A statistical method and system for qualitative identification of new psychoactive substances

Abstract

This invention provides a statistical identification system and method for the qualitative classification of new psychoactive substances, comprising: a probability analysis library for storing the probabilities of first-class, second-class, and third-class substituents in the substituent sets at corresponding substitution sites; a first structure analysis module for performing structural analysis on suspected new psychoactive substances to obtain the first substituents at each substitution site based on the skeleton structure of the suspected new psychoactive substance; and a statistical identification module for calculating the posterior ratio of the first substituents at each substitution site and the posterior distribution probability that the suspected new psychoactive substance belongs to the controlled substances range based on the probabilities in the probability analysis library according to a pre-established statistical model. Beneficial effects: This invention creatively proposes the application of statistical methods to the drug identification process of new psychoactive substances, providing a theoretical reference for drug identification.

Description

Technical Field

[0001] This invention relates to the field of drug identification technology, and in particular to a statistical identification method and system for the qualitative classification of new psychoactive substances. Background Technology

[0002] Fentanyl is a psychoactive substance that acts on opioid receptors. The problem of its abuse arose even as fentanyl-related drugs were being developed. Due to the simple synthetic route of fentanyl, an increasing number of factories illegally synthesize it, modifying the structure of the parent fentanyl compound to synthesize a series of fentanyl analogs with similar physiological and pharmacological properties. Different countries have adopted different legal control measures for fentanyl. In 2019, my country adopted a framework control approach to regulate fentanyl-related new psychoactive substances.

[0003] Compared to analogue control and list control, skeleton control is a relatively moderate legislative model. It can broaden the scope of control and deter illegal synthesis and manufacturing; at the same time, it is relatively feasible in judicial determination. However, skeleton control has limitations in its "catch-all" control of new psychoactive substances. Some fentanyl analogues still exist outside the scope of skeleton control. Although these analogues meet the characteristics of fentanyl-like psychoactive substances, they are not within the scope of fentanyl skeletons stipulated in my country. Examples include U-4700 and Furanylnorfentanyl. These two fentanyl analogues are relatively common new psychoactive substances in the drug market, but they do not meet my country's specific requirements for the modification of substituents on the fentanyl skeleton. Therefore, the skeleton control model can only control a portion of the structure. In the judicial determination process, accurate identification of fentanyl analogues is necessary. This undoubtedly brings certain difficulties to judges. For substances on the control list, in judicial determination, judges determine the chemical results of suspected fentanyl substances based on expert opinions and evidence, and then make corresponding criminal rulings. For fentanyl-related new psychoactive substances not listed in the regulatory catalog but subject to skeleton control, judges often find it difficult to make accurate judgments on professional issues based solely on expert opinions. Therefore, it is necessary to supplement this process with explanations of the expert opinions. This involves professional technicians qualitatively analyzing the structure of the tested substance and, in conjunction with the specific requirements of skeleton control, providing further clarification of the expert results. This clarifies whether the tested substance is a fentanyl-related new psychoactive substance within the legally regulated scope of my country.

[0004] Currently, there is no species identification method in China for fentanyl that is subject to whole-class control. Therefore, it is urgent to establish a statistical method for the qualitative identification of new psychoactive substances such as fentanyl based on whole-class control as a legal basis. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a statistical identification method and system for the qualitative classification of new psychoactive substances. The aim is to establish a Bayesian statistical model to qualitatively determine the species of fentanyl-related new psychoactive substances. This provides technical support for the evidence collection, investigation, and trial of fentanyl-related drug cases.

[0006] The technical problem solved by this invention can be achieved by the following technical solutions:

[0007] A statistical identification system for the qualitative classification of novel psychoactive substances includes:

[0008] A probability analysis library is used to store the set of substituents for each substitution site of all samples based on the skeleton structure, which is statistically obtained from a sample library of a target new psychoactive substance. The substituents in the set of substituents for each substitution site include first-class and second-class substituents that are within the scope of regulation, and third-class substituents that are outside the scope of regulation. The second-class substituents are derived from the first-class substituents. The probability analysis library also stores the statistically obtained probabilities of the first-class substituents, the second-class substituents, and the third-class substituents in the set of substituents for the corresponding substitution sites.

[0009] The first structural analysis module is used to perform structural analysis on a suspected new psychoactive substance to obtain the first substituents of the suspected new psychoactive substance based on each substitution site of the skeleton structure.

[0010] The statistical identification module is connected to the probability analysis library and the first structure parsing module, respectively. It is used to compare the first substituent of each substitution site with the set of substituents of the corresponding substitution site according to the pre-established statistical model, and calculate the posterior ratio of the first substituent of each substitution site and the posterior distribution probability of the suspected new psychoactive substance belonging to the control scope based on the probability statistics in the probability analysis library.

[0011] Preferably, it further includes:

[0012] The second structure analysis module is used to analyze the compound structure of all samples in the pre-established target new psychoactive substance sample library to obtain the set of substituents of the target new psychoactive substance at each substitution site based on the skeleton structure.

[0013] The control scope determination module is connected to the second structure analysis module and is used to divide the set of substituents by combining the compound structure contained in the relevant legislative text of the target new psychoactive substance, and to determine the first and second substituents of the target new psychoactive substance within the skeleton control scope, as well as the third substituents that belong to the non-control scope.

