[0299] Example 10 - Macroscopic and Microscopic Observations of Compound 1 and Compound 2 in Formulations of Tables 8 and 9 Macroscopic observations of the Compound 1 and Compound 2 formulations in Tables 8 and 9 are summarized in Tables 14 and 15.

[0300] Table 14. Macroscopic appearance of placebo and Active Compound 1 formulations at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C. TIFF0007813733000038.tif159155

[0301] Table 15. Macroscopic appearance of placebo and Active Compound 1 formulations at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C. TIFF0007813733000039.tif126128

[0302] The results can be summarized as follows: Aqueous gel formulations containing Compound 1 (active and placebo) were observed to be clear, colorless, low-viscosity, pourable gels at T=0, which were maintained throughout the 4-week stability study at both 25°C and 40°C. While exhibiting most of the macroscopic properties as the other aqueous gel formulations, AG11 was observed to be turbid from T=0 throughout the stability study. The non-aqueous placebo formulation was observed to be clear, colorless, pourable, and of medium viscosity, with a characteristic stringy appearance typically observed for the HPC gel at T=0, which was maintained throughout the 4-week stability study at both 25°C and 40°C. A non-aqueous active formulation containing Compound 1 was observed to be a clear, colorless, non-pourable, stringy, high viscosity gel at T=0. However, after 2 and 4 weeks at 40°C, the viscosity was observed to be medium rather than the high viscosity observed at T=0. The non-aqueous active formulations containing Compound 2 were observed to be clear, pale yellow, pourable, medium viscosity, and stringy at T=0, which was maintained throughout all subsequent time points for NAGs 3, 5, and 6. However, the viscosity of NAG 7 was observed to be higher after 2 and 4 weeks of storage at 40°C. The PO5 formulations (active and placebo) for each of Compound 1 and Compound 2 were observed to be white, opaque, smooth, non-pourable ointments at T=0, which remained so throughout the 4-week stability study at both 25°C and 40°C. The CR5 formulations (active and placebo) for each of Compound 1 and Compound 2 were observed to be off-white, opaque, smooth, non-pourable, and highly viscous creams at T=0, which remained consistent throughout the 4-week stability study at both 25°C and 40°C.

[0303] It should also be noted that the viscosity measurements were performed visually based on the pourability of the formulation, which is itself a subjective measurement of viscosity. However, the results do not suggest that the formulation appears physically stable.

[0304] Microscopic observation Microscopic observations of Compound 1 and Compound 2 formulations in Tables 8 and 9 are summarized below. Aqueous gel formulations containing Compound 1 (active and placebo) were observed to be free of API crystals at T=0, which remained true throughout the 4-week stability study at both 25°C and 40°C. However, AG11 (active and placebo) was observed to have extensive droplets at T=0, which were observed at all subsequent time points, and such droplets were attributed to dimethicone present in the AG11 formulation. The non-aqueous formulations (active and placebo) for both Compound 1 and Compound 2 were observed to be free of API crystals at all time points throughout the stability study. For the PO5 formulations (both Compound 1 and Compound 2), no API crystals were observed at any time point, but PEG crystals (typical of this type of formulation) were observed from T=0 throughout the stability study. The CR5 formulations for both Compound 1 and Compound 2 were also observed to be free of API crystals throughout the stability study, although medium / irregular sized droplets typical of this type of cream formulation were observed from T=0. After 4 weeks of storage at 40°C, excipient crystals were observed in both the active and placebo prototypes, which were attributed to stearic acid (from cetostearyl alcohol). These crystals often appear during the rapid cooling of the oil phase during manufacturing.

[0305] These data suggest that physical stability of both Compound 1 and Compound 2 was achieved in the formulations tested.

[0306] Example 11 - Apparent pH of Compound 1 and Compound 2 in the formulations of Tables 8 and 9 Apparent pH was evaluated for aqueous gel formulations containing Compound 1. For all formulations at T=0, both the active and placebo prototypes were within 0.5 pH units of each other, which remained consistent throughout. The pH of the placebo formulations ranged from pH 5.9 to pH 6.05 at T=0 and from pH 5.83 to pH 6.17 after 4 weeks of storage at 40°C. A similar trend was observed for the active formulations; at T=0, the pH ranged from pH 5.86 to pH 6.17, and at T=4 weeks (40°C), the pH ranged from pH 5.83 to pH 6.20. Overall, there was a slight downward trend in pH decrease over the 4-week stability study for both the active and placebo AG1, 7, and 8 formulations, while AG9, 10, and 11 formulations all exhibited consistent pH throughout the 4-week stability study.

[0307] Example 12 - Additional Solvent Systems The following additional solvent systems were also prepared that can be utilized in various formulation types (Table 16).

[0308] (Table 16) TIFF0007813733000040.tif60145

[0309] Saturation solubility experiments were performed on both Compound 1 and Compound 2.

