Method, system and computer program for the calculation of an optimal individualized dosing regimen, particularly subject to clinical constraints - Patents.com

Abstract

The present invention relates to a method for automatically determining an optimal personalized dosing regimen of at least one drug for a patient suffering from a known disease, the optimal personalized dosing regimen optionally subject to at least one clinical constraint, the method comprising the steps of: providing a mathematical model adapted to model the progression of the disease and the effect of at least one drug on the progression of the disease, the model including personal model parameters associated with the patient; utilizing empirical Bayes estimation to automatically and numerically estimate personal model parameters of the mathematical model utilizing patient data associated with the patient; automatically calculating an optimal personalized dosing regimen for the mathematical model by solving an optimal control problem based on the desired disease progression, the estimated personal model parameters, and an initial guess for the dosing regimen; and optionally adjusting the optimal personalized dosing regimen to accommodate the at least one clinical constraint, resulting in an optimal personalized dosing regimen subject to the at least one clinical constraint.

Description

[Technical field]

[0001] The present invention relates to a method, system and computer program for determining an optimal dosing regimen of at least one drug to a patient suffering from a known disease. [Background technology]

[0002] The majority of diseases remain difficult to treat at an individual level, since disease progression varies between patients and clinical practice. In particular, it is often still a challenge to determine optimal individual dosing regimens, especially in clinical settings, in a sufficiently rapid and reliable manner that ideally allows control of disease progression leading to patient recovery while minimizing treatment-related adverse events.

[0003] In particular, among such diseases, congenital hypothyroidism is the most common congenital endocrine disorder and the most common preventable cause of mental retardation worldwide [Polak 2017]. Disease severity varies greatly among individuals at the time of diagnosis, i.e., thyroid-stimulating hormone (TSH) ranges from 6 to 1200 mU / L, with the norm being 0.5 to 5 mU / L. The primary action of thyroid hormone is interneuron axonal growth and myelination, processes that are ongoing in humans primarily after birth. Newborn screening allows the diagnosis of children with congenital hypothyroidism before they suffer from clinical signs and irreversible neurological deficits. During the last 40 years, the neurological outcome of patients with congenital hypothyroidism has been significantly improved by 1) shortening the time window between screening and initiation of treatment (currently 4–5 days in Switzerland) and 2) increasing the initial dose of levothyroxine (from 5–8 mcg / kg / day to currently 10–15 mcg / kg / day). The goal of replacement treatment with levothyroxine is to correct hypothyroidism as quickly as possible to protect brain development. Clinicians aim to achieve free thyroxine (T4) levels within the upper limit of the normal reference range within 14 days (see Figure 3(a)). However, several studies have revealed that up to 10% of children are overdosed with initial and maintenance doses of 10–15 mcg / kg / day for longer than is appropriate. Furthermore, at age 11 years, their neurological outcomes were comparable to children who had periods of underdosing during follow-up, and both over- and underdosed children had poorer neurological outcomes compared with children on levothyroxine doses that maintained thyroid hormones within the reference range during follow-up.

[0004] Current international guidelines recommend more frequent control during the first 2 years of life to allow more frequent and necessary individual and age-appropriate dosage adjustments to maintain thyroid hormones within the physiological normal reference range. This allows for more rapid detection of over- and underdosing, but it does not prevent episodes of suboptimal dosing. As a result, the final step to improve neurological outcomes in affected patients needs to focus on optimizing alternative dosing over the long term by taking into account clinical and laboratory data for individualized dosing during follow-up. Therefore, being able to determine optimal individualized dosing during the first 2 years of life is particularly highly desirable, which is essential for brain development and normal cognitive function over the long term. Central congenital hypothyroidism is a subgroup of congenital hypothyroidism with low TSH and FT4 values ​​due to pituitary and hypothalamic disorders treated with levothyroxine in the same way.

[0005] Furthermore, congenital hyperthyroidism occurs in approximately 10% of infants born to mothers with autoimmune hyperthyroidism (Graves' disease) due to the placental passage of stimulatory antibodies against the thyroid-stimulating hormone (TSH) receptor. It places the infant at significant risk for morbidity and mortality. In contrast to infants with congenital hypothyroidism, who are approximately 95% asymptomatic at birth and during the first week of life, infants with congenital hyperthyroidism present with typical signs and symptoms ranging from mild tachycardia and sweating to weight loss, vomiting, diarrhea, dehydration, severe hyperpyrexia, seizures, and heart failure. Onset is immediate after birth or delayed until 4-10 days after birth by the placental passage of maternal antithyroid drugs. Again, the severity of the disease varies greatly, from extremely mild forms to life-threatening complications. Delayed onset further complicates optimal treatment, making clinical observation and laboratory control mandatory on days 1, 4, 7, 10, and 14 of life.

[0006] Also, for congenital hyperthyroidism, it is highly desirable to optimize the treatment by predicting which children are at risk of a severe clinical course and when treatment should be initiated, and by finding the minimum effective initiation and maintenance doses adapted to the disease severity in the context of possible severe side effects of antithyroid drugs (agranulocytosis, hepatitis, vasculitis) (see Figure 3(b)).