[0014] The prior distribution statistics module is connected to the first structure analysis module and the control range determination module, respectively. It is used to perform statistics on the compound structure of each sample in the target new psychoactive substance sample library, output a statistical result and store it in the probability analysis library. The statistical result includes at least the probability of the first type of substituent, the second type of substituent and the third type of substituent in the substituent set at the corresponding substitution site.

[0015] Preferably, it further includes:

[0016] A joint distribution model building module is used to build a joint distribution model, wherein the joint distribution model is a correlation function between joint distribution functions constructed based on the substituents at all substitution sites of the target new psychoactive substance;

[0017] The statistical model building module is connected to the joint distribution model building module and the statistical identification module, respectively, and is used to obtain the pre-established statistical model based on the joint distribution function model.

[0018] Preferably, the joint distribution function model is implemented using the following formula:

[0019] P(R1=r1, R2=r2,...,Rn=rn)=P(R1=r1)·P(R2=r2)...·P(Rn=rn)

[0020] Wherein, R1, R2…Rn represent the substituents at each substitution site; r1, r2…rn represent the first substituents at each substitution site of the suspected new psychoactive substance; P(R1=r1,R2=r2,...,Rn=rn) represents the probability that the suspected new psychoactive substance belongs to the target new psychoactive substance.

[0021] Preferably, the statistical identification module is further configured to determine if the posterior ratio of the first substituent at all substitution sites is greater than 1, and the posterior distribution probability of the suspected new psychoactive substance belonging to the controlled area is within a predetermined range; otherwise, the suspected new psychoactive substance belongs to the uncontrolled area.

[0022] Preferably, the statistical model is a Bayesian statistical model.

[0023] Preferably, the Bayesian statistical model is implemented using the following formula:

[0024]

[0025] Among them, R n L represents the first substituent corresponding to substitution site n; RnY represents the compound structure contained in the relevant legislative texts concerning the target new psychoactive substance; Rn The first substituent R of the suspected new psychoactive substance n Events falling within the scope of regulation; N Rn The first substituent R of the suspected new psychoactive substance n Events falling outside the scope of regulation; E represents the expert opinion evidence after the identification of the suspected new psychoactive substance; P(L|Y,E) represents the probability of event L occurring given that events Y and E have occurred; P(L|N,E) represents the probability of event L occurring given that events N and E have occurred; P(L Rn |Y Rn E) represents the known event Y. Rn Given that event E occurs, event L... Rn The probability of occurrence; P(L) Rn |N Rn E) represents known event N Rn Given that event E occurs, event L... Rn The probability of occurrence; LR represents the likelihood ratio; P(Y) Rn |E,L) represents event Y given that events E and L have occurred. Rn The probability of occurrence; P(N) Rn |E,L) represents event N given that events E and L have occurred. Rn The probability of occurrence; P(L|Y) represents the posterior ratio of the first substituent at substitution site n; Rn E) represents the known event Y. Rn The probability of event L occurring given that event E has occurred; P(L|N) Rn E) represents known event N Rn The probability of event L occurring given that event E has occurred; P(Y) Rn |E) represents event Y given that event E has occurred. Rn The probability of occurrence; P(N) Rn |E) represents event N given that event E has occurred. Rn The probability of occurrence; P(N|E,L) represents the posterior distribution probability that the suspected new psychoactive substance belongs to the non-regulated range; P(Y|E,L) represents the posterior distribution probability that the suspected new psychoactive substance belongs to the regulated range.

[0026] This invention also provides a statistical identification method for the qualitative classification of new psychoactive substances, applied to the statistical identification system for the qualitative classification of new psychoactive substances as described above, comprising:

[0027] Step S1: A probability analysis library is provided in advance. The probability analysis library stores the set of substituents for each substitution site of all samples based on the skeleton structure, which is statistically obtained from a sample library of a target new psychoactive substance. The substituents in the set of substituents for each substitution site include first-class substituents and second-class substituents that belong to the controlled scope, and third-class substituents that belong to the uncontrolled scope. The second-class substituents are derived from the first-class substituents. The probability analysis library also stores the statistically obtained probabilities of the first-class substituents, the second-class substituents, and the third-class substituents in the set of substituents for the corresponding substitution sites.

[0028] Step S2: Structural analysis of a suspected new psychoactive substance is performed to obtain the first substituents at each substitution site of the suspected new psychoactive substance based on its skeletal structure.

[0029] Step S3: Based on the pre-established statistical model, the first substituent at each substitution site is compared with the set of substituents at the corresponding substitution site. Based on the probability statistics in the probability analysis library, the posterior ratio of the first substituent at each substitution site and the posterior distribution probability that the suspected new psychoactive substance belongs to the control scope are calculated.

[0030] Preferably, step S1 includes:

[0031] Step S11: Analyze the compound structures of all samples in the pre-established target new psychoactive substance sample library to obtain the set of substituents of the target new psychoactive substance at each substitution site based on the skeleton structure.

[0032] Step S12: Based on the compound structure contained in the relevant legislative text of the target new psychoactive substance, the set of substituents is divided to determine the first and second class substituents within the skeleton control scope of the target new psychoactive substance, as well as the third class substituents outside the control scope.

[0033] Step S13: Statistically analyze the compound structures of each sample in the target new psychoactive substance sample library, output a statistical result and store it in the probability analysis library. The statistical result includes at least the probability of the first type of substituent, the second type of substituent and the third type of substituent in the substituent set at the corresponding substitution site.

[0034] Preferably, step S3 includes:

[0035] Determine whether the posterior ratio of the first substituent at all said substitution sites is greater than 1, and whether the posterior distribution probability of the suspected new psychoactive substance falling within the scope of control is within a predetermined range:

[0036] If so, then the suspected new psychoactive substance falls within the scope of control.

