Optimising covariate allocation at design stage using Fisher Information Matrix for Non-Linear Mixed Effects Models in pharmacometrics

This work focuses on designing experiments for pharmacometrics studies analysed by Non-Linear Mixed Effects Models (NLMEM) including covariates to describe inter-individual variability. Co-variate effects may help identify patient subpopulations at risk of sub-therapeutic or toxic responses, for instance when hepatic or renal impairment reduces drug elimination, increasing safety risks. Before collecting and modelling new clinical trial data, choosing an appropriate design is crucial, particularly to ensure sufficient information to estimate covariate effects and their uncertainty. Assuming a known NLMEM 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 a new trial. It aims achieving better overall parameter estimations and therefore increase power of statistical tests on covariate effects to detect the clinical relevance or non-relevance of relationships. We used the Fisher Information Matrix and developed a fast and deterministic computation method, leveraging Gaussian quadrature and copula modelling. We suggested dividing the domain of continuous covariates into clinically meaningful intervals and optimised their proportions, along with the proportion of each category for the discrete covariates. The optimisation problem was formulated as a convex problem subject to linear constraints, allowing resolution using Projected Gradient Descent algorithm. Different scenarios for a pharmacokinetics model including either biological measurements of renal or hepatic function as covariate were explored. We showed that covariate optimisation reduces the number of subjects needed to achieve desired power in covariate tests for relevance or non-relevance.