Methods, systems, and computer programs for calculating optimal individual dosing plans, especially those constrained by clinical limitations.

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 administration plan for at least one drug to a patient suffering from a known disease. [Background technology]

[0002] Treating most diseases at the individual level remains challenging because disease progression varies among patients and clinical settings. More specifically, determining the optimal individualized treatment plan—particularly in a clinical setting—in a sufficiently rapid and reliable manner to ideally enable control of disease progression, leading to patient recovery while minimizing treatment-related adverse events, is often still a challenge.

[0003] In detail, among these disorders, congenital hypothyroidism is the most common congenital endocrine disorder globally and the most common preventable cause of intellectual disability [Polak 2017]. The severity of the disorder varies greatly from person to person at the time of diagnosis, with thyroid-stimulating hormone (TSH) levels ranging from 6 to 1200 mU / L, while the standard range is 0.5–5 mU / L. The main effects of thyroid hormones are axonal growth and myelin formation of interneurons, processes that are ongoing in humans, primarily after birth. Neonatal screening allows for the diagnosis of children with congenital hypothyroidism before they suffer from clinical signs and irreversible neurological defects. Over the past 40 years, neurological outcomes for patients with congenital hypothyroidism have been significantly improved by 1) shortening the time window between screening and treatment initiation (currently 4-5 days in Switzerland) and 2) increasing the initial dose of levothyroxine (from 5-8 mcg / kg / day to 10-15 mcg / kg / day). The goal of alternative therapy with levothyroxine is to correct hypothyroidism as quickly as possible to protect brain development. Clinicians aim for free thyroxine (T4) levels to reach 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 were overdosed on initial and maintenance doses of 10-15 mcg / kg / day for longer than the appropriate duration. Furthermore, at age 11, their neurological outcomes were comparable to those of children with periods of underdose during follow-up, and both children with overdose and underdose had poorer neurological outcomes compared to children with levothyroxine doses that maintained thyroid hormone levels within the reference range during follow-up.

[0004] Current international guidelines recommend more frequent monitoring during the first two years of life to maintain thyroid hormone levels within the physiologically normal reference range, allowing for more frequent and necessary adjustments to the individual's age-appropriate dosage. This allows for faster detection of overdoses and underdoses, but it does not prevent episodes of suboptimal dosage. Consequently, the final step to improving neurological outcomes in affected patients should focus on optimizing alternative dosing over the long term by considering clinical and research data for individualized dosing during follow-up. Therefore, being able to determine the optimal individualized dosing during the first two years of life is particularly desirable, as it is essential for brain development and long-term normal cognitive function. Central congenital hypothyroidism is a subgroup of congenital hypothyroidism with low TSH and FT4 levels resulting from pituitary and hypothalamic dysfunction, treated in the same manner with levothyroxine.

[0005] Furthermore, congenital hyperthyroidism occurs in approximately 10% of newborns of mothers with autoimmune hyperthyroidism (Graves' disease), resulting from the placental transfer of stimulating antibodies against thyroid-stimulating hormone (TSH) receptors. It exposes infants to significant risk of morbidity and mortality. In contrast to infants with congenital hypothyroidism, who are asymptomatic in about 95% of cases 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 fever, epileptic seizures, and heart failure. Onset can occur immediately after birth or be delayed until 4-10 days postpartum due to the placental transfer of maternal antithyroid medications. Again, the severity of the disease varies greatly, from extremely mild forms to life-threatening complications. Delayed onset further complicates optimal treatment, necessitating clinical observation and laboratory monitoring at 1, 4, 7, 10, and 14 days postnatally.

[0006] Furthermore, for congenital hyperthyroidism, it is highly desirable to optimize 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 that are appropriate for disease severity, given the potential for serious side effects of antithyroid drugs (agranulocytosis, hepatitis, vasculitis) (see Figure 3(b)).