[0037] If not, then the suspected new psychoactive substance falls outside the scope of regulation.

[0038] The advantages or beneficial effects of the technical solution of this invention are as follows:

[0039] This invention creatively proposes to apply statistical methods to the drug identification process of new psychoactive substances. By analyzing the structural structure of the skeleton of new psychoactive substances through legislative regulation and using statistical models for probability analysis, it provides a theoretical reference for drug identification. Attached Figure Description

[0040] Figure 1 A block diagram of a statistical identification system for the qualitative classification of novel psychoactive substances, as described in a preferred embodiment of the present invention.

[0041] Figure 2 A flowchart illustrating a statistical identification method for the qualitative classification of novel psychoactive substances, as described in a preferred embodiment of the present invention.

[0042] Figure 3 This is a flowchart illustrating the specific implementation of step S1 in a preferred embodiment of the present invention.

[0043] Figure 4 The following are structural diagrams of fentanyl and fentanyl-like new psychoactive substances in the prior art;

[0044] Figure 5 In a preferred embodiment of the present invention, a flowchart is provided for the identification of fentanyl as a suspected new psychoactive substance. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The present invention is not limited to this embodiment; other embodiments that conform to the spirit of the present invention may also fall within the scope of the present invention.

[0046] See Figure 1 In a preferred embodiment of the present invention, based on the above-mentioned problems existing in the prior art, a new statistical identification system for the qualitative classification of psychoactive substances is provided, comprising:

[0047] A probability analysis library 1 is used to store the set of substituents for each substitution site of all samples based on the skeleton structure, which is statistically obtained from a sample library of a target new psychoactive substance. The substituents in the set of substituents for each substitution site include first-class and second-class substituents that are within the scope of regulation, and third-class substituents that are not within the scope of regulation. The second-class substituents are derived from the first-class substituents. The probability analysis library 1 also stores the statistically obtained probabilities of the first-class, second-class, and third-class substituents in the set of substituents for their respective substitution sites.

[0048] The first structure analysis module 2 is used to perform structural analysis on a suspected new psychoactive substance (hereinafter referred to as: suspected substance) to obtain the first substituents of the suspected new psychoactive substance based on each substitution site of the skeleton structure.

[0049] The statistical identification module 3 is connected to the probability analysis library 1 and the first structure analysis module 2, respectively. It is used to compare the first substituent of each substitution site with the set of substituents of the corresponding substitution site according to the pre-established statistical model, and calculate the posterior ratio of the first substituent of each substitution site and the posterior distribution probability of the suspected new psychoactive substance belonging to the control scope based on the probability statistics in the probability analysis library 1.

[0050] Specifically, in this embodiment, the suspected substance is analyzed by the first structure analysis module 2 to obtain the first substituents at each substitution site of the suspected substance based on the skeleton structure; the first substituents at all substitution sites are input into a pre-established statistical model to determine which category the first substituent at each substitution site belongs to, i.e., the first category of substituents, the second category of substituents, or the third category of substituents. Then, according to the determined substituent category, the corresponding probability is obtained from the probability analysis library 1 and substituted into the pre-established statistical formula to calculate the final posterior distribution probability.

[0051] This invention creatively proposes to apply statistical methods to the drug identification process of new psychoactive substances. By analyzing the structural structure of the skeleton of new psychoactive substances through legislative regulation and using statistical models for probability analysis, it provides a theoretical reference for drug identification.

[0052] In a preferred embodiment, it further includes:

[0053] The second structure analysis module 4 is used to analyze the compound structure of all samples in the pre-established target new psychoactive substance sample library to obtain the set of substituents at each substitution site based on the skeleton structure of the target new psychoactive substance.

[0054] The control scope determination module 5 is connected to the second structure analysis module 4. It is used to divide the set of substituents by combining the compound structure contained in the relevant legislative text of the target new psychoactive substance, and to determine the first and second substituents of the target new psychoactive substance within the skeleton control scope, as well as the third substituents that belong to the non-control scope.

[0055] The prior distribution statistics module 6 is connected to the second structure analysis module 4 and the control range determination module 5, respectively. It is used to perform statistics on the compound structure of each sample in the target new psychoactive substance sample library, output a statistical result and store it in the probability analysis library 1. The statistical result includes at least the probability of the first type of substituent, the second type of substituent and the third type of substituent in the substituent set of the corresponding substitution site.

[0056] Specifically, in this embodiment, the legislation concerning the target new psychoactive substance is structurally analyzed, and the corresponding legislative text is professionally analyzed, including its chemical structure.

[0057] Furthermore, by classifying and comparing the different types of target new psychoactive substances and their analogues that have appeared on the market, we can accurately and comprehensively describe the entire category of target new psychoactive substances.

[0058] Furthermore, in this embodiment, the types of substituents on the core structure of the target new psychoactive substance are determined according to specific circumstances and are not limited in the implementation method.

[0059] In a preferred embodiment, it further includes:

[0060] Module 7 for establishing a joint distribution model is used to establish a joint distribution model, which is a correlation function between joint distribution functions constructed based on the substituents at all substitution sites of the target new psychoactive substance.

[0061] The statistical model building module 8 is connected to the joint distribution model building module 7 and the statistical identification module 3, respectively, and is used to obtain a pre-established statistical model based on the joint distribution function model.