[0007] Moreover, acquired hyperthyroidism [Leger 2014] occurs in children at a prevalence of 0.5-2:100000 in Europe and in adults at a prevalence of 25-90:100000 in Brazil, China and India, with the highest prevalence, ranging from 0.75-1.25% of the population, respectively. The severity of hyperthyroidism likewise varies greatly between individuals at the time of diagnosis, with FT4 values ​​ranging from 22 to over 100 pmol / L, whereas the norm is 11-21 pmol / L. Restoration of physiological FT4 levels should be achieved after 4-6 weeks, in contrast to congenital thyroid diseases, where normalization should be aimed for as quickly as possible. The simplest treatment used to be block and replace therapy: a dose of antithyroid drugs was chosen to completely block the thyroid gland, and replacement with levothyroxine was added. In the context of the increasing frequency of side effects (agranulocytosis, hepatitis, vasculitis) associated with higher doses of antithyroid drugs, such an approach is no longer recommended according to international guidelines. Currently, the minimum effective dose of antithyroid drugs needs to be determined at the individual level to reduce the risk of overdosing leading to iatrogenic hypothyroidism or underdosing leading to persistent hyperthyroidism. Both hyperthyroidism and hypothyroidism adversely affect growth and pubertal development (retarded or accelerated, respectively), as well as cognitive function, leading to declines in academic and sports performance. Finally, due to the additional complexity during childhood, the disease course is more severe and the risk of hyperthyroidism recurrence is much higher in young or prepubertal children compared to older (over 10 years) or pubertal and postpubertal children, making pediatric Graves' disease a therapeutic challenge.

[0008] Also for Graves' disease, a treatment that would allow the calculation of an optimal individual starting dose depending on clinical and laboratory parameters in order to reach steady state and the minimum effective maintenance dose and avoid relapse during follow-up would be highly desirable (see Figure 3(d)).

[0009] Moreover, hypothyroidism is common worldwide, with a prevalence of up to 0.2-5.3% of the adult population in Europe. The most frequent cause of acquired hypothyroidism is Hashimoto's thyroiditis in iodine-sufficient parts of the world. The goal of treatment of acquired hypothyroidism (1.2% incidence) is to slowly normalize free T4 levels to avoid signs and symptoms of hyperthyroidism after prolonged hypothyroidism. As with other diseases, optimal initiation and maintenance dosages are necessary to normalize physical development, cognitive function and, consequently, academic achievement, but not to overdose pediatric patients (see Figure 3(c)). Furthermore, central hypothyroidism due to disorders of the pituitary and hypothalamus (e.g., trauma, tumors, infections, among others) can cause further forms of acquired hypothyroidism. Summary of the Invention [Problem to be solved by the invention]

[0010] In summary, based on the foregoing, the problem to be solved by the present invention is to provide a method, a system, a computer program, a computer readable non-transitory storage medium, and a data carrier signal that allows for improved individualized dosing, especially for pediatric thyroid diseases. Due to the severity of such diseases, it is of great clinical relevance to improve the treatment and outcome of affected patients. [Means for solving the problem]

[0011] This problem is solved by a method having the features of claim 1, a system having the features of claim 10, a computer program having the features of claim 12, a computer-readable non-transitory storage medium having the features of claim 13 and a data carrier signal having the features of claim 14.

[0012] Preferred embodiments of these aspects of the invention are set out in the corresponding dependent claims and are described below.

[0013] According to claim 1, there is provided a method for automatically determining an optimal individualized dosing regimen of at least one drug for a patient (e.g. a neonate, infant, child, adolescent or adult) suffering from a disease, in particular the optimal individualized dosing regimen being subject to at least one clinical constraint, the method comprising: (a) providing a computer-implemented mathematical model adapted to model (particularly characterize and predict) the disease progression of said disease and in particular the effect of at least one drug on the disease progression, which model comprises individual model (or clinical routine) parameters associated with a given patient (particularly with a given disease and its disease severity and progression, as well as with the applied dosing regimen); (b) using empirical Bayes estimation to automatically and numerically estimate individual model parameters of the mathematical model using patient data, in particular individual medication information, for a given patient; (c) automatically calculating an optimal personalized dosing regimen for the mathematical model by solving an optimal control problem based on the desired disease progression, the estimated personalized model parameters, and an initial guess for the dosing regimen; (d) adjusting the optimal individualized dosing regimen to accommodate at least one clinical constraint to result in an optimal individualized dosing regimen subject to said at least one clinical constraint; Including, Steps (b)-(d) are performed at each visit of a number x of subsequent visits of the patient, where for x>1, the patient data in step b) includes patient data from x-1 previous visit(s), and the empirical Bayes estimation in step b) further uses all doses of the at least one drug actually administered to the patient up to the current visit.

[0014] Advantageously, the present invention allows for individualized dosing to take drug therapy to the next level. For many diseases, particularly for hyperthyroidism or hypothyroidism, new pharmacological approaches have not been developed and improvements in determining individual dosing regimens are key in improving treatment outcomes.

[0015] In particular, as outlined above and shown in FIG. 3, the present invention is particularly applicable to modeling different clinical conditions that need to be modeled separately in order to develop disease-specific algorithms for initiation and maintenance dosing.

[0016] Within the framework of the present invention, the following concepts and definitions are frequently mentioned.

[0017] patient The patient can be a virtual / in-silico (non-human) object (e.g., the average of a patient population) or an actual human patient.

[0018] Visit A patient visit can be (i) any time of interest, (ii) a non-inpatient clinical visit at a hospital, or (iii) a time a clinician sees an inpatient at a hospital.