[0310] Aqueous gel solvent system The effects of different preservatives, benzalkonium chloride, benzyl alcohol, and phenoxyethanol, were evaluated in SSA15, SSA16, and SSA17, respectively. To mitigate the greasy feel of the aqueous gels (caused by high PEG 400 content), the inclusion of glycerol to reduce the PEG 400 content was evaluated in SSAG16 and SSAG21. Glycerol was also included in SSAG17 and SSAG20 in place of Transcutol P. The water content was maintained at 10% w / w to maintain a balance between API solubility and the required aesthetic properties of the gel, allowing for the inclusion of polymers other than HPC (necessary to maintain physical stability in non-aqueous gel systems).

[0311] The saturated solubility of Compound 1 in aqueous gel solvent systems was evaluated, and a similar trend to previous formulations was observed. Solubilities ranged from 0.09% (SSAG21) to 0.36% (SSAG15). As expected, systems with high Transcutol P content and / or no glycerol yielded the highest solubility of Compound 1.

[0312] Systems 15, 18, and 19, which did not contain glycerol but contained a wide range of levels of Transcutol P, water, and PEG 400, all yielded solubility levels of 0.36%, 0.35%, and 0.31%, respectively. Glycerol was included to improve the aesthetic properties of the gel, but was observed to have a negative effect on the solubility of Compound 1, with the glycerol-containing system having a maximum solubility of 0.26%.

[0313] Non-aqueous gel solvent system The solubility of both Compound 1 and Compound 2 was evaluated in a non-aqueous gel solvent system. The inclusion of IPM was evaluated in SSNA10 to assess its impact on formulation aesthetics and its potential for incorporation into the formulation as a penetration enhancer. Glycerol and propylene glycol, both at 20% w / w, were included in SSNA12, while the PEG 400 content was reduced to approximately 15%. Diisopropyl adipate was also included in the non-aqueous gel as a skin conditioner and potential penetration enhancer to determine its impact on physical stability and drug solubility.

[0314] As expected, the solubility of Compound 1 remained low in non-aqueous gel solvent systems, with a maximum solubility of 0.19% observed in SSNA10, consistent with that observed in previous examples.

[0315] Previously, good solubility (approximately 2–5%) of compound 2 in non-aqueous gel solvent systems was observed, but the inclusion of diisopropyl adipate significantly reduced drug solubility to 0.60–0.78% w / w for both SSNA11 and SSNA12, suggesting that the addition of diisopropyl adipate in SSNA11 and diisopropyl adipate / propylene glycol / glycerol in SSNA12 significantly affected the solubility of T-3774394.

[0316] Cream solvent-based The solubility of both Compound 1 and Compound 2 was evaluated in a cream solvent system. Both SSCs 9 and 11 contained 20% w / w glycerol to improve the aesthetic properties of the resulting cream. The inclusion of the preservatives benzyl alcohol or phenoxyethanol as preservative systems was evaluated in SSCs 9 and 11, respectively. The same trend of drug solubility in the cream systems was observed, with low solubility evident for both Compound 1 and Compound 2 in the cream solvent system. The inclusion of glycerol also had a detrimental effect on the solubility of both APIs, with values ​​of 0.07% or less observed.

[0317] Example 13 - Further formulations Table 17 shows the compositions of AG11 and NAG6, which were used as base and additional placebo formulations to evaluate various factors leading to improved stability, aesthetic quality, and optimization of excipient levels. The formulations are shown in Table 18.

[0318] Table 17: Theoretical composition (% w / w) of active formulations containing Compound 1 and Compound 2 Cream formulations (Compound 1 and Compound 2) TIFF0007813733000041.tif135128

[0319] Table 18. Theoretical composition of placebo aqueous gel formulations (% w / w) TIFF0007813733000042.tif58136TIFF0007813733000043.tif56128

[0320] Aqueous gel formulation Utilizing AG11 as the base for all aqueous gel formulations, the following modifications were made and evaluated:

[0321] Utilizing SSA3 / AG11 as the substrate, the turbidity of AG11 was investigated and various approaches were evaluated as follows (Table 61).

[0322] To reduce the turbidity of the aqueous gel, the dimethicone 350 content was reduced to 0.5% in AG12, but the formulation remained cloudy. To reduce the turbidity, the manufacturing process was modified in AG13. The order in which the excipients were initially combined in AG11 was changed to the following:

[0323] 1. Dimethicone 350 + PEG 400 + TransP resulted in a cloudy gel with oily droplets.

[0324] 2. Dimethicone + TransP + PEG 400 resulted in a less turbid gel, but the gel remained cloudy.

[0325] The inclusion of a surfactant to reduce turbidity was evaluated in AG15, which contained Etocas 35 with dimethicone 350, but the gel remained cloudy. The inclusion of cyclomethicone 5-NF instead of dimethicone was evaluated in AG16, but this had no beneficial effect on gel turbidity, as the gel remained cloudy.