[0062] Specifically, in this embodiment, by establishing a joint distribution function, when determining whether a single compound belongs to a legally controlled narcotic category, the substituents R1, R2, ..., Rn at each substitution site on the backbone structure should be analyzed separately and comprehensively described. Therefore, a joint distribution function should be used to study the comprehensive evaluation of the legislative control of each substituent on the backbone of new psychoactive substances. This method is the first to use statistical methods for drug identification.

[0063] Furthermore, the statistical model for species identification of new psychoactive substances in this invention is not limited to establishing joint distribution scores on different substituents; similar statistical models are all within the scope of protection of this patent.

[0064] Module 8 of the statistical model building section employs mathematical statistical methods to perform probabilistic analysis on the identification results, transforming the instrumental analysis results of suspected fentanyl-like substances into a universally applicable format. It presents the final fentanyl-like physical and chemical properties and legal attributes as dual qualitative results through numerical analysis. When the chemical structure of a suspected substance is confirmed through identification, according to Bayes' theorem, if the probability P(Y|E,L) is greater than or equal to 99.987%, and the likelihood ratio of a single substituent is greater than 1, it indicates that, under the conditions of the identification opinion and legal provisions, the suspected substance is more likely to be a controlled fentanyl.

[0065] Furthermore, this invention does not impose strict limitations on the interpretation results of Bayesian theory in fentanyl evidence; P(Y|E,L) can be within 70-100%.

[0066] This invention provides a statistical method for classifying fentanyl-related new psychoactive substances under the regulation of class-based control of new psychoactive substances.

[0067] In a preferred embodiment, the joint distribution function model is implemented using the following formula:

[0068] P(R1=r1, R2=r2,...,Rn=rn)=P(R1=r1)·P(R2=r2)...·P(Rn=rn)

[0069] Where R1, R2…Rn represent the substituents at each substitution site; r1, r2…rn represent the first substituent at each substitution site of the suspected new psychoactive substance; P(R1=r1,R2=r2,...,Rn=rn) represents the probability that the suspected new psychoactive substance belongs to the target new psychoactive substance.

[0070] In a preferred embodiment, the statistical identification module 3 is further used to determine whether the suspected new psychoactive substance is within the controlled range if the posterior ratio of the first substituent at all substitution sites is greater than 1 and the posterior distribution probability of the suspected new psychoactive substance being within the controlled range is within a predetermined range; otherwise, the suspected new psychoactive substance is outside the controlled range.

[0071] In a preferred embodiment, the statistical model is a Bayesian statistical model.

[0072] In a preferred embodiment, the Bayesian statistical model is implemented using the following formula:

[0073]

[0074] Among them, R n L represents the first substituent corresponding to substitution site n; Rn Y represents the compound structure contained in the relevant legislative texts concerning the target new psychoactive substance; Rn The first substituent R of a suspected new psychoactive substance n Events falling within the scope of regulation; N Rn The first substituent R of a suspected new psychoactive substance n Events falling outside the scope of regulation; E represents the expert opinion evidence after identifying a suspected new psychoactive substance; P(L|Y,E) represents the probability of event L occurring given that events Y and E have occurred; P(L|N,E) represents the probability of event L occurring given that events N and E have occurred; P(L Rn |Y Rn E) represents the known event Y. Rn Given that event E occurs, event L... Rn The probability of occurrence; P(L) Rn |N Rn E) represents known event N Rn Given that event E occurs, event L... Rn The probability of occurrence; LR represents the likelihood ratio; P(Y) Rn |E,L) represents event Y given that events E and L have occurred. Rn The probability of occurrence; P(N) Rn |E,L) represents event N given that events E and L have occurred. Rn The probability of occurrence; P(L|Y) represents the posterior ratio of the first substituent at substitution site n; Rn E) represents the known event Y. Rn The probability of event L occurring given that event E has occurred; P(L|N) Rn E) represents known event N Rn The probability of event L occurring given that event E has occurred; P(Y) Rn |E) represents event Y given that event E has occurred. Rn The probability of occurrence; P(N) Rn |E) represents event N given that event E has occurred. Rn The probability of occurrence; P(N|E,L) represents the probability of event N occurring given that events E and L have occurred, i.e., the posterior distribution probability that the suspected new psychoactive substance belongs to the non-controlled area; P(Y|E,L) represents the probability of event Y occurring given that events E and L have occurred, i.e., the posterior distribution probability that the suspected new psychoactive substance belongs to the controlled area.

[0075] Furthermore, the aforementioned Bayesian statistical model characterizes the ratio of the posterior probability of a suspected new psychoactive substance falling within the regulated scope to the posterior probability of it falling outside the regulated scope. This ratio is the product of the posterior ratios of the substituents at each substitution site of the suspected substance. Further, the likelihood ratio is introduced into the posterior ratio calculation; that is, the posterior ratio of the substituent at each substitution site is the product of the likelihood ratio of the substituent at the corresponding substitution site and the prior probability distribution.

[0076] The aforementioned prior probability distribution and likelihood ratio can both be calculated from the probabilities statistically analyzed in probability analysis library 1. Specifically, the prior probability distribution is the sum of the probabilities of the first and second class substituents in the substituent set at the corresponding substitution site, and then the ratio of this sum to the probability of the third class substituent in the substituent set at the corresponding substitution site. This likelihood ratio represents the probability corresponding to the class of the first substituent at each substitution site.