[0019] Wearable Devices and Sensors Wearable devices and sensors are non-invasive devices worn by patients to monitor vital signs, such as heart rate (beats per minute), blood pressure (mmHg), body temperature (°C), respiratory rate (breaths / min), oxygen saturation and step count (counts per day).

[0020] Laboratory Measurements A laboratory measurement is a routine biochemical test of a biomarker (e.g., hormone) that is analyzed in a medical laboratory or by a health care professional such as a doctor, nurse, medical assistant, or pharmacist. In the case of thyroid hormones, one hormone is synthesized and secreted by the pituitary gland (a regulatory hormone of the peripheral endocrine gland called thyroid stimulating hormone or thyroid stimulating hormone (TSH) for the pituitary-thyroid axis) and one is secreted by the thyroid gland (an endocrine gland under the control of the pituitary gland, which is thyroxine (T4) and triiodothyronine (T3) in bound (T3, T4) and free (FT3, FT4) forms).

[0021] Demographics / Anthropometric Characteristics Demographic data are, for example, age (days (newborn), months (infant), age (child or adult)), gestational age at birth (premature or full-term) and sex. Anthropometric data are, for example, weight (kg), height (cm) and head circumference (cm).

[0022] Covariate Covariates are patient characteristics (e.g., demographic / anthropometric characteristics) that may, but do not necessarily, change over time. Time-invariant covariates are, for example, birth weight, gestational age, mode of delivery, all characteristics at baseline, etc. Examples for time-varying covariates are weight, height, heart rate, blood pressure, respiratory rate, etc.

[0023] Patient Data The patient data is a combination of data from wearable devices or sensors, laboratory measurements, and covariates from all available visits. In addition, the patient data includes all information regarding medication dosage from all available visits.

[0024] Pharmacokinetic Model A pharmacokinetic (PK) model describes the concentration of a drug (or, e.g., its metabolites) or an exogenous substance, e.g., due to absorption, distribution, metabolism, and excretion processes. The route of administration of a drug can be (i) oral, (ii) intravenous, or (iii) subcutaneous. PK models are typically characterized by one or more differential equations.

[0025] Pharmacokinetic / pharmacodynamic model A pharmacokinetic / pharmacodynamic (PKPD) model describes, for example, the response of a biomarker or disease progression caused by the stimulatory / inhibitory effect of one or more drugs (so-called pharmacodynamics), which are characterized by a PK model. For several drug combinations, the drugs can be administered simultaneously or sequentially. PKPD models are typically characterized by one or more differential equations.

[0026] Basic mathematical model The basic mathematical model can be a PK model alone or a PKPD model. The basic mathematical model may include a combination of physiologically based mechanistic assumptions, maturation-related processes and / or data-driven assumptions. The basic mathematical model is controlled by one or several drug dosages. The basic mathematical model includes model parameters summarized in a vector θ, some of which may already be known while others need to be estimated. A disease state is a state variable or a combination of several state variables of the basic mathematical model that characterize disease progression.

[0027] Individual model parameters The individual model parameters are i to characterize an individual patient based on personal data. The index i denotes the ith individual in a population with N patients, i.e., i=1,...,N. All or only some of the model parameters may have physiological, biological or other meaning. For example, the model parameters may describe the rate of a process (e.g., production or excretion), may describe the volume of a compartment, or may have other meaning.

[0028] Favorable disease progression The desired disease progression is given by the clinician / user and characterizes the goal for an individual patient. For example, for a patient who is being treated with a drug and shows an increase in a biomarker, the goal is to normalize the biomarker value to a normal (age-specific) reference range within a given time period. Or in the example of a PK model, the desired disease progression may be a goal for drug exposure, e.g., to reach a certain area under the concentration curve. The desired disease progression under drug therapy is characterized by a mathematical function.

[0029] Dosage regimen A dosing regimen is information regarding the administration of a drug or drugs. It includes the drug(s) themselves, the route of administration (oral, intravenous, subcutaneous), the time of administration, and the dosage.

[0030] Optimal individual dosing regimen An optimal individualized dosing regimen is one that has an optimal dosage (with respect to the desired disease progression) for an individual patient.

[0031] Optimal individualized dosing schedules subject to constraints in clinical applications An optimal individualized dosing plan subject to a clinical application constraint is an optimal individualized dosing plan adjusted to a clinical application constraint. This can be, for example, the available tablet sizes. Different strategies can be used to adjust the optimal dose between two available dosage sizes, for example: 1) Round to the nearest available dosage size, or 2) Selecting the higher or lower available dose based on the lower corresponding cost functional value (as in mixed integer optimization [Belotti 2013]); can be applied.

[0032] Nonlinear mixed-effects modeling approach In the nonlinear mixed effects (NLME) modeling approach [Lavielle 2014], patients with the same disease are assumed to form clusters with common or similar characteristics. For each individual i,

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[0033] Mathematical Model The mathematical model is a basic mathematical model that describes a given population of patients by its population parameter p together with the application of the NLME modeling approach. Such a mathematical model is therefore sometimes also denoted as a fully developed mathematical model.