[0326] Utilizing SSA18 and SSA19 as solvent-based bases, different gelling agents were evaluated and the turbidity and viscosity of the resulting formulations were assessed (Table 61).

[0327] Diisopropyl adipate and Carbopol 980NF (1% w / w) were added to SSA18, resulting in formulation AG17, which had a low viscosity (injectable), was slightly cloudy, and appeared slightly oily. Diisopropyl adipate and HPC-JF (1% w / w) were added to SSA18, resulting in formulation AG18, which had a very low viscosity (easily pourable) and appeared clear. Diisopropyl adipate and Sapineo 600 (2.5% w / w) were added to SSA18, resulting in formulation AG19, which had a very low viscosity (easily pourable) and appeared cloudy. AG17 was then reconstituted, including a pH adjustment step (target pH 6-6.5), resulting in a clear, medium-viscosity gel (AG20). AG18 was redeveloped twice, increasing the HPC-JF content to 2% w / w and then 4% w / w, to produce more viscous gels (AG21 and AG23). However, while both formulations remained clear, they were still observed to have low viscosity. AG19 was redeveloped by increasing the Sapineo 600 content from 2.5% w / w to 4.5% w / w, but the resulting formulation (AG22) remained low viscosity and cloudy. HPC-HF and HPC-MF were evaluated in AG24 and AG25, respectively, and both resulting formulations were observed to be colorless, slightly cloudy, and of medium viscosity (injectable). SSA19 was also evaluated in combination with three gelling agents: HPC-HF, HPC-JF, and HPC-MF, yielding AG26, AG27, and AG28, respectively. AG26 and AG28 were colorless, slightly cloudy, and highly viscous (not pourable). On the other hand, AG27 was clear, colorless, and had a low viscosity (pourable).

[0328] Non-aqueous gel formulation Based on NAG6, non-aqueous gel formulations were designed to evaluate the inclusion of different gelling agents, IPM, glycerol, and propylene glycol. The compositions of the non-aqueous gel formulations are detailed in Table 19.

[0329] Table 19. Theoretical composition of placebo non-aqueous gel formulations (% w / w) TIFF0007813733000044.tif54146

[0330] Both NAG8 and NAG10 incorporated an alternative gelling agent, HPC-JF, at 1% and 4% w / w, respectively. At 1% w / w HPC-JF, the formulation remained clear and was observed to have a very low (injectable) viscosity. At 4% w / w, the formulation remained clear but was observed to have a medium (injectable) viscosity.

[0331] Both NAG9 and NAG11 contained diisopropyl adipate (a skin conditioner) and reduced Transcutol P content, but the gelling agents used were different: HPC-JF was used in NAG9 and HPC-HF in NAG11. NAG9 was observed to be clear and very low viscosity (injectable), while NAG11 was observed to be colorless, slightly turbid, and of medium viscosity (injectable).

[0332] NAG12 was designed to contain the skin conditioners diisopropyl adipate and glycerol, and the penetration enhancer propylene glycol. NAG12 also contained HPC-JF at 2.5% w / w, which resulted in a clear, low-viscosity (injectable gel).

[0333] NAG13 contains the skin conditioner IPM instead of IPP, and it was initially observed that formulations containing IPP were oily, a trait undesired by the sponsor. Therefore, IPM was incorporated into the formulation, which resulted in a colorless, slightly cloudy, medium viscosity (pourable) gel, but was observed to be slightly oily.

[0334] Cream formulation In addition to the aqueous and non-aqueous gels developed, cream formulations were evaluated. CR5 (SSC8) was utilized as the starting point for the development of the creams discussed below. The compositions of the cream formulations evaluated are detailed in Table 20 below.

[0335] Table 20. Theoretical composition of placebo cream formulation (% w / w) TIFF0007813733000045.tif73147TIFF0007813733000046.tif88149

[0336] CR6 and CR7, both based on SSC9, contain a different oil phase from the original CR5, and CR7 also contains the skin conditioning agent dimethicone 350. Both formulations were observed to be white in appearance and medium-viscosity (non-pourable) creams, which phase-separated after 2 minutes of centrifugation. However, it should be noted that CR7 was noticeably more viscous than CR6.

[0337] CR8, CR9, and CR10 were all based on CR5; CR8 was developed with a 15% oil phase (initially 20%), CR9 was developed with diisopropyl adipate instead of GTCC, and CR10 was developed with equal amounts of diisopropyl adipate and GTCC. All three formulations were observed to have the same macroscopic properties: off-white color, thick cream, and slightly greasy. The formulations differed during accelerated stability via centrifugation; CR8 and CR10 (both containing GTCC) experienced phase separation after 20 and 18 minutes, respectively, while CR9 phase separated after 2 minutes of centrifugation.