[0077] This invention also provides a statistical identification method for the qualitative classification of new psychoactive substances, applicable to the statistical identification system for the qualitative classification of new psychoactive substances as described above, such as... Figure 2 As shown, it includes:

[0078] Step S1: A probability analysis library 1 is provided in advance. The probability analysis library 1 stores the set of substituents for each substitution site of all samples based on the skeleton structure, which is statistically obtained from a sample library of a target new psychoactive substance. The substituents in the set of substituents for each substitution site include first-class substituents and second-class substituents that are within the scope of regulation, and third-class substituents that are not within the scope of regulation. The second-class substituents are derived from the first-class substituents. The probability analysis library 1 also stores the statistically obtained probabilities of the first-class substituents, second-class substituents, and third-class substituents in the set of substituents for the corresponding substitution sites.

[0079] Step S2: Structural analysis of a suspected new psychoactive substance is performed to obtain the first substituents at each substitution site of the suspected new psychoactive substance based on its skeletal structure.

[0080] Step S3: Based on the pre-established statistical model, the first substituent of each substitution site is compared with the set of substituents of the corresponding substitution site. Based on the probability statistics in probability analysis library 1, the posterior ratio of the first substituent of each substitution site and the posterior distribution probability that the suspected new psychoactive substance belongs to the control scope are calculated.

[0081] In a preferred embodiment, such as Figure 3 As shown, step S1 includes:

[0082] Step S11: Analyze the compound structure of all samples in the pre-established target new psychoactive substance sample library to obtain the set of substituents at each substitution site based on the skeleton structure of the target new psychoactive substance.

[0083] Step S12: Based on the compound structure contained in the relevant legislative text of the target new psychoactive substance, the set of substituents is divided to determine the first and second class substituents within the skeleton control scope of the target new psychoactive substance, as well as the third class substituents that are not within the control scope.

[0084] Step S13: Statistically analyze the compound structures of each sample in the target new psychoactive substance sample library, output a statistical result and store it in the probability analysis library 1. The statistical result includes at least the probability of the first type of substituent, the second type of substituent and the third type of substituent in the substituent set of the corresponding substitution site.

[0085] In a preferred embodiment, step S3 includes:

[0086] Determine whether the posterior ratio of the first substituent at all substitution sites is greater than 1, and whether the posterior distribution probability of the suspected new psychoactive substance falling within the scope of regulation is within a predetermined range:

[0087] If so, then the suspected new psychoactive substance falls under the scope of control;

[0088] If not, then the suspected new psychoactive substance falls outside the scope of regulation.

[0089] Furthermore, the aforementioned predetermined range can be 70-100%.

[0090] This invention does not impose strict limitations on the types of target new psychoactive substances. In addition to the identification of fentanyl-related substances, the method of this invention is also applicable to synthetic cannabinoids and other new psychoactive substances that are not currently fully regulated.

[0091] A statistical identification method for the qualitative characterization of new psychoactive substances (taking fentanyl as an example) includes the following steps:

[0092] I. Structural Analysis of Legislation on Fentanyl-Class New Psychoactive Substances

[0093] According to relevant legislative descriptions, fentanyl-class new psychoactive substances have four substitution sites in their skeletal structure, namely R1-R4, see [link to legislation]. Figure 4 , Figure 4 The left image shows the structure of fentanyl, a new psychoactive substance, while the right image shows the structure of fentanyl-like new psychoactive substances.

[0094] According to the legislative definition, fentanyl is a substance that meets one or more of the following conditions:

[0095] 1. "Applicable substitution of propionyl groups": Fentanyl compounds within the scope of this legislation should have a propionyl group or other acyl structures at the R1 substituent site. The author analyzed 140 fentanyl-related compounds currently known internationally. The propionyl group structure contains eight different types of substituents, including alkyl, alkenyl, ether, and phenyl groups, forming various acyl structures. Additionally, a few structures use non-acyl structures to replace the propionyl group. For example, in 4-ANPP, the propionyl group is replaced by a hydrogen atom at the R1 site.

[0096] 2. "Using any substituted or unsubstituted monocyclic aromatic group to replace the phenyl group directly attached to the nitrogen atom": Fentanyl within the scope of this legislation should be a monocyclic aromatic structure where the R2 substituent site is a benzene ring or contains substituents. Statistical analysis of the sample library revealed alkyl, ether, and halogen groups as the main substituents. Additionally, a small number of fentanyl analogs with hydrogen-substituted benzene rings were found, such as U-4700 and U-4900.

[0097] 3. "Using any other substituent (except hydrogen atom) to replace phenethyl": Fentanyl within the scope of this legislation should have R3 in the form of phenethyl or other substituents, and R3 cannot be a hydrogen atom. Statistical analysis of the sample library revealed that cases where other substituents replace phenethyl are not common, although some structures do exist where phenethyl is replaced by hydrogen atoms, such as Furanylnorfentanyl.

[0098] 4. "The piperidine ring contains alkyl, alkenyl, or other substituents": Fentanyl within the scope of this legislation should have R4 as a hydrogen atom or an alkyl, alkenyl, or other substituent. This provision also indicates that the piperidine ring is an essential structure in the fentanyl skeleton. If other structures replace the piperazine ring, those structures are not within the scope of this legislation, such as U-4800.

[0099] II. Establishing the joint distribution function of fentanyl-like substances

[0100] When (X,Y) is a two-dimensional random variable, for any (x,y)∈R2, F(x,y)=P(X≤x,Y≤y) is called the joint distribution function of the random variable (X,Y).