[0034] Empirical Bayes Estimation Empirical Bayes estimation, also known as maximum a posteriori estimation [Bassett, Deride 2019], is a method to estimate the probability distribution of a population with population parameters ρ for individual i at time t. i The measurement w observed at i The estimated individual model parameters φ that are most likely to predict i Mathematically, we calculate the conditional probability density function

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[0035] Optimal Control Problem The optimal control problem is solved to calculate a control (i.e., a dose of one or several drugs) such that one state variable or a combination of several state variables of a mathematical model (e.g., a patient's disease state) reaches the desired disease progression as close as possible. This is achieved by minimizing a cost functional that characterizes the difference between the disease state resulting from a particular control and the desired disease progression. The optimal control problem can be solved with an optimal control algorithm, such as the OptiDose algorithm disclosed in the paper: "Bachmann F, Koch G, Pfister M, Szinnai G, Schropp J (2021) OptiDose: Computing the Individualized Optimal Drug Dosing Regimen Using Optimal Control. Journal of Optimization Theory and Applications 189:46-6," which is incorporated herein by reference in its entirety. In detail, the optimization is an iterative procedure that starts with (i) an initial control, (ii) solves a mathematical model to obtain the pathology, (iii) solves the adjoint equation (relating the pathology to the cost functional), and (iv) updates the control utilizing the gradient of the cost functional. Steps (iii)-(iv) are repeated within each iteration.

[0036] According to a preferred embodiment of the method according to the invention, the method comprises the steps of: (d) adjusting the optimal individualized dosing regimen to accommodate at least one clinical constraint to yield an optimal individualized dosing regimen subject to said at least one clinical constraint. The method further includes the step of:

[0037] Further, according to one embodiment of the method, the mathematical model is preferably or includes a pharmacometric, pharmacokinetic / pharmacodynamic (PKPD) model.

[0038] Furthermore, according to one embodiment of the method, the desired disease progression is given in the form of a mathematical function.

[0039] Further, according to one embodiment of the method, steps (b)-(c), and more particularly (b)-(d), are performed at each visit of a plurality of x subsequent visits of the patient, wherein for x>1, the patient data in step (b) includes all patient data from x-1 previous visit(s), and wherein the empirical Bayes estimation in step (b) further uses all doses of the at least one drug actually administered to the patient up to the current visit.

[0040] Furthermore, according to one embodiment of the method, at least a part of the algorithm performing steps (b)-(c), in particular (b)-(d), is approximated by an artificial neural network (ANN).

[0041] An artificial neural network (ANN) is a universal approximator and therefore can approximate any input / output relationship to a certain degree of accuracy, depending on the amount of available training data and the structure of the ANN. An ANN can therefore also approximate any algorithm to a certain degree of accuracy, i.e. it can learn the function of an algorithm and eventually imitate that algorithm. The advantage of a trained ANN is that it can compute the learned input / output relationships instantly on a standard computer and therefore can replace computationally time-consuming algorithms.

[0042] In particular, according to a preferred embodiment, steps (a)-(c), and optionally step (d), are approximated by an ANN.

[0043] Specifically, in contrast, in one embodiment, multiple simulations are performed for each part of the algorithm / step of the method that is to be replaced / approximated by an ANN, and these simulations are then used as training data for the ANN, and the resulting trained ANN is instead included in the iterative algorithm (or used in the method). Thus, the computational cost of some parts of the algorithm can be outsourced to the algorithm development by pre-training the ANN. This can significantly reduce the computational cost for daily clinical application.

[0044] Further, according to one embodiment of the method, the disease is one of: acquired hypothyroidism (autoimmune and non-autoimmune), acquired hyperthyroidism (autoimmune and non-autoimmune), congenital hypothyroidism, congenital hyperthyroidism.

[0045] Further, according to one embodiment of the method, the drug is levothyroxine (C 15 H 11 I4NO4, CAS number 51-48-9), Carbimazole (C7H 10 N2O2S, CAS number 22232-54-8), methimazole (C4H6N2S, CAS number 60-56-0), propylthiouracil (C7H 10 N2OS, CAS No. 51-52-5).

[0046] Further, according to one embodiment of the method, at least a portion of the patient data is measured by a wearable device worn by the patient.

[0047] The wearable device is one of: a watch, in particular a smartwatch, a mobile phone, in particular a smartphone. In particular, a smartphone comprises at least one processor configured to execute a computer program and a display for displaying information, the display being able to be a touchscreen forming part of the user interface. Similarly, a smartwatch in particular comprises at least one processor configured to execute a computer program and a display for displaying information, the display being able to be a touchscreen forming part of the user interface of the watch.

[0048] Furthermore, according to one embodiment of the method according to the invention, the patient data includes vital signs such as the patient's heart rate, and the patient's vital signs (e.g., heart rate) are measured by a wearable device. Other vital signs / physiological data that can be measured by the wearable device are at least one of: blood pressure (mmHg), body temperature (°C), respiratory rate (breaths / min), oxygen saturation, and step count (counts per day).

[0049] Yet another aspect of the present invention relates to a system for automatically determining an optimal personalized dosing regimen of at least one drug for a patient suffering from a known disease, optionally subject to at least one clinical constraint, the system comprising at least one processor configured to perform the steps of the method according to the present invention.

[0050] According to one embodiment of the system, the system further comprises a wearable device configured to measure at least a portion of said patient data. In particular, the wearable device can be configured to measure physiological data of the patient. In one embodiment, the wearable device can be configured to measure heart rate.

[0051] A computer program comprising instructions which, when executed on a computer or a system according to the invention, cause the computer (or the system) to perform the steps of the method according to the invention. In particular, the system or computer is adapted to receive patient data, in particular a heart rate (or another vital sign as described herein) measured by a wearable device, in particular for using said patient data in the method according to the invention as described herein.