[0007] Furthermore, acquired hyperthyroidism [Leger 2014] occurs in Europe at a rate of 0.5–2:100,000 in children and 25–90:100,000 in adults, with the highest prevalence in Brazil, China, and India, affecting 0.75–1.25% of the population, respectively. Similarly, the severity of hyperthyroidism varies greatly from person to person at diagnosis, with FT4 levels ranging from 22–100+ pmol / L, compared to the standard 11–21 pmol / L. Recovery of physiological FT4 levels should be achieved within 4–6 weeks, in contrast to congenital thyroid disorders, where normalization should be aimed for as quickly as possible. The simple treatment previously involved block and replace therapy: dosages of antithyroid drugs were selected to completely block the thyroid, with the addition of levothyroxine as a substitute. According to international guidelines, in situations where the frequency of side effects (agranulocytosis, hepatitis, vasculitis) associated with higher doses of antithyroid drugs increases, such approaches are no longer recommended according to international guidelines. Currently, the minimum effective dose of antithyroid drugs needs to be determined at the individual level to mitigate the risk of overdose causing iatrogenic hypothyroidism or underdose causing persistent hyperthyroidism. Both hyperthyroidism and hypothyroidism negatively affect growth and adolescent development (delayed or accelerated, respectively), as well as cognitive function, leading to decreased academic and athletic performance. Finally, because the complexity increases further in childhood, the disease course is more severe in younger or pre-adolescent children compared to older (10 years and older) or adolescents and post-adolescent children, and the risk of hyperthyroidism recurrence is much higher, making childhood Graves' disease a treatment challenge.

[0008] Regarding Graves' disease as well, a treatment method that enables calculation of an optimal individual starting dose according to clinical and laboratory parameters in order to avoid recurrence during follow-up after reaching a steady state and a minimum effective maintenance dose is highly desirable (see Fig. 3(d)).

[0009] Moreover, hypothyroidism is common worldwide, with a prevalence in Europe of 0.2 - 5.3% of the adult population. The most common cause of acquired hypothyroidism is Hashimoto's thyroiditis in iodine-sufficient regions of the world. The goal of treatment for acquired hypothyroidism (incidence rate of 1.2%) is to slowly normalize the free T4 level and avoid signs and symptoms of hyperthyroidism after long-term hypothyroidism. As with other diseases, optimal starting and maintenance doses are necessary to normalize physical growth, cognitive function, and as a result academic performance, but without over-dosing pediatric patients (see Fig. 3(c)). Furthermore, central hypothyroidism caused by disorders of the pituitary and hypothalamus (e.g., in particular, trauma, tumors, infections) can cause a further form of acquired hypothyroidism. Summary of the Invention Problems to be Solved by the Invention

[0010] In summary, based on the above, the problem to be solved by the present invention is, in particular, to provide a method, a system, a computer program, a computer-readable persistent storage medium, and a data carrier signal that enable improvement of individualized dosing determination for pediatric thyroid diseases. Improving the treatment and outcome of affected patients due to the severity of such diseases is clinically highly appropriate. Means for Solving the Problems

[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 persistent 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 present invention are described below, as set forth in the corresponding dependent claims.

[0013] According to claim 1, a method for automatically determining an optimal individualized dosing plan for at least one drug in a patient suffering from a disease (e.g., a neonatal, infant, child, adolescent, or adult), wherein the optimal individualized dosing plan is subject to at least one clinical constraint, and the method is (a) Providing a computer-implemented mathematical model adapted to model (more specifically characterize and predict) the disease progression of the disease and, in particular, the effect of at least one drug on the disease progression, the model comprising a personal model (or clinical routine) parameter associated with a given patient (more specifically, a given disease, its severity and progression, and the applied dosing regimen), (b) The step of using empirical Bayesian estimation to automatically and numerically estimate the personal model parameters of a mathematical model using patient data of a given patient, in particular, personal medication information, (c) The steps include automatically calculating the optimal individual dosing plan for a mathematical model by solving the optimal control problem based on the desired disease progression, estimated individual model parameters, and initial estimations for the dosing plan, (d) A step of adjusting an optimal individual dosing plan to absorb at least one clinical constraint to obtain an optimal individual dosing plan conditioned on the at least one clinical constraint. Includes, Steps (b) to (d) are performed at each of the patient's multiple subsequent visits, where for x > 1, the patient data in step b) includes patient data from the previous x-1 visits, and the empirical Bayesian 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] Conveniently, the present invention enables personalized administration to elevate drug therapy to the next level. For many diseases, and more specifically for hyperthyroidism or hypothyroidism, no new pharmacological approaches have been developed, and improvements in determining individualized dosing plans are key to improving treatment outcomes.