[0338] CR11, CR12, CR13, and CR14 all used the same aqueous phase but had different oil phase compositions compared to CR5. Both CR11 and CR12 contained IPM, Span 60, and Tween 80, with diisopropyl adipate also present in CR11. CR13 contained 13% w / w GTCC compared to the 10% found in CR5, and CR14 contained cyclomethicone-5NF. All four formulations were observed to be off-white and slightly greasy in appearance. CR14 was the only formulation observed to be of medium viscosity; all others were of high viscosity. During accelerated stability, all four formulations phase separated, with those containing higher GTCC content able to withstand longer centrifugation periods before phase separation.

[0339] Example 14 - Short-term formulation stability The formulations shown in Tables 64 and 65 were prepared and their short-term stability was evaluated.

[0340] Formulations of Compound 1 (shown in Table 21) were: AG1 (previously evaluated), AG11 (similar to AG1 but containing dimethicone 350), AG20 / 23 (based on SSA18 and containing a different gelling agent), AG29 (based on SSA19 with reduced levels of Transcutol P), NAG6 (based on SSNA7 with reduced levels of Transcutol P), and CR8 / 14 (each based on SSC8, with a reduced oil phase and containing cyclomethicone).

[0341] The following non-aqueous gels were selected for Compound 2 (shown in Table 22): NAG6 (the same formulation with reduced drug levels, as well as previously evaluated: 0.5% w / w Compound 2), NAG10 (similar to NAG6 but containing an alternative gelling agent), and NAG14 (based on SSNA12 containing glycerol and propylene glycol), AG11 (based on SSA3), CR8 (reduced amount of oil phase), and CR14 (containing cyclomethicone) were also selected for Compound 2.

[0342] Table 21: Theoretical composition of active formulations containing Compound 1 (% w / w) TIFF0007813733000047.tif84150

[0343] Table 22: Theoretical composition of active formulations containing Compound 2 (% w / w) TIFF0007813733000048.tif85145

[0344] The contents and purities of Compound 1 and Compound 2 in the preparations in Tables 64 and 65 are shown in Tables 23 to 25.

[0345] Table 23: Percent recovery of Compound 1, expressed as a percentage of the theoretical concentration in Compound 1 active formulations, at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C. TIFF0007813733000049.tif67143

[0346] Table 24: Percent recovery of Compound 2, expressed as a percentage of the theoretical concentration in the Compound 2 active formulation, at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C. TIFF0007813733000050.tif59144

[0347] Table 25. Peak Purity Percentage (% Area) of Compound 2 in Developed Compound 2 Active Formulations at T=0 and After 2 and 4 Weeks of Storage at 25°C and 40°C TIFF0007813733000051.tif66142 * An impurity peak at TR 12.33 min (0.79% a / a) was detected in only n=1 replicate. ** An impurity peak at TR approximately 12.10–12.21 min was detected in only one of the replicates. *** An impurity peak at TR 14.96 min (0.17% a / a) was detected in only n=1 replicate. *** An impurity peak at TR 12.20 min (0.36% a / a) was detected in only n=3 replicates.

[0348] Table 26: Peak Purity Percentage (%a / a) of Compound 2 in Developed Compound 2 Active Formulations at T=0 and After 2 and 4 Weeks of Storage at 25°C and 40°C TIFF0007813733000052.tif59141 * An impurity peak at TR approximately 12.10–12.21 min was detected in only one of the replicates. ** An impurity peak at TR 12.22 min (0.16% a / a) was detected in only n=2 replicates.

[0349] Compound 1 recovery (Table 23) remained fairly consistent throughout the 4-week stability study. Recovery at T=0 ranged from 98% to 106%, with higher recoveries observed in the cream formulations (CR8 - 101.71% and CR14 - 105.32%). As previously mentioned, this is likely due to less efficient recovery from the more complex matrix system (emulsion).

[0350] After the T=4-week time point, both aqueous and non-aqueous gel formulations maintained recoveries between 97% and 99%, although a slight trend toward decreased recovery was observed. Higher recovery variability was observed for the cream formulations. CR8 remained consistent (98-101%) through the 2-week time point and the 25°C / 4-week condition, but at the 40°C / 4-week condition, recovery was 108.72%. Similar variability was observed for the CR14 formulation; at the 40°C / 2-week condition, recovery was 109.40%, but at the 40°C / 4-week condition, recovery was 105.82%.

[0351] The recovery of Compound 2 followed the same trend as Compound 1, whereby the recovery remained fairly consistent throughout the 4-week stability period. At T=0, the recoveries of all formulations ranged from 98% to 109%, with higher recoveries observed for NAG6 (102.54%) and NAG14 (108.12%).

[0352] Although no major changes were observed, a slight trend toward decreased recovery was observed for all formulations by the end of the 4-week stability study, resulting in recoveries ranging from 96 to 107%. The purity of both Compound 1 (Table 68) and Compound 2 (Table 69) remained above 99.6% throughout the 4-week stability period, at all conditions for all formulations. No apparent decrease in purity was observed for either formulation under any of the conditions, consistent with that observed for similar formulations as discussed above.

