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Abstract Neural ordinary differential equations (NODEs) are an emerging machine learning (ML) method to model pharmacometric (PMX) data. Combining mechanism‐based components to describe “known parts” and neural networks to learn “unknown parts” is a promising ML‐based PMX approach. In this work, the implementation of low‐dimensional NODEs in two widely applied PMX software packages (Monolix and NONMEM) is explained. Inter‐individual variability is introduced to NODEs and proposals for the practical implementation of NODEs in such software are presented. The potential of such implementations is shown on various demonstrational datasets available in the Monolix model library, including pharmacokinetic (PK), pharmacodynamic (PD), target‐mediated drug disposition (TMDD), and survival analyses. All datasets were fitted with NODEs in Monolix and NONMEM and showed comparable results to classical modeling approaches. Model codes for demonstrated PK, PKPD, TMDD applications are made available, allowing a reproducible and straight‐forward implementation of NODEs in available PMX software packages.

Abstract Background In pediatric rheumatic diseases (PRD), adalimumab is dosed using fixed weight-based bands irrespective of methotrexate co-treatment, disease activity (DA) or other factors that might influence adalimumab pharmacokinetics (PK). In rheumatoid arthritis (RA) adalimumab exposure between 2–8 mg/L is associated with clinical response. PRD data on adalimumab is scarce. Therefore, this study aimed to analyze adalimumab PK and its variability in PRD treated with/without methotrexate. Methods A two-center prospective study in PRD patients aged 2–18 years treated with adalimumab and methotrexate (GA-M) or adalimumab alone (GA) for ≥ 12 weeks was performed. Adalimumab concentrations were collected 1–9 (maximum concentration; Cmax), and 10–14 days (minimum concentration; Cmin) during ≥ 12 weeks following adalimumab start. Concentrations were analyzed with enzyme-linked immunosorbent assay (lower limit of quantification: 0.5 mg/L). Log-normalized Cmin were compared between GA-M and GA using a standard t-test. Results Twenty-eight patients (14 per group), diagnosed with juvenile idiopathic arthritis (71.4%), non-infectious uveitis (25%) or chronic recurrent multifocal osteomyelitis (3.6%) completed the study. GA-M included more females (71.4%; GA 35.7%, p = 0.13). At first study visit, children in GA-M had a slightly longer exposure to adalimumab (17.8 months [IQR 9.6, 21.6]) compared to GA (15.8 months [IQR 8.5, 30.8], p = 0.8). Adalimumab dosing was similar between both groups (median dose 40 mg every 14 days) and observed DA was low. Children in GA-M had a 27% higher median overall exposure compared to GA, although median Cmin adalimumab values were statistically not different (p = 0.3). Cmin values ≥ 8 mg/L (upper limit RA) were more frequently observed in GA-M versus GA (79% versus 64%). Overall, a wide range of Cmin values was observed in PRD (0.5 to 26 mg/L). Conclusion This study revealed a high heterogeneity in adalimumab exposure in PRD. Adalimumab exposure tended to be higher with methotrexate co-treatment compared to adalimumab monotherapy although differences were not statistically significant. Most children showed adalimumab exposure exceeding those reported for RA with clinical response, particularly with methotrexate co-treatment. This highlights the need of further investigations to establish model-based personalized treatment strategies in PRD to avoid under- and overexposure. Trial registration NCT04042792 , registered 02.08.2019.

Abstract Missing data create challenges in clinical research because they lead to loss of statistical power and potentially to biased results. Missing covariate data must be handled with suitable approaches to prepare datasets for pharmacometric analyses, such as population pharmacokinetic and pharmacodynamic analyses. To this end, various statistical methods have been widely adopted. Here, we introduce two machine‐learning (ML) methods capable of imputing missing covariate data in a pharmacometric setting. Based on a previously published pharmacometric analysis, we simulated multiple missing data scenarios. We compared the performance of four established statistical methods, listwise deletion, mean imputation, standard multiple imputation (hereafter “Norm”), and predictive mean matching (PMM) and two ML based methods, random forest (RF) and artificial neural networks (ANNs), to handle missing covariate data in a statistically plausible manner. The investigated ML‐based methods can be used to impute missing covariate data in a pharmacometric setting. Both traditional imputation approaches and ML‐based methods perform well in the scenarios studied, with some restrictions for individual methods. The three methods exhibiting the best performance in terms of least bias for the investigated scenarios are the statistical method PMM and the two ML‐based methods RF and ANN. ML‐based approaches had comparable good results to the best performing established method PMM. Furthermore, ML methods provide added flexibility when encountering more complex nonlinear relationships, especially when associated parameters are suitably tuned to enhance predictive performance.