[0015] More specifically, as outlined above and shown in Figure 3, the present invention is particularly applicable to the modeling of different clinical symptoms that need to be modeled separately in order to develop disease-specific algorithms for initiation and maintenance administration.

[0016] The following concepts and definitions are frequently referred to within the framework of this invention.

[0017] patient A 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's visit may occur (i) at any point in time for the subject, (ii) at the time of a non-inpatient's outpatient visit to the hospital, or (iii) at the time when a clinician sees an inpatient at the 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 (beats per minute), oxygen saturation, and steps (counts per day).

[0020] Laboratory measurement Laboratory testing is a routine biochemical examination of biomarkers (e.g., hormones) that are analyzed in a medical laboratory or by a healthcare professional such as a physician, nurse, medical assistant, or pharmacist. In the case of thyroid hormones, one hormone is synthesized and secreted by the pituitary gland (thyroid-stimulating hormone, or thyroid-stimulating hormone (TSH) for the pituitary-thyroid axis), and peripheral hormones are secreted by the thyroid gland (thyroxine (T4) and triiodothyronine (T3) in bound (T3, T4) and free (FT3, FT4) forms, which are endocrine glands under the control of the pituitary gland).

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

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

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

[0024] Pharmacokinetic models Pharmacokinetic (PK) models describe the concentration of a drug (or, for example, its metabolites) or exogenous substance through processes such as absorption, distribution, metabolism, and elimination. The route of drug administration can be (i) orally, (ii) intravenously, or (iii) subcutaneously. PK models are typically characterized by one or more differential equations.

[0025] Pharmacokinetic / pharmacodynamic models Pharmacokinetic / pharmacodynamic (PKPD) models describe the response of biomarkers or disease progression (so-called pharmacodynamics) caused by the stimulative / inhibitory effects of one or more drugs, as characterized by PK models. For combinations of several drugs, the drugs can be administered simultaneously or sequentially. PKPD models are typically characterized by one or more differential equations.

[0026] Basic mathematical models The basic mathematical model can be a PK model only, 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 the dosage of one or more drugs. 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. The disease state is one state variable or a combination of several state variables in the basic mathematical model that characterizes disease progression.

[0027] Personal Model Parameters The individual model parameters are θ i This summarizes and characterizes individual patients based on their personal data. Index i represents the i-th individual in a population of N patients, i.e., i=1,...,N. All or some of the model parameters may have physiological, biological, or other meanings. For example, model parameters may describe the rate of a process (e.g., generation or discharge), the volume of a compartment, or have other meanings.

[0028] Desirable disease progression The desirable disease progression is defined by the clinician / user and characterizes the goal for the individual patient. For example, for a patient being treated with a drug and showing an increase in a biomarker, the goal is to normalize that biomarker value to a normal (age-specific) reference range within a given time. Or, in the case of a PK model, the desirable disease progression might be a goal related to drug exposure, e.g., reaching a certain region under the concentration curve. The desirable disease progression under drug therapy is characterized by a mathematical function.

[0029] Dosage plan A drug administration plan is information regarding the administration of one or more drugs. It includes the drug(s) themselves, the route of administration (oral, intravenous, subcutaneous), the timing of administration, and the dosage.

[0030] Optimal Individual Dosage Plan An optimal individualized dosing plan is one that contains the optimal dosage for each individual patient (in relation to the desired disease progression).