[0353] Data generated during this study for Compound 1 highlighted that chemical stability was achieved for all formulations at 25°C and 40°C. While variable recovery was observed for the cream formulation, purity remained above 99% and no trend toward degradation was observed. Similar conclusions can be drawn for the Compound 2 formulation; although a slight downward trend and slight recovery variation were observed, purity remained consistent throughout, indicating that chemical stability of the drug was achieved.

[0354] Example 15 - Macroscopic Observations The macroscopic observations of the formulations (i.e., color, clarity, and visual viscosity) are detailed in Tables 27 and 28, and the results are summarized below.

[0355] Table 27. Macroscopic appearance of placebo and Active Compound 1 formulations at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C TIFF0007813733000053.tif70156TIFF0007813733000054.tif42155

[0356] Table 28. Macroscopic appearance of placebo and active compound 2 formulations at T=0 and after 2 and 4 weeks of storage at 25°C and 40°C TIFF0007813733000055.tif69156TIFF0007813733000056.tif41155

[0357] After 4 weeks of stability storage, the aqueous gel formulations for both Compound 1 and Compound 2 did not change from the characteristics observed at T=0. Regardless of the gelling agent used, all aqueous gel formulations were observed to have low viscosity. All aqueous gels were colorless and clear, except for AG11, which was observed to be cloudy. Both the active and placebo aqueous gel formulations were observed to be the same throughout the stability study.

[0358] The non-aqueous gel formulations followed the same trend as the aqueous gels, with no observable changes recorded after the initial T=0 results. The main notable observation was the difference in color between the active and placebo formulations for NAG6 and NAG10. The active versions were observed to have a light yellow color, while the associated placebo was colorless. Another characteristic that was consistent across both the active and placebo formulations, i.e., all non-aqueous gel formulations, was observed to be clear throughout the stability study. The cream formulation was observed to show the most significant change throughout the stability study.

[0359] The active and placebo formulations were observed to be identical throughout, and therefore any changes observed in the placebo formulation were also observed in the active counterpart. CR8 (for both Compound 1 and Compound 2) was observed to phase separate after 4 weeks of storage at 40°C. CR14 containing Compound 1 was observed to remain similar to the T=0 result, while CR14 containing Compound 2 was observed to increase in visual viscosity from low to medium. Phase separation at elevated temperatures is not uncommon in cream formulations, as higher temperatures can dissolve solid oil phase components, which in turn can change the physical characteristics of the formulation both before and after cooling.

[0360] It should also be noted that the viscosity measurements were performed visually based on the pourability of the formulation, which is itself a subjective measurement of viscosity. However, the results do not suggest that the formulation is physically stable.

[0361] Example 16 - Microscopy and Apparent pH Microscopic observations of formulations containing both Compound 1 and Compound 2 in Table 64 and subsequent formulations are discussed below.

[0362] The aqueous gel formulations were observed to have no API crystals present at T=0, which remained consistent throughout the 4-week stability study. AG11 was also observed to contain a wide range of small to medium-sized droplets, which was attributed to the presence of dimethicone in the formulation. The non-aqueous gel formulations remained fairly consistent throughout the stability study, with no API crystals observed in any formulation at any time or condition. However, NAG14 was observed to be inconsistently nearly free of large droplets; NAG14 contains DIPA (19%), which is lipophilic and may therefore have a tendency to form droplets.

[0363] As with the other formulation types, the cream formulations were not observed to contain any API crystals throughout the stability study. This was consistent across all time points and conditions for both Compound 1 and Compound 2. However, CR14 was observed to contain excipient crystals at 40°C, most likely due to cetostearyl alcohol, which has a tendency to crystallize upon cooling, i.e., during transfer from stability storage to ambient room temperature for analysis. In summary, no significant changes were observed in any formulation containing either Compound 1 or Compound 2, indicating that physical stability of the formulations was achieved.

[0364] Apparent pH Apparent pH was evaluated only for aqueous gel formulations containing Compound 1 and Compound 2. A slight trend in pH decrease was observed for all formulations (active and placebo) after 4 weeks of storage at both 25°C and 40°C. At t=0, pH varied between formulations; AG11 and AG20 both underwent pH adjustment to ensure proper hydration of Carbopol, resulting in a pH of approximately pH 6. On the other hand, AG23 and AG29 both used HPC and therefore their pH was not adjusted, resulting in a pH of approximately pH 8.

[0365] The active and placebo formulations differed slightly in pH, with the Compound 1 active formulation exhibiting a slightly lower pH value, while the Compound 2 active gel formulation was slightly higher than its placebo counterpart. The pH of all aqueous gel formulations underwent only negligible changes in pH throughout the 4-week stability study.

