Freya Bachmann 1, Britta Steffens 2,3, Mona Kasper 1, Jan Rohleff 1, Marc Pfister 2,4, Gilbert Koch 2, Gabor Szinnai 4,5, Johannes Schropp 1
1 Department of Mathematics and Statistics, University of Konstanz (Konstanz, Germany), 2 Pediatric Pharmacology and Pharmacometrics, University Children's Hospital Basel (UKBB), University of Basel (Basel, Switzerland), 3 School of Life Sciences, University of Applied Sciences and Arts Northwestern Switzerland (FHNW) (Muttenz, Switzerland), 4 Department of Clinical Research, University of Basel and University Hospital Basel (Basel, Switzerland), 5 Pediatric Endocrinology and Diabetology, University Children's Hospital Basel (UKBB), University of Basel (Basel, Switzerland)
Objectives
In pediatric thyroid care, precise treatment is essential, as hormone imbalance can impair neurodevelopment, cognition, and growth. Despite guideline-based dosing and clinicians’ expertise, variability in disease dynamics makes achieving and maintaining target free thyroxine (FT4) levels difficult, resulting in persistent over- and underdosing even with frequent monitoring and dose adjustments.
In this work, our objectives are to (i) apply the optimal drug dosing algorithm OptiDose [1,2,3] to compute optimal individual drug doses for pediatric Graves’ Disease patients at each visit, (ii) address clinical restrictions such as available tablet sizes, and (iii) evaluate propagation of uncertainty to the optimal doses.
Methods
FT4 dynamics under drug treatment are characterized by a nonlinear mixed-effects (NLME) population pharmacometrics (PMX) model. Individual model parameters, predicting individual dynamics, are obtained via empirical Bayes estimates (EBEs) conditional on all available individual observations, and updated if new observations are taken at a clinical visit. Then, the optimal dose until the next scheduled visit is computed with the OptiDose algorithm, i.e., by minimizing an objective function quantifying the difference between target FT4 levels (therapeutic goal) and the individual model prediction.
Clinical restrictions, such as available tablet sizes, are incorporated by visualizing FT4 predictions for lower and upper available tablet sizes closest to the mathematically optimal dose, together with an observation-level prediction interval based on residual uncertainty.
Uncertainty in individual parameters was quantified by sampling from the conditional posterior distribution, e.g., in Monolix, or via Laplace approximation based on inverse Hessian at the conditional mode. For each draw, FT4 predictions and the corresponding optimal dose were computed. Uncertainty was summarized using posterior standard deviations and credible intervals at both the prediction and dose level. Relative decrease in interval width was quantified as the proportional reduction in interval width between consecutive visits.
To propagate both population- and individual-level uncertainty, a hierarchical (two-step) Monte Carlo approach was applied. Population parameters were sampled from the estimated variance-covariance matrix from the NLME fit. For each sample, few conditional individual parameter draws were obtained, and corresponding optimal individual doses were computed, providing a distribution of optimal doses reflecting both population- and individual-level uncertainty.
Results
For pediatric Graves’ disease, a PMX model was developed based on a dataset of 41 pediatric individuals from Switzerland [4] predicting FT4 dynamics under treatment. Patients received daily anti-thyroid drug (ATD) doses either as monotherapy, or in combination with levothyroxine as block-and-replace therapy. However, retrospective dose optimization suggested that all patients can reach their therapeutic goal with monotherapy at lower ATD dose levels compared to observed clinical practice.
For prospective optimization, dosing is daily and fixed inbetween visits, i.e., the next dose is chosen by the clinician at each visit, where FT4 predictions for lower and upper available tablet sizes closest to the mathematically optimal dose are visualized. Posterior 90% credible interval widths were evaluated at each visit. For typically 4-6 visits within the first 120 days after treatment initiation, uncertainty decreased with each visit at both prediction- and dose-level. Largest relative decrease in interval width was 42% at second compared to initial visit, as we cannot estimate some individual model parameters (IC50, and weight growth rate) from only one measurement. Relative decrease in interval width for later visits was 2 to 20%. For 1000 samples each, Laplace approximation based on the inverse Hessian yielded credible intervals comparable to those obtained from Monolix, with slightly wider interval widths. Incorporating population parameter uncertainty resulted in modest additional variability in optimal doses compared to EBE uncertainty alone.
Conclusion
The presented application of OptiDose in pediatric Graves’ disease enhances model-informed precision dosing for individual patients by computing their optimal doses to achieve their therapeutic goals at each visit. Dose uncertainty was primarily driven by individual parameter uncertainty and decreased with accumulating observations, supporting the structural stability of OptiDose. An international clinical study evaluating OptiDose in pediatric thyroid diseases compared to standard-of-care is currently being conducted.
References:
[1] Bachmann F, Koch G, Bauer RJ, Steffens B, Szinnai G, Pfister M, Schropp J (2024). Computing optimal drug dosing regarding efficacy and safety: the enhanced OptiDose method in NONMEM. J Pharmacokinet Pharmacodyn. https://doi.org/10.1007/s10928-024-09940-9
[2] Bachmann F, Koch G, Bauer RJ, Steffens B, Szinnai G, Pfister M, Schropp J (2023). Computing optimal drug dosing with OptiDose: implementation in NONMEM. J Pharmacokinet Pharmacodyn. https://doi.org/10.1007/s10928-022-09840-w
[3] Bräm D (2025). R package optiDoseR. https://github.com/braemd/optiDoseR
[4] Steffens B, Koch G, Gächter P, Claude F, Gotta V, Bachmann F, Schropp J, Janner M, l’Allemand D, Konrad D, Welzel T, Szinnai G and Pfister M (2023). Clinically practical pharmacometrics computer model to evaluate and personalize pharmacotherapy in pediatric rare diseases: application to Graves’ disease. Front. Med. 10:1099470. doi: 10.3389/fmed.2023.1099470
Reference: PAGE 34 (2026) Abstr 12074 [www.page-meeting.org/?abstract=12074]
Poster: Clinical Applications