[0031] Optimal individualized dosing plans subject to clinical application constraints An optimal individual dosing plan, constrained by clinical application limitations, is an optimal individual dosing plan adjusted for those constraints. This could be, for example, the available tablet size. Different strategies may be used to adjust the optimal dosage between two available dosing sizes, for example, 1) Round to the nearest available dose size, or 2) Select the higher or lower available dose based on the lower corresponding cost functional value (as seen in mixed-integer optimization [Belotti 2013]), This can be applied.

[0032] Nonlinear mixed-effects modeling approach In the non - linear mixed - effect (NLME) modeling approach [Lavielle 2014], patients with the same disease are assumed to form a population with common or similar characteristics. For each individual \(i\), at time points

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[0033] Mathematical model The mathematical model is a fundamental mathematical model that describes a given population of patients by its population parameter ρ, along with the application of the NLME modeling approach. Such a mathematical model is therefore sometimes also referred to as a fully developed mathematical model.

[0034] Empirical Bayesian estimation Empirical Bayesian estimation, also known as maximum posterior estimation [Bassett, Deride 2019], estimates time t for an individual i belonging to a population with population parameter ρ. i Measurements observed in w i The estimated individual model parameter φ is most likely to predict i We calculate this. Mathematically, the conditional probability density function.

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[0035] Optimal control problem The optimal control problem is solved by calculating a control (i.e., the dosage of one or more drugs) such that one state variable or a combination of state variables in a mathematical model (e.g., a patient's condition) comes as close as possible to a desired disease progression. This is achieved by minimizing the cost functional that characterizes the difference between the condition resulting from a particular control and the desired disease progression. The optimal control problem can be solved by 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, optimization is an iterative procedure that (i) starts with an initial control, (ii) solves a mathematical model to obtain the disease state, (iii) solves the adjoint equations (associating the disease state with the cost functional), and (iv) updates the control using the gradient of the cost functional. Steps (iii) to (iv) are repeated in each iteration.

[0036] According to a preferred embodiment of the method in accordance with the present invention, the method is (d) Adjusting the optimal individual dosing plan to absorb at least one clinical constraint to result in an optimal individual dosing plan conditioned on the at least one clinical constraint. This further includes the step of performing the following:

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

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

[0039] Furthermore, according to one embodiment of the present method, steps (b) to (c), more specifically (b) to (d), are performed at each of several subsequent visits of the patient, where for x > 1, the patient data in step (b) includes all patient data from the previous x-1 visits, and the empirical Bayesian estimation in step (b) further uses all the doses of the at least one drug actually administered to the patient up to the current visit.

[0040] Furthermore, according to one embodiment of this method, at least part of the algorithm that performs steps (b) to (c), and more specifically (b) to (d), is approximated by an artificial neural network (ANN).

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

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

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

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

[0045] Furthermore, according to one embodiment of this method, the drug is levothyroxine (C) for the treatment of any type of hypothyroidism. 15 H 11 I4NO4, CAS number 51-48-9), carbimazole (C7H) for the treatment of any type of hyperthyroidism. 10 N2O2S, CAS number 22232-54-8), Methimazole (C4H6N2S, CAS number 60-56-0), Propylthiouracil (C7H 10 It is selected from the group consisting of N2OS (CAS numbers 51-52-5).

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

[0047] Wearable devices include: a wristwatch, more specifically a smartwatch, a mobile phone, and more specifically a smartphone. More specifically, a smartphone includes at least one processor configured to run computer programs and a display for displaying information, the display may be a touchscreen that forms part of the user interface. Similarly, a smartwatch, in particular, includes at least one processor configured to run computer programs and a display for displaying information, the display may be a touchscreen that forms part of the user interface of the watch.

[0048] Furthermore, according to one embodiment of the method according to the present 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 sign / physiological data that can be measured by the wearable device are at least one of the following: blood pressure (mmHg), body temperature (°C), respiratory rate (rates / minute), oxygen saturation, and steps (counts per day).