ObjectivesGraves' disease (GD) with onset in childhood or adolescence is a rare disease (ORPHA:525731). Current pharmacotherapeutic approaches use antithyroid drugs, such as carbimazole, as monotherapy or in combination with thyroxine hormone substitutes, such as levothyroxine, as block-and-replace therapy to normalize thyroid function and improve patients' quality of life. However, in the context of fluctuating disease activity, especially during puberty, a considerable proportion of pediatric patients with GD is suffering from thyroid hormone concentrations outside the therapeutic reference ranges. Our main goal was to develop a clinically practical pharmacometrics computer model that characterizes and predicts individual disease activity in children with various severity of GD under pharmacotherapy.MethodsRetrospectively collected clinical data from children and adolescents with GD under up to two years of treatment at four different pediatric hospitals in Switzerland were analyzed. Development of the pharmacometrics computer model is based on the non-linear mixed effects approach accounting for inter-individual variability and incorporating individual patient characteristics. Disease severity groups were defined based on free thyroxine (FT4) measurements at diagnosis.ResultsData from 44 children with GD (75% female, median age 11 years, 62% receiving monotherapy) were analyzed. FT4 measurements were collected in 13, 15, and 16 pediatric patients with mild, moderate, or severe GD, with a median FT4 at diagnosis of 59.9 pmol/l (IQR 48.4, 76.8), and a total of 494 FT4 measurements during a median follow-up of 1.89 years (IQR 1.69, 1.97). We observed no notable difference between severity groups in terms of patient characteristics, daily carbimazole starting doses, and patient years. The final pharmacometrics computer model was developed based on FT4 measurements and on carbimazole or on carbimazole and levothyroxine doses involving two clinically relevant covariate effects: age at diagnosis and disease severity.DiscussionWe present a tailored pharmacometrics computer model that is able to describe individual FT4 dynamics under both, carbimazole monotherapy and carbimazole/levothyroxine block-and-replace therapy accounting for inter-individual disease progression and treatment response in children and adolescents with GD. Such clinically practical and predictive computer model has the potential to facilitate and enhance personalized pharmacotherapy in pediatric GD, reducing over- and underdosing and avoiding negative short- and long-term consequences. Prospective randomized validation trials are warranted to further validate and fine-tune computer-supported personalized dosing in pediatric GD and other rare pediatric diseases.

The field of medicine is undergoing a fundamental change, transforming towards a modern data-driven patient-oriented approach. This paradigm shift also affects perinatal medicine as predictive algorithms and artificial intelligence are applied to enhance and individualize maternal, neonatal and perinatal care. Here, we introduce a pharmacometrics-based mathematical-statistical computer program (PMX-based algorithm) focusing on hyperbilirubinemia, a medical condition affecting half of all newborns. Independent datasets from two different centers consisting of total serum bilirubin measurements were utilized for model development (342 neonates, 1,478 bilirubin measurements) and validation (1,101 neonates, 3,081 bilirubin measurements), respectively. The mathematical-statistical structure of the PMX-based algorithm is a differential equation in the context of non-linear mixed effects modeling, together with Empirical Bayesian Estimation to predict bilirubin kinetics for a new patient. Several clinically relevant prediction scenarios were validated, i.e., prediction up to 24 h based on one bilirubin measurement, and prediction up to 48 h based on two bilirubin measurements. The PMX-based algorithm can be applied in two different clinical scenarios. First, bilirubin kinetics can be predicted up to 24 h based on one single bilirubin measurement with a median relative (absolute) prediction difference of 8.5% (median absolute prediction difference 17.4 μmol/l), and sensitivity and specificity of 95.7 and 96.3%, respectively. Second, bilirubin kinetics can be predicted up to 48 h based on two bilirubin measurements with a median relative (absolute) prediction difference of 9.2% (median absolute prediction difference 21.5 μmol/l), and sensitivity and specificity of 93.0 and 92.1%, respectively. In contrast to currently available nomogram-based static bilirubin stratification, the PMX-based algorithm presented here is a dynamic approach predicting individual bilirubin kinetics up to 48 h, an intelligent, predictive algorithm that can be incorporated in a clinical decision support tool. Such clinical decision support tools have the potential to benefit perinatal medicine facilitating personalized care of mothers and their born and unborn infants.