[0052] A further aspect of the invention relates to a computer readable non-transitory storage medium having stored thereon a computer program according to the invention.

[0053] Moreover, a further aspect of the invention relates to a data carrier signal carrying a computer program according to the invention. Effect of the Invention

[0054] Further features and advantages of the invention as well as embodiments of the invention are explained below with reference to the drawings. [Brief description of the drawings]

[0055] [Figure 1A] Showing an overview of all components and the relationships between all components according to one embodiment of the present invention. (1)-(4) are four components of one embodiment of the method / algorithm according to the present invention. (A)-(G) are additional components that interact with components (1)-(4). [Figure 1B] 2 illustrates diagrammatically the steps of one embodiment of the method according to the invention; [Diagram 2] 1 shows a schematic representation of an iteration procedure over a number of visits performed by an embodiment of a method / algorithm according to the present invention, where x denotes the current visit. [Diagram 3]A schematic overview of four thyroid disease situations is shown as an example of the application of the present invention. The normal range of thyroid hormone (free thyroxine (FT4)) is marked by a horizontal shaded area S1, and the desired time interval for normalization of FT4 values ​​in all four thyroid diseases is highlighted by another shaded area. In congenital hyper- and hypothyroidism, FT4 should be within the upper limit of the normal reference range as quickly as possible, ideally within 2 weeks, to protect brain development. In acquired hyper- and hypothyroidism, FT4 values ​​should not increase or decrease too rapidly to avoid side effects of treatment, and ideally the normal reference range is achieved within 4-6 weeks. The desired FT4 increase or decrease is indicated by a dashed line L1 in each graph. Over- or underdosing is indicated by a solid line L2 above and below the normal range (horizontal shaded area S1). The drug for congenital and acquired hypothyroidism is levothyroxine, and for congenital and acquired hyperthyroidism are carbimazole, methimazole or propylthiouracil. a) Congenital hypothyroidism, b) Congenital hyperthyroidism, solid line L3 shows the most frequent delayed peak of hyperthyroidism between 4 and 10 days of age, c) Acquired hypothyroidism, d) Acquired hyperthyroidism. The interrupted time axis shows the initial correction period of hyperthyroidism and hypothyroidism as well as the long-term maintenance period of treatment. [Figure 4] 1 shows an example of an optimal individual dosing regimen calculated by the method / computer program according to the invention. [Diagram 5] 1 illustrates an iterative procedure according to an example of the present invention for acquired hyperthyroidism. [Figure 6] The improvement achieved by the present invention (right side) is now shown in terms of FT4 response compared to standard dose calculations (left side). DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0056] Components of an embodiment of the method / algorithm according to the invention The algorithm, in detail, consists of four components (FIG. 1A; (1)-(4)) and their interactions. In addition, all additional components that interact with components (1)-(4) are shown in FIG. 1A; (A)-(G). A description of all four components and their input / output relationships is presented below and in FIG. 1A.

[0057] Application of mathematical model (Figure 1A; (1)) The development of the mathematical model can be performed in two different ways. First, a mathematical model is already available. This mathematical model can then be applied in our algorithm and the steps in this paragraph are skipped. Second, such a mathematical model is not available and therefore needs to be developed as follows: input: 1) Basic mathematical model 2) Nonlinear mixed-effects modeling approach 3) Retrospective patient data from the population output: 1) Mathematical model

[0058] Application of empirical Bayes estimation (Figure 1A; (2)) Empirical Bayes estimation estimates personal model parameters for new patients based on the mathematical model and their individual patient data. input: 1) Mathematical model 2) New patient data output: 1) New patient's personal model parameters

[0059] Application of optimal control algorithms (Fig. 1A; (3)) The optimal control problem is specifically solved in the OptiDose algorithm, which calculates the optimal dosing regimen for an individual patient. input: 1) Mathematical model 2) New patient's personal model parameters 3) the desired disease progression provided by a mathematical function 4) Dosage regimen output: 1) Optimal individual dosing regimen

[0060] Optionally, if specifically indicated: adjustment of the optimal individual dosing regimen subject to clinical constraints (Figure 1A; (4)) In a subsequent step, the optimal individual dosing regimen is adjusted to accommodate constraints in clinical application, such as limitations due to available tablet sizes. input: 1) Mathematical model 2) New patient's personal model parameters 3) the desired disease progression provided by a mathematical function 4)Clinical constraints 5) Optimal individual dosing regimen output: 1) Optimal individual dosing schedule subject to clinical application constraints

[0061] In particular, the present invention combines mathematical models, empirical Bayesian estimation, optimal control algorithms and, optionally, the inclusion of constraints in clinical applications, to calculate optimal personalized dosing regimens for patients subject to said constraints.

[0062] The method / algorithm according to the invention is an iterative procedure over a number of visits (Figure 2). At every visit, an optimal personalized dosing plan, optionally subject to clinical constraints, is calculated by running one iteration of the algorithm. This optimal personalized dosing plan remains valid until the next scheduled visit.