[0049] A further aspect of the present invention relates to a system for automatically determining an optimal individualized dosing plan (optionally subject to at least one clinical constraint) for a patient suffering from a known disease, the system comprising at least one processor configured to perform steps of a method according to the present invention.

[0050] According to one embodiment of the system, the system further includes a wearable device configured to measure at least a portion of the patient data. More specifically, the wearable device may be configured to measure the patient's physiological data. In one embodiment, the wearable device may be configured to measure heart rate.

[0051] A computer program including instructions, which, when executed on a computer or a system according to the present invention, causes the computer (or system) to perform steps of a method according to the present invention. More specifically, the system or computer is configured to receive patient data, more specifically, heart rate (or other vital signs as described herein) measured by a wearable device, in particular for using the said patient data in a manner according to the present invention as described herein.

[0052] A further aspect of the present invention relates to a computer-readable persistent storage medium on which a computer program according to the present invention is stored.

[0053] Furthermore, yet another aspect of the present invention relates to a data carrier signal for carrying a computer program according to the present invention. [Effects of the Invention]

[0054] Further features and advantages of the present invention, as well as embodiments of the present invention, will be described below with reference to the drawings. [Brief explanation of the drawing]

[0055] [Figure 1A] This shows an overview of all components according to one embodiment of the present invention and the relationships between all components. (1) to (4) are four components of one embodiment of the method / algorithm according to the present invention. (A) to (G) are additional components that interact with components (1) to (4). [Figure 1B] The steps of one embodiment of the method according to the present invention are schematically shown. [Figure 2] This diagram schematically illustrates an iterative procedure over a number of visits performed by one embodiment of the method / algorithm according to the present invention, where x represents the current visit. [Figure 3]A schematic overview of four thyroid disease conditions 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 desirable time interval for normalization of FT4 values ​​in all four thyroid diseases is highlighted by another shaded area. In congenital hyperthyroidism and hypothyroidism, FT4 should be brought to the upper limit of the normal reference range as quickly as possible, ideally within two weeks, to protect brain development. In acquired hyperthyroidism and hypothyroidism, FT4 values ​​should not increase or decrease too rapidly to avoid treatment side effects, and ideally the normal reference range should be achieved within four to six weeks. Desired increases or decreases in FT4 are indicated by dashed lines L1 in each graph. Excess or underdosing is indicated by solid lines L2 above and below the normal range (horizontal shaded area S1). The drug for congenital and acquired hypothyroidism is levothyroxine, and the drugs for congenital and acquired hyperthyroidism are carbimazole, methimazole, or propylthiouracil. a) Congenital hypothyroidism, b) Congenital hyperthyroidism, the solid line L3 shows the most frequent delayed peak of hyperthyroidism between 4 and 10 days postnatology, c) Acquired hypothyroidism, d) Acquired hyperthyroidism. The interrupted time axis shows the initial correction period and the long-term maintenance period of treatment for hyperthyroidism and hypothyroidism. [Figure 4] An example of an optimal individual dosage plan calculated by a method / computer program according to the present invention is shown. [Figure 5] An example of a repeatable procedure according to the present invention relating to acquired hyperthyroidism is shown. [Figure 6] The improvements achieved by the present invention (right side) are shown here with respect to the FT4 response compared to standard dose calculations (left side). [Modes for carrying out the invention]

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

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

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

[0059] Application of the optimal control algorithm (Figure 1A; (3)) The optimal control problem is solved, in detail, by the OptiDose algorithm, which calculates the optimal dosage plan for each individual patient. input: 1) Mathematical model 2) New patient individual model parameters 3) Desired disease progression provided by mathematical functions 4) Dosage plan output: 1) Optimal individual dosage plan

[0060] Optional, and especially when necessary: ​​Adjustment of the optimal individual dosage plan based on clinical constraints (Figure 1A; (4)) In the post-hoc step, an optimal individualized dosing plan is adjusted to address limitations in clinical application, such as those arising from available tablet sizes. input: 1) Mathematical model 2) New patient individual model parameters 3) Desired disease progression provided by mathematical functions 4)Clinical constraints 5) Optimal individual dosage plan output: 1) Optimal individualized dosing plans subject to clinical application constraints

[0061] More specifically, the present invention combines mathematical models, empirical Bayesian estimation methods, optimal control algorithms, and, at an option, the inclusion of constraints in clinical application, to calculate an optimal individualized dosing plan for patients subject to said constraints.