[0366] Example 17: Performance of Compound 1 and 2 Test Formulations in sRICA The anti-inflammatory activity of IRAK4 / TrkA inhibitors was determined in a skin-resident immune cell assay (sRICA). In this model, human surgical skin waste was cultured in a transwell system, with the dermis in contact with cell culture medium and the stratum corneum exposed to air. To perform the assay, each human skin sample was defatted and harvested at 750 μm. Next, 8 mm punch biopsies were obtained and placed in membrane transwells. Biopsies were prepared using a barrier ring to contain the formulation and prevent leakage. The transwells were inserted into culture wells containing complete medium, and a cocktail of cytokines and antibodies and / or inflammatory stimuli was added to promote polarization of skin-resident immune cells and / or induce specific inflammatory responses. Transwells were treated with LPS as a positive control, vehicle as a negative control, and various dual IRAK / TrkA inhibitors. TNFα protein expression was measured, and the average TNFα protein level in LPS-treated samples was set to 100%.

[0367] Compounds were formulated at 80% saturated solubility. 10 ul of the test solvent system or prototype formulation was applied to topically prepared sRICA samples and allowed to penetrate the skin overnight. LPS was added the following day, and medium was collected 48 hours after activation. N=6 per group. Statistical significance was determined using an unpaired, two-tailed Student's t-test.

[0368] The performance of two IRAK4 inhibitors in formulations representing a cream ("C" and "CR" formulations), an aqueous gel ("AG" formulation), a non-aqueous gel ("NAG" formulation), and an ointment ("PO" formulation) was evaluated in two rounds of sRICA. Tables 29 and 30 provide the compositions of the formulations evaluated in the first round, and Tables 31 and 32 provide the compositions of the formulations evaluated in the second round.

[0369] Table 29. Formulation compositions of aqueous and non-aqueous gel Compound 1 and 2 formulations at 80% saturation solubility determined in the corresponding solvent systems evaluated in the first round of sRICA. TIFF0007813733000057.tif68128

[0370] Table 30. Formulation composition of cream and ointment formulations evaluated in the first round of sRICA at 80% saturation solubility determined in the corresponding solvent system. TIFF0007813733000058.tif54128

[0371] Table 31. Formulation compositions of aqueous and non-aqueous gels at 80% saturation solubility determined in the corresponding solvent systems evaluated in the second round of sRICA. TIFF0007813733000059.tif67128

[0372] Table 32. Formulation compositions of creams and ointments evaluated in the second round of sRICA at 80% saturation solubility determined in the corresponding solvent systems. TIFF0007813733000060.tif65128

[0373] The combined results of these studies are shown in Figure 1 (for compound 1) and Figure 2 (for compound 2).

[0374] Regarding compound 1 (Figure 1): All Compound 1 formulations were prepared at 80% saturation (active formulation = blue bars, vehicle formulation = yellow bars). The combined results of six independent studies (six different skin donors) are shown. Each study was normalized to the % of maximum TNFα production (i.e., the mean TNFα concentration in LPS-activated skin alone was set at 100%), and all other values ​​(untreated, unactivated, and treated samples) were obtained as percentages of this. N = 9–18 per group. Formulated clobetasol (Dermovate) was utilized in these studies and served as a positive control for inhib...

Claims

1. A pharmaceutically effective amount of: 2-(2-((2,2-difluoroethyl)amino)pyridin-4-yl)-N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-1,3-oxazole-4-carboxamide, N-(3-((3S,4S)-4-hydroxy-3-methyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, 2-(2-((cyclopropylmethyl)amino)pyridin-4-yl)-N-(3-(3-(2-hydroxyethyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3,3-dimethyl-4-((methylamino)methyl)-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3-isopropyl-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((dimethylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(3-(2-hydroxypropyl)-2-oxoimidazolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, N-(3-(4-((cyclopropylamino)methyl)-3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-methyl-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide, and N-(3-(3,3-dimethyl-2-oxopyrrolidin-1-yl)-1-(oxetan-3-yl)-1H-pyrazol-4-yl)-2-(2-((2,2,2-trifluoroethyl)amino)pyridin-4-yl)-1,3-oxazole-4-carboxamide or a stereoisomer, tautomer, or pharmaceutically acceptable salt thereof; and a solvent system comprising one or more solvents; an antioxidant including butylated hydroxytoluene (BHT); Including, A topical composition, wherein the solvent system comprises diethylene glycol monoethyl ether (Transcutol® P) in an amount from 15% to 25% by weight of the composition, and PEG 400 in an amount from about 35% to about 70% by weight of the composition.

2. 10. The topical composition of claim 1, wherein the solvent system further comprises one or more solvents selected from ethanol, benzyl alcohol, glycerol, and propylene glycol.

3. 3. The topical composition of claim 1 or 2, wherein the solvent system comprises PEG 400 in an amount from about 35% to about 50% by weight of the composition, or from about 40% to about 45% by weight of the composition, or from about 55% to about 65% by weight of the composition, or about 40%, about 45%, about 50%, about 55%, or about 60% by weight of the composition.