[0101] In the control of the skeletons of new psychoactive substances, according to relevant legislative provisions, when determining whether a single compound belongs to the legally controlled narcotics category, each substituent R1, R2, ..., Rn in the skeleton structure should be analyzed separately and comprehensively described. Therefore, a joint distribution function should be used to study the comprehensive evaluation of the legislative control of the skeletons of new psychoactive substances by each substituent.

[0102] R1, R2, ..., Rn are n-dimensional random variables. Therefore, according to the definition of the joint distribution function, we can generalize to obtain F(r1, r2, ..., rn) = P(R1≤r1, R2≤r2, ..., Rn≤rn). Furthermore, since the substituents are independent of each other, according to the probability model of discrete random variables...

[0103] P(R1=r1, R2=r2,...,Rn=rn)=P(R1=r1)·P(R2=r2)...·P(Rn=rn)

[0104] Based on the analysis of the fentanyl structural formula above, the joint distribution function of fentanyl-like compounds can be expressed as:

[0105] P 芬 =P R1 ·P R2 ·P R3 ·P R4

[0106] Wherein, for any compound structure F, the probability P that it is fentanyl 芬 The sample space is associated with the substituent characteristics of the four substitution sites, and P is Ω(R1,R2,R3,R4). R1 P R2 P R3 P R4 The respective sample spaces are: Ω1, Ω2, Ω3, and Ω4. Among them, Ω1 = {propionyl group, other acyl structures, and non-acyl structures}, Ω2 = {benzene ring, any substituted or unsubstituted monocyclic aromatic group, and hydrogen atom}, Ω3 = {phenethyl group, other substituents, and hydrogen atom}, and Ω4 = {hydrogen atom, other substituents, and non-piperidine core structure}.

[0107] III. Research on the Application of Bayesian Theory in the Interpretation of Fentanyl Evidence

[0108] 1. Bayes' Theorem Calculation Rules

[0109] like Figure 5 As shown, the substituent feature comparison of fentanyl-related substances is mainly based on a Bayesian statistical model, which is calculated by introducing the likelihood ratio.

[0110] According to Bayes' theorem, we can obtain:

[0111]

[0112] The likelihood ratio is:

[0113]

[0114] Based on the analysis of the fentanyl structural formula above, the joint distribution function of fentanyl-like compounds can be expressed as:

[0115] P 芬 =P R1 ·P R2 ·P R3 ·P R4

[0116] For any compound structure F, the probability P that it is fentanyl 芬 The sample space is Ω(R1,R2,R3,R4), which is related to the substituent characteristics of the four substitution sites. Therefore, the likelihood ratio for the Bayesian formula application of fentanyl-like substances is:

[0117]

[0118]

[0119] 2. Sample Calculation

[0120] This invention selects 140 fentanyl compounds from both domestic and international sources as samples for analysis (Appendix 1). By statistically analyzing the structural characteristics, substituent positions, and frequencies of occurrence of the compounds within the samples, the information provided by the samples is used to infer unknown quantities in the overall distribution. The statistical analysis results of the 140 results in the samples, based on their spatial characteristics, are shown in Table 1:

[0121] Table 1: Probabilities of Class I, Class II, and Class III substituents in the sample within the substituent set at their respective substitution sites.

[0122]

[0123] The identification results are analyzed probabilistically using mathematical and statistical methods, which currently transform the specialized technical analysis results of pharmaceutical analysis into a universally applicable format. The final qualitative results, presented numerically, demonstrate both the physical and chemical properties and legal attributes of fentanyl.

[0124] Analysis of sample data for 140 fentanyl analogs, calculated using the aforementioned formula, showed that under both event E and event L conditions, the likelihood ratio (LR) for fentanyl analogs classified as legally regulated fentanyl ranged from 8.23E3 to 8.89E5, with a probability of P(Y|E,L) of 99.987% to 99.999%. Simultaneously, the likelihood ratios (LR) for single substituents R1, R2, R3, and R4 ranged from 0.935 to 102.87. According to fentanyl analog legislation, each substituent must be replaced by other substituents according to a prescribed modification pattern to be classified as a fentanyl-like substance. Therefore, when a suspected substance's chemical structure is confirmed through identification, according to Bayes' theorem, a probability of P(Y / E,L) greater than or equal to 99.987%, and a single substituent likelihood ratio greater than 1, indicates that, under both the identification opinion and legal conditions, the compound is more likely to be a controlled fentanyl. Only when both of the above restrictions are met can the substance be determined to be a fentanyl-related substance within the scope of legal control.

[0125] The following two specific embodiments utilize the joint distribution function and Bayesian statistics method provided by this invention to identify sufentanil and N-benzylfuranylnorfentanyl, new psychoactive substances of fentanyl, to further illustrate and explain this technical solution:

[0126] Example 1: Sufentanil

[0127] Structural analysis of sufentanil confirmed that its R1 substituent = propionyl group; R2 substituent = phenyl group; R3 substituent = other substituents; and R4 substituent = other substituents.

[0128] The posterior ratio of the R1 substituent in sufentanil is:

[0129]

[0130] The posterior ratio of the R2 substituent in sufentanil is:

[0131]

[0132] The posterior ratio of the R3 substituent in sufentanil is:

[0133]

[0134] The posterior ratio of the R4 substituent in sufentanil is:

[0135]

[0136] The posterior ratio of sufentanil is the product of the posterior ratios of the substituents at all substitution sites, i.e.:

[0137]

[0138] therefore:

[0139]

[0140] Therefore, it can be calculated that:

[0141] P(Y / E,L) = 99.998%

[0142] Based on the requirements of this explanation, it can be determined that the identification result of sufentanil, P(Y / E,L) = 99.998%, and the posterior ratios of single substituents are 35.94, 24.96, 18.71, and 3.16, all of which are greater than 1. Therefore, the final identification conclusion can be obtained as follows: sufentanil belongs to the fentanyl class of new psychoactive substances within the legal control scope of my country.