[0062] The method / algorithm according to the present invention is an iterative procedure over the number of visits (Figure 2). For each visit, an optimal individual dosage plan, subject to optional clinical constraints, is calculated by running the algorithm once. This optimal individual dosage plan remains valid until the next scheduled visit.

[0063] One iteration of the algorithm at the time of the patient's visit. Step 1) Estimation of individual model parameters: Based on available patient data from current and past visits, and the dosage up to the current visit (Figure 1A; (A)~(D)), estimate the patient's individual model parameters φ i (Figure 1A; (E)) is estimated using empirical Bayesian estimation with mathematical models (Figure 1A; (1)~(2)). Step 2) "Optimal Individual Dosage Plan": Estimated individual model parameters (Figure 1A; (E)) are applied to calculate the optimal individual dosage plan (Figure 1A; (1), (3), (F), (G)) for the period until the next scheduled visit. Step 3) (Optional) "Optimal individualized dosing plan subject to clinical constraints": The optimal individualized dosing plan (Figure 1A; (3)) is adjusted to absorb the constraints in clinical application (Figure 1A; (4), (E), (F), (G)).

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

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

[0066] As already mentioned above, thyroid hormones are crucial for normal brain development, growth, and puberty. However, treating rare thyroid disorders such as congenital hypothyroidism (absence or insufficient thyroid hormone production) and childhood-onset Graves' disease (excessive thyroid hormone production) is challenging. Firstly, a carefully selected initial dose based on clinical experience is necessary. Secondly, after achieving physiological balance in thyroid hormones, continuous adjustment of the individual's dosage according to age, weight, and disease severity is required to maintain normal thyroid function. To mitigate the risk of poor neurological outcomes, it is important to establish an optimal, personalized medication strategy that is continuously fine-tuned to address the specific needs of neonates, infants, and children with hyperthyroidism or hypothyroidism.

[0067] In more detail, in one embodiment of the present invention, the disease for which the optimal administration plan should be determined is one of the following four thyroid diseases, which provide solutions to the current medical problems formulated in the introduction.

[0068] According to one embodiment, as described above, an artificial neural network (ANN) may be included in this approach to compute the optimal individual dosage plan in a short amount of time, specifically within seconds. In other words, an ANN can be used to accelerate the method, system and / or computer program / algorithm according to the present invention, but is not essential to the present invention (see, for example, Figure 1; (1), (3), (F), (G) and step c) in particular of the method according to the present 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 the disease. For all individual patients in this population, the optimal dosage can be calculated. Next, 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, parameterized θ = (R 0 ,k in ,E max EC 50 In this context, the indirect response model is used as a fundamental mathematical model.

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[0071] A sufficient number n sufEach individual patient is sampled from the population parameter ρ, covering a larger dimensional space with all combinations of individual parameters. Consider the following table as an example: [Table 1]

[0072] For all these individual parameters, an optimal individual dosing plan (Step 2 or Claim 1c) is calculated, optionally, that absorbs at least one clinical constraint (Step 3 or Claim 1d) according to the determined dosing plan, and is compared to the section “Optimal Control Problem”. In this example, six doses d=(D1,...,D6) for six subsequent time units are calculated to obtain the following dataset, which is compared to the following table: [Table 2]

[0073] This constructed dataset is split into training, validation, and test datasets for developing the ANN. The input to the ANN is 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 individual dosing plan. Thus, this trained ANN can replace step 2) "optimal individual dosing plan": (Figure 1A; (1), (3), (F), (G)) and claim 1(c), respectively.