[0063] Running one iteration of the algorithm at a visit Step 1) "Estimate personal model parameters": Based on the available patient data from the current and past visits, and the dosage administered up to the current visit (Figure 1A; (A)-(D)), estimate the patient's personal model parameters φ i (Figure 1A; (E)) is estimated using an empirical Bayesian estimation method that utilizes a mathematical model (Figure 1A; (1)-(2)). Step 2) “Optimal individual dosing schedule”: The estimated individual model parameters (Figure 1A; (E)) are applied to calculate the optimal individual dosing schedule (Figure 1A; (1), (3), (F), (G)) for the time period until the next scheduled visit. Step 3) (Optional) "Optimal individual dosing plan subject to clinical constraints": The optimal individual dosing plan (Figure 1A; (3)) is adjusted to accommodate constraints in clinical application (Figure 1A; (4), (E), (F), (G)).

[0064] These steps are repeated iteratively for every visit. During the first visit in this iterative process, only the information from this visit is applied.

[0065] In a preferred embodiment of the invention, the individual aspects of the invention (in particular the methods, systems and computer programs according to the invention) are applied to thyroid diseases in children and adults.

[0066] As already indicated above, thyroid hormones are crucial for normal brain development, growth and puberty. However, the treatment of the rare thyroid disorders congenital hypothyroidism (absent or too low thyroid hormone production) and childhood-onset Graves' disease (too high thyroid hormone production) is challenging. First, a carefully selected starting dose based on clinical experience is required. Second, after reaching a physiological balance of thyroid hormones, continuous adjustment of the individual dosage according to age, weight and disease severity is required to maintain euthyroidism. To reduce the risk of poor neurological outcome, it is important to establish an optimal, individual dosing strategy that is continuously fine-tuned to absorb the specific needs in neonates, infants and children with hyper- or hypothyroidism.

[0067] In particular, in one embodiment of the present invention, the disease for which the optimal dosing regimen is to be determined is one of the following four thyroid diseases that provide solutions to the current medical problems formulated in the introduction:

[0068] According to one embodiment, as mentioned above, an artificial neural network (ANN) can be included in the approach in order to calculate the optimal individual dosing regimen within a few seconds, in particular within a few seconds. In other words, an ANN can be used to accelerate the method, system and / or computer program / algorithm according to the invention, but is not essential to the invention (see, for example, FIG. 1; (1), (3), (F), (G) and especially step c) of the method according to the invention).

[0069] As an example, consider a given disease characterized by a given mathematical model. Then, a sufficient number of patients, each represented by their own individual model parameters, are sampled from the given mathematical model to characterize the entire patient population with said disease. For every individual patient in this population, an optimal dosage can be calculated. Then, an ANN is trained using the individual model parameters as input and the optimal dosage as output. Thus, the trained ANN calculates the optimal dosage for the given individual model parameters. This trained ANN can replace step 2) "optimal individual dosage plan": (Figure 1A; (1), (3), (F), (G)) and claim 1(c), respectively.

[0070] As an example, the parameterization θ = (R 0 ,k in ,E max ,EC 50 ) The indirect reaction model is used as the basic mathematical model.

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[0071] A sufficient number n sufindividual patients are sampled from the population parameter ρ to cover a larger dimensional space with all kinds of individual parameter combinations. As an example, consider the following table: [Table 1]

[0072] For all these individual parameters, an optimal individual dosing plan (step 2 or claim 1c) is calculated, optionally absorbing at least one clinical constraint (step 3 or claim 1d) according to the determined dosing plan, contrasting section "Optimal control problem". In this example, six doses d=(D1,...,D6) for six subsequent time units are calculated to obtain the following data set, contrasting the following table: [Table 2]

[0073] This constructed dataset is divided into training, validation and test datasets to develop the ANN. The input of the ANN is the individual model parameters (R 0 ,k in ,E max ,EC 50 ), and the output of the ANN is the optimal dose d = (D1, ..., D6) from the optimal personalized dosing schedule. Thus, this trained ANN can replace step 2) "optimal personalized dosing schedule": (Figure 1A; (1), (3), (F), (G)) and claim 1(c), respectively.

[0074] For a new patient with new individual measurements, new estimated individual model parameters φ serve as inputs for the ANN. i Empirical Bayesian estimation is applied to calculate the optimal individualized dosing schedule. The ANN is then applied to calculate the optimal individualized dosing schedule. Thus, step 2) "optimal individualized dosing schedule": (FIG. 1A; (1), (3), (F), (G)) and claim 1(c) are each replaced by the ANN.

[0075] Patients with congenital hypothyroidism: For congenital hypothyroidism, artificially produced T4 hormone (e.g., levothyroxine, produced in different herbal forms (e.g., tablets, drops) by different pharmaceutical companies) is administered as replacement therapy to normalize thyroid hormones (T3, FT3, T4, FT4, TSH) to the normal reference range. The generic concept from the main claim is applied to this disease area for pediatric patients from birth. A mathematical model for congenital hypothyroidism with levothyroxine replacement therapy was published by us in 2021 [Koch 2021].

[0076] Patients with acquired hypothyroidism: Similar to congenital hypothyroidism, acquired hypothyroidism in children, pregnant women, and adults can be modeled using the same approach.

[0077] Patients with acquired hyperthyroidism: For acquired hyperthyroidism, in pediatric and adult patients, two different treatments are applied in clinical practice to normalize thyroid hormones (T3, FT3, T4, FT4, TSH) to the normal reference range: 1) Administration of antithyroid drugs alone (e.g., carbimazole) to suppress excess thyroid hormone production 2) Concomitant administration of antithyroid drugs (e.g., carbimazole) to suppress thyroid function and levothyroxine as replacement therapy to increase T4 hormone.