4. 4. The topical composition of claim 1, wherein the solvent system comprises diethylene glycol monoethyl ether (Transcutol® P) in an amount of about 15%, about 20%, or about 25% by weight of the composition.

5. 5. The topical composition of claim 1, wherein the solvent system further comprises one or more preservatives, such as an alcohol having 2 to 10 carbon atoms, such as benzyl alcohol or phenoxyethanol.

6. 6. The topical composition of any one of claims 1 to 5, wherein the solvent system further comprises one or more preservatives in an amount from about 0.01% to about 20% by weight of the composition, or from about 0.1% to about 10% by weight of the composition, or from about 0.5% to about 5% by weight of the composition, or from about 1% to about 3% by weight of the composition, or about 2% by weight of the composition.

7. 7. The topical composition of any one of claims 1 to 6, wherein the solvent system is present in an amount from about 50% to about 90% by weight of the composition, or from about 75% to about 90% by weight of the composition, or from about 80% to about 90% by weight of the composition, or from about 85% to about 90% by weight of the composition, or from about 55% to about 65% by weight of the composition, or from about 55% to about 60% by weight of the composition.

8. 8. The topical composition according to any one of claims 1 to 7, wherein the antioxidant is present in an amount of about 0.001 wt. % to about 1 wt. %, such as about 0.01 wt. % to about 1 wt. %, such as about 0.2 wt. %, based on the total weight of the composition.

9. The topical composition of any one of claims 1 to 8, further comprising a non-solvent.

10. 10. The topical composition of claim 9, wherein the non-solvent is water, a silicone oil (e.g., dimethicone 350), or a mixture thereof.

11. 11. The topical composition of claim 10, wherein the water is present in an amount from about 5% to about 30% by weight of the composition, or from about 5% to about 15% by weight of the composition, or from about 15% to about 25% by weight of the composition, or about 10%, or about 15%, or about 20% by weight of the composition; and the silicone oil is Dimethicone 350 and is present in an amount from about 0.01% to about 2% by weight of the composition, or from about 0.1% to about 1.5% by weight of the composition, or from about 0.5% to about 1% by weight of the composition, or about 0.75% by weight of the composition.

12. 12. The topical composition of any one of claims 1 to 11, further comprising a polymeric gelling agent selected from one or both of crosslinked polyacrylic acid and non-ionic cellulose ethers, such as a Carbopol® polymer and hydroxypropyl cellulose, such as one or more of Carbopol® 980 NF and hydroxypropyl cellulose HF, wherein the gelling agent is present in an amount of from 0.01% to about 5% by weight of the composition, or from about 0.1% to about 3% by weight of the composition, or from about 0.5% to about 2% by weight of the composition, or from about 0.75% to about 1.25% by weight of the composition, or about 1% by weight of the composition.

13. 13. The topical composition of any one of claims 1 to 12, further comprising a skin conditioning agent, such as diisopropyl adipate or a silicone oil, such as dimethicone 350, wherein the skin conditioning agent is present in an amount of from 0.1% to about 15% by weight of the composition, or from about 0.1% to about 5% by weight of the composition, or from about 0.1% to about 2% by weight of the composition, or from about 5% to about 15% by weight of the composition, or about 1% by weight of the composition, or about 10% by weight of the composition.

14. 14. The topical composition of any one of claims 1 to 13, further comprising an emollient, for example, the emollient is a triglyceride, for example a medium chain triglyceride, for example Crodamol™ GTCC, in an amount of from 0.1% to about 15% by weight of the composition, or from about 0.1% to about 5% by weight of the composition, or from about 0.1% to about 2% by weight of the composition, or from about 5% to about 15% by weight of the composition, or about 1% by weight of the composition, or about 10% by weight of the composition.

15. For example, one or more C14-C30 fatty alcohols, celluloses, acrylate polymers or crosspolymers, or carbomers; for example, hydroxypropyl cellulose, hydroxymethyl cellulose, hydroxypropyl methyl cellulose (e.g., Benecel™ E4M), cetostearyl alcohol, poloxamer (Pluronic® PF127), carbomers (e.g., Carbomer® 980, Carbomer® 1342, and 15. The topical composition of any one of claims 1 to 14, further comprising a viscosity increasing agent selected from: hydroxypropyl cellulose (e.g., hydroxypropyl cellulose Klucel® EF, GF, MF, and / or HF having a molecular weight of 850,000 to 1,150,000 Daltons), Pluronic® PF 127, Carbomer® 980, and / or Carbomer® 1342 (Pemulen® TR-1, TR-2, and / or Carbopol® ETD 2020); for example, cetostearyl alcohol, wherein the viscosity increasing agent is present in an amount of from 0.1% to about 15% by weight of the composition, or from about 1% to about 10% by weight of the composition, or from about 3% to about 7% by weight of the composition, or about 5% by weight of the composition.

