Lucie Fayette1,2, Karl Brendel2, France Mentré1
1Université Paris Cité et Université Sorbonne Paris Nord, INSERM, IAME, UMR 1137, 2Pharmacometrics, Ipsen Innovation
Objectives This work focuses on designing experiments for pharmacometrics studies using Non-Linear Mixed Effects Models (NLMEM) including covariates to describe between-subject variability. Before collecting and modelling new clinical trial data, choosing an appropriate design is crucial. Clinical trial simulations are recommended[1] for power assessment and sample size computation although it is computationally expensive and non-exhaustive. Alternative methods using the Fisher Information Matrix (FIM)[2] have been shown to efficiently optimize sampling times. However, few studies have explored how to allocate covariates to provide most information. Assuming a known model with covariate effects and a joint distribution for covariates in the target population from previous clinical studies, we propose to optimise the allocation of covariates among the subjects to be included in the new trial. It aims achieving better overall parameter estimations and therefore increase power of statistical tests on covariate effects to detect significance, and clinical relevance or non-relevance of relationships. Methods We suggested dividing the domain of continuous covariates into clinically meaningful intervals and optimised their proportions, along with the proportion of each category for discrete covariates. We developed a fast and deterministic FIM computation method, leveraging Gauss-Legendre quadrature (GLQ) and copula modelling[3]. The optimisation problem was formulated as a convex problem subject to linear constraints, allowing resolution using Projected Gradient Descent algorithm. We applied this approach for a one-compartment population pharmacokinetic model with IV bolus, linear elimination, random effects on volume (V) and clearance (Cl) and a combined error (as in [4]). Additive effects of Sex and body mass index (BMI) were included on log(V) and creatinine clearance (CLCR) on log(Cl). The design includes 24 subjects receiving 250 mg of drug at time 0 and with samples collected at 1, 4 and 12-hours post-dose. Initial covariate distribution was imported from NHANES as in [3]. BMI was segmented into the 3 usual intervals: Obesity, Overweight and Healthy Weight. CLCR was segmented into 4 usual intervals to define renal function (RF): Normal, Mild, Moderate and Severe RF. Combining Sex, BMI, and CLCR intervals resulted in 24 covariate combinations. Due to low representation (1.2%), Severe RF data were pooled by Sex, ensuring copula fit adequacy. It led to 20 combinations, with FIM computed for each using copula and GLQ with 25 nodes. Results Methods were implemented in R using the package PFIM6.1[5]. First, univariate analysis showed equal distribution between more extreme classes and disappearance of intermediate values when there is no constraint. In the multivariate case, optimal distributions had many combinations with a weight of 0. Because being a Female reduces V while V increases with BMI, in optimal distributions there were more Female with Healthy Weight while more Male with Obesity. Similarly, because having Severe RF decreases Cl, there were only Female Severe RF. Various constraint settings were explored to better reflect real-life conditions. With constraint that each interval should represent at least 5% of subjects (‘Lower constraints’), Mild and Moderate RF and Overweight were to their minimum. With an additional upper limit of 10% for Severe RF, Severe RF was at 10%, replaced by more Moderate RF. The number of subjects needed (NSN) to get 80% power on the significance of the three effects and on their relevance (for Sex and CLCR)/non-relevance (for BMI) was initially 596 and fell to respectively 197 for both ‘No constraint’ and ‘Lower constraints’ optimisation and to 229 with additional upper bound on Severe RF. Thus, even the more constrained optimisation reduced the NSN by more than 60%. Conclusion We introduced a new method to integrate the FIM for NLMEM with covariates to efficiently optimise covariate allocation among patients for future studies. We showed an important reduction in NSN to achieve desired power in covariate tests. As perspective, joint optimisation between covariates and elementary design may be valuable. Lastly, this approach assumes known model, parameters and covariate distribution making it sensitive to misspecifications and robust approaches should be explored. Adaptive Designs, especially two stages[6], could also be a solution to refine covariate distribution midway through inclusion.
[1] FDA Guidance for Industry Population Pharmacokinetics. https://www.fda.gov/media/128793/download, 2022 [2] Mentré F, Chenel M, Comets E et al. Current use and developments needed for optimal design in pharmacometrics: a study performed among ddmore’s european federation of pharmaceutical industries and associations members. CPT: Pharmacometrics & Systems Pharmacology 2013; 2(6): 1–2. [3] Guo Y, Guo T, Knibbe CA et al. Generation of realistic virtual adult populations using a model-based copula approach. Journal of Pharmacokinetics and Pharmacodynamics 2024; : 1–12. [4] Fayette L, Brendel K and Mentré F. Using fisher information matrix to predict uncertainty in covariate effects and power to detect their relevance in non-linear mixed effect models in pharmacometrics. medRxiv 2024; : 2024–10. [5] Mentré F, Leroux R, Seurat J, Fayette L.: PFIM: Population Fisher Information Matrix. R package version 6.1. Available from: https://CRAN.R-project.org/package=PFIM. [6] Fayette L, Leroux R, Mentré F et al. Robust and adaptive two-stage designs in nonlinear mixed effect models. The AAPS Journal 2023; 25(4): 71.
Reference: PAGE 33 (2025) Abstr 11431 [www.page-meeting.org/?abstract=11431]
Poster: Methodology - Covariate/Variability Models