[0078] So far, the dosing of carbimazole, with or without simultaneous levothyroxine, is based on laboratory tests of thyroid hormones T3, FT3, T4, FT4, and TSH. A new approach would be the use of the patient's heart rate, a well-established and very sensitive clinical sign for too high levels of thyroid hormones. Patients diagnosed with hyperthyroidism always have too high heart rate values, which only normalize over a few weeks when thyroid hormone levels return to the normal range with carbimazole treatment. Heart rate is monitored with the aid of a wearable device. This allows to establish a relationship between FT4 and heart rate, with the goal of providing medical advice and drug administration remotely (telemedicine) based on resting heart rate, without the need for consultations and blood tests. This approach would be important, especially in remote areas and in low- and middle-income countries where laboratory tests are not available everywhere.

[0079] Patients with congenital hyperthyroidism: Similar to acquired hyperthyroidism, congenital hyperthyroidism in children can be modeled by the same approach.

[0080] Example of a mathematical model for congenital hypothyroidism A mathematical model for levothyroxine treatment and the resulting FT4 concentrations is presented [Koch 2021]. Due to replacement therapy, the model can be considered a pure PK model. A one-compartment model with an absorption compartment and an additional endogenous generation term was developed:

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[0081] Estimated individual model parameters

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[0082] Example of a mathematical model for acquired hyperthyroidism A mathematical model for carbimazole treatment, additional block and replace (combination with levothyroxine) therapy, and the resulting free thyroxine (FT4) concentrations is presented. Structurally, this can be considered as a PKPD model, where PK is the methimazole (metabolized carbimazole) concentration resulting from carbimazole treatment, and PD is the FT4 biomarker. The developed model is applicable to both carbimazole monotherapy and block and replace therapy.

[0083] Carbimazole is a prodrug and several PK properties are known, including distribution, metabolism, etc. A detailed carbimazole PK model is presented.

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[0084] Amount of carbimazole in the central compartment A C teeth,

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[0085] Methimazole concentration C M The inhibitory effect of carbimazole on the endogenous T4 production rate by (t) was

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[0086] Estimated individual model parameters

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[0087] The continuous and time-dependent weight W(t) can be modeled, for example, by a weight gain model given by a mathematical function, e.g., the Leffler function for newborns and infants, depending on additional model parameters that can be estimated using the weight measurements or as time-varying covariates with interpolation between weight measurements.

[0088] Finally, FIG. 4 shows a schematic example of an optimal individual dosing regimen calculated by the method / computer program according to the invention.

[0089] The desired disease progression (left panel, solid curve B1) and the resulting biomarker concentrations (left panel, solid curve B2) are shown for the calculated optimal individual dosing regimen (right panel, crosses). The solid line C1 is the corresponding drug concentration resulting from the optimal individual dosing regimen.

[0090] In the following further aspects of the invention and embodiments thereof, they are set out as clauses, which may however also be explicitly set out as claims in the present application.

[0091] Item 1: A method for determining an optimal personalized dosing regimen of at least one drug for a patient suffering from a known disease, the method comprising: (a) providing a mathematical model adapted to model disease progression of said disease and the effect of at least one drug on disease progression, the model including individual model parameters associated with a patient; (b) using empirical Bayesian estimation to estimate individual model parameters of a mathematical model that utilizes patient data; (c) calculating an optimal individual dosing regimen for the mathematical model by solving an optimal control problem based on the desired disease progression, the estimated individual model parameters, and an initial guess for the dosing regimen; The method includes the step of:

[0092] Item 2: A method according to item 1, comprising: (d) adjusting the optimal individualized dosing regimen to accommodate at least one clinical constraint to yield an optimal individualized dosing regimen subject to said at least one clinical constraint. The method further includes the step of:

[0093] Item 3: The method according to items 1 or 2, wherein the mathematical model is a pharmacokinetic / pharmacodynamic (PKPD) model.

[0094] Item 4: A method according to one of the preceding items, wherein the desired disease progression is given in the form of a mathematical function.

[0095] Item 5: A method according to one of the preceding items, wherein steps (b)-(c), in particular steps (b)-(d), are performed at each visit of a plurality of x subsequent visits of the patient, wherein for x>1, the patient data in step b) includes all patient data from x-1 previous visit(s), and the empirical Bayes estimation in step b) further uses all doses of the at least one drug actually administered to the patient up to the current visit.

[0096] Item 6: A method according to one of the preceding items, wherein at least a part of the algorithm for performing steps (b)-(c), in particular steps (b)-(d), is approximated by an artificial neural network (ANN).

[0097] Item 7: A method according to one of the preceding items, wherein the disease is one of: acquired hypothyroidism, particularly autoimmune and / or non-autoimmune; acquired hyperthyroidism, particularly autoimmune and / or non-autoimmune; congenital hypothyroidism, congenital hyperthyroidism.

[0098] Item 8: The method according to one of the preceding items, wherein the drug is selected from the group consisting of levothyroxine, carbimazole, and propylthiouracil.

[0099] Item 9: A method according to one of the preceding items, wherein at least a portion of the patient data is measured by a wearable device worn by the patient.

[0100] Item 10: The method according to item 9, wherein the wearable device is one of a wristwatch, particularly a smartwatch, and a mobile phone, particularly a smartphone.

[0101] Item 11: The method according to item 9 or 10, wherein the patient data includes a heart rate, and the patient's heart rate is measured by a wearable device.