16. 16. The topical composition of any one of claims 1 to 15, further comprising a surfactant, for example, the surfactant is selected from one or more of polyoxyethylene fatty ethers; nonoxynol, polysorbate, polyoxyethylene alcohols, polyoxyethylene fatty acid esters, sodium lauryl sulfate, and sorbitan monostearate; for example, Brij™ S2 or Brij™ S 20, and the surfactant is present in an amount of 0.1% to about 15% by weight of the composition, or about 1% to about 5% by weight of the composition, or about 1%, about 2%, about 3%, about 4%, about 5%, about 7%, or about 10% by weight of the composition.

17. For example, C1-20 alkanols (e.g., oleyl alcohol, cetyl alcohol, octyldodecanol, cetostearyl alcohol, benzyl alcohol), saturated or unsaturated fatty acid esters, saturated or unsaturated fatty acid esters, polyoxyethylene fatty ethers, polyoxyethylene fatty acid esters, diethylene glycol monoethyl ether, 1,3-dimethyl-2-imidazolidinone, and / or dimethyl isosorbide; for example, oleyl alcohol, cetyl alcohol, octyldodecanol, cetostearyl alcohol, mineral oil, benzyl alcohol, isopropyl myristate, diisopropyl adipate, ethylhexyl hydroxystearate, steareth-2 (Brij™ S2), stearyl alcohol, hydroxypropyl methyl esters, methyl ...

17. The topical composition of any one of claims 1-16, further comprising an additional excipient selected from one or more of Areth-20 (Brij™ S20), glyceryl stearate, stearic acid, magnesium stearate, diethylene glycol monoethyl ether, 1,3-dimethyl-2-imidazolidinone, and / or dimethyl isosorbide; e.g., propylene glycol, oleyl alcohol, diisopropyl adipate, and isopropyl myristate; e.g., propylene glycol, wherein the penetration enhancer is present in an amount from 0.1% to about 20% by weight of the composition, or from about 1% to about 15% by weight of the composition, or from about 5% to about 15% by weight of the composition, or about 10% by weight of the composition.

18. 18. The topical composition of any one of claims 1 to 17, in the form of a cream, lotion, foam, aqueous gel, non-aqueous gel, spray, or ointment (e.g., a polyethylene glycol-based ointment).

19. 19. The topical composition of any one of claims 1 to 18, having an apparent pH of from about 3.5 to about 7.5, from about 4 to about 7, from about 4.5 to about 6.5, or from about 5 to about 6.5, or from about 5.5 to about 6.5, or about 6.

20. 20. The topical composition of any one of claims 1 to 19, applied to a patient's skin three times a day, twice a day, once a day, every other day, once a week, or once a month.

21. 21. The topical composition of any one of claims 1 to 20, administered to a patient suffering from a dermatological condition characterized by inflammation, such as rosacea, psoriasis, atopic dermatitis, hidradenitis suppurativa, seborrheic dermatitis, contact dermatitis, urticaria, dermatitis herpetiformis, nummular eczema, lichen planus, pityriasis rosea, cutaneous lupus, acne, cancer of the skin (e.g., cutaneous T-cell lymphoma), or miliaria.

22. 21. The topical composition of claim 20, wherein the skin is mammalian skin (e.g., human skin).

23. The topical composition of any one of claims 1 to 22, wherein the topical composition is an aqueous gel, the solvent system comprising PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is from about 0.7 to about 1.1, such as from about 0.8 to about 1.0, such as about 0.

9.

24. The topical composition of any one of claims 1 to 22, wherein the topical composition is a non-aqueous gel, the solvent system comprising PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is from about 2.2 to about 2.6, such as from about 2.3 to about 2.5, for example about 2.

4.

25. The topical composition of any one of claims 1 to 22, wherein the topical composition is a cream, the solvent system comprises PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is from about 2.6 to about 3.2, such as from about 2.7 to about 3.1, such as about 2.

9.

26. 23. The topical composition of any one of claims 1 to 22, wherein the topical composition is an ointment, the solvent system comprising PEG 400 and Transcutol® P, and the w / w ratio of PEG 400 / Transcutol® P is from about 3.5 to about 4.5, such as from about 3.8 to about 4.2, for example about 4.

27. ​​A topical composition described in any one of claims 1 to 26 for inhibiting the production of TNFα.

28. A topical composition according to any one of claims 1 to 27 for treating an inflammatory dermatological disorder in a subject.

29. A topical composition according to any one of claims 1 to 27 for reducing inflammation in mammalian skin.

30. A topical composition according to any one of claims 1 to 27 for reducing inflammation and vascular dysfunction in mammalian skin.

31. 29. The topical composition of claim 28, wherein the inflammatory dermatological disorder is rosacea, psoriasis, atopic dermatitis, hidradenitis suppurativa, seborrheic dermatitis, contact dermatitis, urticaria, dermatitis herpetiformis, nummular eczema, lichen planus, pityriasis rosea, cutaneous lupus, acne, cancer of the skin (e.g., cutaneous T-cell lymphoma), or miliaria.

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