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 using Non-Linear Mixed Effects Models including covariates to describe between-subject variability. Before collecting and modelling new clinical trial data, choosing an appropriate design is crucial. 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 the power of statistical tests on covariate effects to detect significance, and more importantly, clinical relevance or non-relevance of relationships. 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. We used the Fisher Information Matrix and developed a fast and deterministic computation method, leveraging Gaussian quadrature and copula modelling. 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 were explored. We showed the benefit of covariate optimisation in reducing the number of subjects needed to achieve desired power in covariate tests.