[0102] Item 12: A system for determining an optimal personalized dosing regimen of at least one drug for a patient suffering from a known disease, the system including at least one processor configured to perform the steps of a method according to one of the preceding items.

[0103] Item 13: The system according to item 12, further comprising a wearable device configured to measure at least a portion of the patient data.

[0104] Item 14: A computer program comprising instructions which, when executed on a system according to item 12 or 13, cause the system to carry out a method according to one of items 1 to 11.

[0105] Item 15: A computer-readable non-transitory storage medium having stored thereon a computer program according to item 14.

[0106] Item 16: A data carrier signal carrying the computer program of item 14.

[0107] References [Polak 2017]:Polak M,Refetoff,S,Szinnai G,van Vliet G.Part III:Thyroid Gland Disorders.Pediatric Endocrinology and Inborn Errors of Metabolism.Editors:K.Sarafoglou,GFHoffmann,KSRoth,McGraw-Hill Education,New York,2nd Edition,2017,pp.481-512

[0108] [Leger 2014]:Leger J,Kaguelidou F,Alberti C,Carel JC.Graves'disease in children.Best Pract Res Clin Endocrinol Metab.2014;28(2):233-243

[0109] [Belotti 2013]:Belotti P et al.(2013)Mixed-integer nonlinear optimization.Acta Numerica 22:1-131

[0110] [Lavielle 2014]:Lavielle M(2014)Mixed effects models for the population approach:models,tasks,methods and tools.Chapman & Hall / CRC Biostatistics Series Book 66

[0111] [Bassett 2018]:Bassett R,Deride J(2019)Maximum a posteriori estimators as a limit of Bayes estimators.Mathematical Programming 174:129-144

[0112] [Bachmann 2021]:Bachmann F,Koch G,Pfister M,Szinnai G,Schropp J(2021)OptiDose:computing the individualized optimal drug dosing regimen using optimal control.Journal of Optimization Theory and Applications 189:46-65

[0113] [Koch 2021]:Koch G et al.(2021)Modeling of levothyroxine in newborns and infants with congenital hypothyroidism:challenges and opportunities of a rare disease multi-center study.J Pharmacokinet Pharmacodyn 48(5):711-723

Claims

1. A computer-implemented method for determining an optimal personalized dosing regimen of at least one drug for a patient suffering from a known disease associated with a disease progression model that follows a nonlinear mixed-effects modeling approach, referred to as the NLME modeling approach, said method comprising: (a) accessing a mathematical model adapted to model disease progression of said disease, said mathematical model comprising a base mathematical model involving the application of an NLME modeling approach to describe a given population of patients by their population parameters, covariates, and parameter distributions, said base mathematical model being a pharmacokinetic or pharmacokinetic / pharmacodynamic model characterized by one or more differential equations including disease state as a variable characterizing disease progression; (b) calculating estimated individual model parameters for patients belonging to the given population by maximizing an individual conditional probability density function having the population parameters and patient data of the patients based on patient data and the mathematical model using empirical Bayes estimation; (c) calculating an optimal personalized dosing regimen for the patient by solving an optimal control problem using an optimal control algorithm by minimizing a cost functional that characterizes the difference between a disease state and a desired disease progression based on the mathematical model and the patient's personal model parameters, and starting from an initial control corresponding to an initial guess for the dosing regimen; comprising the step of: method.

2. (d) adjusting an optimal individualized dosing plan between two available doses taking into account at least one clinical constraint, by rounding to the nearest available dose size, or by selecting the higher or lower available dose based on the lower corresponding cost functional value, thereby resulting in said optimal individualized dosing plan subject to at least one clinical constraint. The method of claim 1 further comprising:

3. The method of claim 1 , wherein the desired disease progression is given in the form of a mathematical function.

4. 10. The method of claim 1, wherein at least a portion of the algorithm that performs steps (b)-(c) is approximated by an artificial neural network (ANN).

5. 2. The method of claim 1, wherein the disease is one of acquired hypothyroidism, particularly of the autoimmune and / or non-autoimmune type, acquired hyperthyroidism, particularly of the autoimmune and / or non-autoimmune type, congenital hypothyroidism, congenital hyperthyroidism.

6. 10. The method of claim 1, wherein the at least one drug is selected from the group consisting of levothyroxine, carbimazole, and propylthiouracil.

7. The method of claim 1 , wherein at least a portion of the patient data is measured by a wearable device worn by the patient.

8. The method of claim 7 , wherein the wearable device is one of a wristwatch, particularly a smartwatch, and a mobile phone, particularly a smartphone.

9. The method of claim 7 or claim 8, wherein the patient data includes a heart rate, and the heart rate of the patient is measured by the wearable device.

10. A computer system for determining an optimal personalized dosing regimen of at least one drug for a patient suffering from a known disease associated with a disease progression model according to a nonlinear mixed-effects modeling approach, the system comprising at least one processor configured to perform the steps of a computer-implemented method according to claim 1.

11. The system of claim 10 , wherein the system further comprises a wearable device configured to measure at least a portion of the patient data.

12. A computer program product for determining an optimal personalized dosing regimen of at least one drug for a patient suffering from a known disease associated with a disease progression model according to a nonlinear mixed-effects modeling approach, the computer program product including instructions that, when executed on the system according to claim 10, cause the system to perform the method according to claim 1.

13. A computer-readable non-transitory storage medium having stored thereon the computer program according to claim 12.

14. 13. A data carrier signal carrying the computer program of claim 12.

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