[0143] Example 2 uses N-benzyl furanyl methyl fentanyl as an example.

[0144] Structural analysis of n-benzylfuranmethylfentanyl confirmed that its R1 substituent = other acyl structures; R2 substituent = phenyl; R3 substituent = hydrogen atom; and R4 substituent = hydrogen atom.

[0145] The posterior ratio of the R1 substituent in benzylfuran methyl fentanyl is:

[0146]

[0147] The posterior ratio of the R2 substituent in benzylfuran methyl fentanyl is:

[0148]

[0149] The posterior ratio of the R3 substituent in benzylfuran methyl fentanyl is:

[0150]

[0151] The posterior ratio of the R4 substituent in benzylfuran methyl fentanyl is:

[0152]

[0153]

[0154] The posterior ratio of benzylfuran methylfentanyl is the product of the posterior ratios of the substituents at all substitution sites, i.e.:

[0155]

[0156] therefore:

[0157]

[0158] Therefore, it can be calculated that:

[0159] P(Y / E,L) = 99.998%

[0160] Based on the requirements of this explanation, it can be determined that the identification result of n-benzylfuran methylfentanyl is P(Y / E,L) = 99.998%, and the posterior ratios of single substituents are: 102.87, 24.96, 0.935, and 29.84, where the R3 likelihood ratio is less than 1. Therefore, the final identification conclusion can be drawn as follows: n-benzylfuran methylfentanyl is not a new psychoactive substance of the fentanyl class within the legally regulated scope of fentanyl in my country.

[0161] The application of Bayes' theorem and the legal characterization methods should be explained in the technical standards for the identification of fentanyl-related substances. In the identification report, in addition to confirming the structure of the target substance, the legal attributes of the target substance should also be confirmed according to the calculation methods and data requirements in the standards.

[0162] The above technical solution has at least the following advantages:

[0163] (1) This invention is the first to propose the application of statistical methods in drug identification, which has certain theoretical innovation.

[0164] (2) This invention provides a professional analysis of the fentanyl legislative text, including its chemical structure, and interprets the legal provisions professionally, providing a theoretical reference for fentanyl identification.

[0165] (3) This invention proposes to use Bayesian theory to analyze the identification results through probability statistics, use mathematical expression mode to determine the results, and build a statistical model for fentanyl-like new psychoactive substances.

[0166] The above description is merely a preferred embodiment of the present invention and does not limit the implementation and protection scope of the present invention. Those skilled in the art should realize that any equivalent substitutions and obvious changes made using the content of this specification and illustrations should be included within the protection scope of the present invention.

Claims

1. A statistical identification system for the qualitative classification of novel psychoactive substances, characterized in that, include: A probability analysis library is used to store the set of substituents for each substitution site of all samples based on the skeleton structure, which is statistically obtained from a sample library of a target new psychoactive substance. The substituents in the set of substituents for each substitution site include first-class and second-class substituents that are within the scope of regulation, and third-class substituents that are outside the scope of regulation. The second-class substituents are derived from the first-class substituents. The probability analysis library also stores the statistically obtained probabilities of the first-class substituents, the second-class substituents, and the third-class substituents in the set of substituents for the corresponding substitution sites. The first structural analysis module is used to perform structural analysis on a suspected new psychoactive substance to obtain the first substituents of the suspected new psychoactive substance based on each substitution site of the skeleton structure. The statistical identification module is connected to the probability analysis library and the first structure parsing module, respectively. It is used to compare the first substituent of each substitution site with the set of substituents of the corresponding substitution site according to the pre-established statistical model, and calculate the posterior ratio of the first substituent of each substitution site and the posterior distribution probability of the suspected new psychoactive substance belonging to the control scope based on the probability statistics in the probability analysis library.

2. The statistical identification system for the qualitative classification of new psychoactive substances according to claim 1, characterized in that, Also includes: The second structure analysis module is used to analyze the compound structure of all samples in the pre-established target new psychoactive substance sample library to obtain the set of substituents of the target new psychoactive substance at each substitution site based on the skeleton structure. The control scope determination module is connected to the second structure analysis module and is used to divide the set of substituents by combining the compound structure contained in the relevant legislative text of the target new psychoactive substance, and to determine the first and second substituents of the target new psychoactive substance within the skeleton control scope, as well as the third substituents that belong to the non-control scope. The prior distribution statistics module is connected to the second structure analysis module and the control range determination module, respectively. It is used to perform statistics on the compound structure of each sample in the target new psychoactive substance sample library, output a statistical result and store it in the probability analysis library. The statistical result includes at least the probability of the first type of substituent, the second type of substituent and the third type of substituent in the substituent set at the corresponding substitution site.

3. The statistical identification system for the qualitative classification of new psychoactive substances according to claim 1, characterized in that, Also includes: A joint distribution model building module is used to build a joint distribution model, wherein the joint distribution model is a correlation function between joint distribution functions constructed based on the substituents at all substitution sites of the target new psychoactive substance; The statistical model building module is connected to the joint distribution model building module and the statistical identification module, respectively, and is used to obtain the pre-established statistical model based on the joint distribution function model.