[0074] For new patients with new individual measurements, a new estimated individual model parameter φ serves as the input to ANN. i To calculate this, empirical Bayesian estimation is applied. ANN is then applied to calculate the optimal individual dosing plan. Thus, step 2) "optimal individual dosing plan": (Figure 1A; (1), (3), (F), (G)) and claim 1(c) are replaced by ANN, respectively.

[0075] Patients with congenital hypothyroidism: For congenital hypothyroidism, artificially produced T4 hormone (manufactured by different pharmaceutical companies in different herbal forms (e.g., tablets, intravenous infusions), e.g., levothyroxine) is administered as replacement therapy to normalize thyroid hormones (T3, FT3, T4, FT4, TSH) to the normal reference range. The comprehensive concept from the main claim applies 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, two different treatment approaches are applied in clinical practice to normalize thyroid hormones (T3, FT3, T4, FT4, TSH) to the normal reference range in both pediatric and adult patients: 1) Administration of antithyroid drugs (e.g., carbimazole) alone to suppress the overproduction of thyroid hormones. 2) Concurrent administration of antithyroid drugs (e.g., carbimazole) to suppress thyroid function and levothyroxine as replacement therapy to increase T4 hormone.

[0078] To date, carbimazole administration, with or without concurrent levothyroxine, has been based on clinical testing of thyroid hormones T3, FT3, T4, FT4, and TSH. A new approach would involve the use of the patient's heart rate, a well-established and highly sensitive clinical indicator for excessively high levels of thyroid hormones. Patients diagnosed with hyperthyroidism always have excessively high heart rate readings, which only normalize over several weeks once thyroid hormone levels return to the normal range with carbimazole treatment. Heart rate is monitored using wearable devices. This allows for the establishment of a relationship between FT4 and heart rate, with the goal of providing physician advice and medication remotely (telemedicine) based on resting heart rate without requiring a physical examination and blood tests. This approach would be particularly important in low- and middle-income countries where remote locations and clinical testing are not readily available everywhere.

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

[0080] Examples of mathematical models for congenital hypothyroidism A mathematical model for levothyroxine treatment and the resulting FT4 concentration are presented [Koch 2021]. Due to replacement therapy, this model can be considered a pure PK model. A one-compartment model with an absorption compartment and an additional endogenous component have been developed:

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[0081] Estimated individual model parameters

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[0082] Examples of mathematical models for acquired hyperthyroidism A mathematical model for carbimazole treatment, additional block-and-replace (combination with levothyroxine) therapy, and the resulting free thyroxine (FT4) concentration are presented. Structurally, this can be considered a PKPD model, in which 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 of its pharmacokinetic (PK) properties, such as distribution and metabolism, are known. 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 rate of T4 production in the body by (t) is due to the inhibitory action.

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[0086] Estimated individual model parameters

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

[0088] Finally, Figure 4 shows a schematic example of an optimal individual dosage plan calculated by the method / computer program according to the present invention.

[0089] The desired disease progression (left panel, solid curve B1) and the resulting biomarker concentrations (left panel, solid curve B2) are shown against the calculated optimal individual dosing plan (right panel, cross). Solid line C1 represents the corresponding drug concentration resulting from the optimal individual dosing plan.

[0090] Further aspects and embodiments of the present invention are described as items. These items, however, can also be clearly described as claims of this application.

[0091] Item 1: A method for determining an optimal individualized dosing plan for at least one drug for a patient with a known disease, wherein the method is (a) To provide 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, wherein the model includes patient-associated individual model parameters. (b) Use empirical Bayesian estimation to estimate individual model parameters of mathematical models that utilize patient data. (c) Calculating the optimal individual dosing plan for a mathematical model by solving the optimal control problem based on the desired disease progression, estimated individual model parameters, and initial inferences for the dosing plan. This includes the step of performing the following:

[0092] Item 2: A method in accordance with Item 1, and this method is (d) Adjusting the optimal individual dosing plan to absorb at least one clinical constraint to result in an optimal individual dosing plan conditioned on the at least one clinical constraint. This further includes the step of performing the following:

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

[0094] Item 4: A method following one of the preceding items, in which the desirable disease progression is given in the form of a mathematical function.