4. The statistical identification system for the qualitative classification of new psychoactive substances according to claim 3, characterized in that, The joint distribution function model is implemented using the following formula: P(R1=r1,R2=r2,...,Rn=rn)=P(R1=r1)·P(R2=r2)...·P(Rn=rn) Wherein, R1, R2…Rn represent the substituents at each substitution site; r1, r2…rn represent the first substituents at each substitution site of the suspected new psychoactive substance; P (R1=r1, R2=r2, ..., Rn=rn) represents the probability that the suspected new psychoactive substance belongs to the target new psychoactive substance.

5. The statistical identification system for the qualitative classification of new psychoactive substances according to claim 1, characterized in that, The statistical identification module is further configured to determine if the posterior ratio of the first substituent at all substitution sites is greater than 1, and if the posterior distribution probability of the suspected new psychoactive substance falling within the control scope is within a predetermined range; otherwise, the suspected new psychoactive substance falls outside the control scope.

6. The statistical identification system for the qualitative classification of new psychoactive substances according to claim 1, characterized in that, The statistical model is a Bayesian statistical model.

7. The statistical identification system for the qualitative classification of new psychoactive substances according to claim 6, characterized in that, The Bayesian statistical model is implemented using the following formula: ； Among them, R n L represents the first substituent corresponding to substitution site n; Rn Y represents the compound structure contained in the relevant legislative texts concerning the target new psychoactive substance; Rn The first substituent R of the suspected new psychoactive substance n Events falling within the scope of regulation; N Rn The first substituent R of the suspected new psychoactive substance n Events falling outside the scope of regulation; E represents the expert opinion evidence after identifying the suspected new psychoactive substance; P(L|Y,E) represents the probability of event L occurring given that events Y and E have occurred; P(L|N,E) represents the probability of event L occurring given that events N and E have occurred; P(L Rn |Y Rn E) represents the known event Y. Rn Given that event E occurs, event L... Rn The probability of occurrence; P(L) Rn |N Rn E) represents known event N Rn Given that event E occurs, event L... Rn The probability of occurrence; LR represents the likelihood ratio; P(Y) Rn (E, L) represents event Y given that events E and L have occurred. Rn The probability of occurrence; P(N) Rn |E,L) represents event N given that events E and L have occurred. Rn The probability of occurrence; P(L|Y) represents the posterior ratio of the first substituent at substitution site n; Rn E) represents the known event Y. Rn The probability of event L occurring given that event E has occurred; P(L|N) Rn E) represents known event N Rn The probability of event L occurring given that event E has occurred; P(Y) Rn |E) represents event Y given that event E has occurred. Rn The probability of occurrence; P(N) Rn |E) represents event N given that event E has occurred. Rn The probability of occurrence; P(N|E,L) represents the posterior distribution probability that the suspected new psychoactive substance belongs to the non-regulated range; P(Y|E,L) represents the posterior distribution probability that the suspected new psychoactive substance belongs to the regulated range.

8. A statistical identification method for the qualitative classification of new psychoactive substances, characterized in that, The statistical identification system for the qualitative classification of new psychoactive substances as described in any one of claims 1-7 includes: Step S1: A probability analysis library is provided in advance. The probability analysis library stores the set of substituents for each substitution site of all samples based on the skeleton structure, which is statistically obtained from a sample library of a target new psychoactive substance. The substituents in the set of substituents for each substitution site include first-class substituents and second-class substituents that belong to the controlled scope, and third-class substituents that belong to the uncontrolled scope. The second-class substituents are derived from the first-class substituents. The probability analysis library also stores the statistically obtained probabilities of the first-class substituents, the second-class substituents, and the third-class substituents in the set of substituents for the corresponding substitution sites. Step S2: Structural analysis of a suspected new psychoactive substance is performed to obtain the first substituents at each substitution site of the suspected new psychoactive substance based on its skeletal structure. Step S3: Based on the pre-established statistical model, the first substituent at each substitution site is compared with the set of substituents at the corresponding substitution site. Based on the probability statistics in the probability analysis library, the posterior ratio of the first substituent at each substitution site and the posterior distribution probability that the suspected new psychoactive substance belongs to the control scope are calculated.

9. The statistical identification method for the qualitative classification of new psychoactive substances according to claim 8, characterized in that, Step S1 includes: Step S11: Analyze the compound structures of all samples in the pre-established target new psychoactive substance sample library to obtain the set of substituents of the target new psychoactive substance at each substitution site based on the skeleton structure. Step S12: Based on the compound structure contained in the relevant legislative text of the target new psychoactive substance, the set of substituents is divided to determine the first and second class substituents within the skeleton control scope of the target new psychoactive substance, as well as the third class substituents outside the control scope. Step S13: Statistically analyze the compound structures of each sample in the target new psychoactive substance sample library, output a statistical result and store it in the probability analysis library. The statistical result includes at least the probability of the first type of substituent, the second type of substituent and the third type of substituent in the substituent set at the corresponding substitution site.

10. The statistical identification method for the qualitative classification of new psychoactive substances according to claim 8, characterized in that, Step S3 includes: Determine whether the posterior ratio of the first substituent at all said substitution sites is greater than 1, and whether the posterior distribution probability of the suspected new psychoactive substance falling within the scope of control is within a predetermined range: If so, the suspected new psychoactive substance falls within the scope of control. If not, then the suspected new psychoactive substance falls outside the scope of regulation.

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