[0095] Item 5: A method following one of the preceding items, wherein steps (b) to (c), more specifically, steps (b) to (d), are performed at each of several subsequent visits of the patient, and for x > 1, the patient data in step b) includes all patient data from the previous x-1 visits, and the empirical Bayesian 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 following one of the preceding items, wherein at least part of the algorithm that performs steps (b) to (c), more specifically steps (b) to (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: acquired hypothyroidism, in detail, autoimmune and / or non-autoimmune; acquired hyperthyroidism, in detail, autoimmune and / or non-autoimmune; congenital hypothyroidism, one of congenital hyperthyroidism.

[0098] Item 8: A 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: In accordance with Item 9, the wearable device is one of the following: a wristwatch, more specifically a smartwatch, a mobile phone, or more specifically a smartphone.

[0101] Item 11: A method in accordance with Item 9 or 10, wherein the patient data includes heart rate, and the patient's heart rate is measured by a wearable device.

[0102] Item 12: A system for determining an optimal individualized dosing plan for at least one drug for a patient with a known disease, the system comprising at least one processor configured to perform steps of a method according to one of the preceding items.

[0103] Item 13: A system in accordance with Item 12, further comprising a wearable device configured to measure at least a portion of the patient data.

[0104] Item 14: A computer program containing instructions, which, when executed on a system conforming to Item 12 or 13, cause the system to perform an action in accordance with one of Items 1 through 11.

[0105] Item 15: A computer-readable persistent storage medium on which a computer program conforming to Item 14 is stored.

[0106] Item 16: A data carrier signal that carries 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-based method for determining an optimal individualized dosing plan for at least one drug for a patient with a known disease associated with a disease progression model that follows a nonlinear mixed-effects modeling approach called the NLME modeling approach, wherein the method is: (a) Accessing a mathematical model adapted to model the disease progression of the disease, wherein the mathematical model includes a basic mathematical model involving the application of an NLME modeling approach to describe a given population of patients by its population parameters, covariates, and parameter distributions, and the basic mathematical model is a pharmacokinetic or pharmacokinetic / pharmacodynamic model characterized by one or more differential equations including disease state as a variable characterizing disease progression, (b) Using empirical Bayesian estimation, calculate estimated individual model parameters for patients belonging to the given population by maximizing the conditional probability density function of individuals having the population parameters and the patient data of the patients, based on the patient data and the mathematical model. (c) Calculating the optimal individual dosing plan for the patient by solving the optimal control problem using an optimal control algorithm, by minimizing the cost functional that characterizes the difference between the disease state and the desired disease progression based on the mathematical model and the patient's individual model parameters, and by starting with an initial control corresponding to the initial estimation for the dosing plan, The steps include performing the following: method.

2. (d) To obtain the optimal individual dosing plan subject to at least one clinical constraint by adjusting the optimal individual dosing plan between two available doses, taking into account at least one clinical constraint, and rounding to the nearest available dose size, or by selecting the higher or lower available dose based on the lower corresponding cost functional value. The method according to claim 1, further comprising:

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

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

5. The method according to claim 1, wherein the disease is one of acquired hypothyroidism, more specifically autoimmune and / or non-autoimmune; acquired hyperthyroidism, more specifically autoimmune and / or non-autoimmune; congenital hypothyroidism; or congenital hyperthyroidism.

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

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

8. The method according to claim 7, wherein the wearable device is a wristwatch, more specifically a smartwatch, a mobile phone, and more specifically a smartphone.

9. The method according to claim 7 or 8, wherein the patient data includes heart rate, and the patient's heart rate is measured by the wearable device.

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

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

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

13. A computer-readable persistent storage medium on which the computer program according to claim 12 is stored.

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