Using Fisher Information Matrix to predict uncertainty in covariate effects and power to detect their relevance in Non-Linear Mixed Effect Models in pharmacometrics.

This work focuses on design of experiments for Pharmacokinetic (PK) and Pharmacodynamic (PD) studies. Non-Linear Mixed Effects Models (NLMEM) modelling allows the identification and quantification of covariates that explain inter-individual variability (IIV). The Fisher Information Matrix (FIM), computed by linearization, has already been used to predict uncertainty on covariate parameters and power of test to detect statistical significance. A covariate effect is deemed statistically significant if it is different from 0 according to a Wald comparison test and clinically relevant if the ratio of change it causes in the parameter is relevant according to a test inspired by the two one-sided tests (TOST) as in bioequivalence studies. FIM calculation was extended by computing its expectation on the joint distribution of the covariates, discrete and continuous. Three methods were proposed: using a provided sample of covariate vectors, simulating covariate vectors, based on provided independent distributions or on estimated copulas. Thereafter, CI of ratios, power of tests and number of subjects needed to achieve desired confidence were derived. Methods were implemented in a working version of the R package PFIM6.1. A simulation study was conducted under various scenarios, including different sample sizes, sampling points, and IIV. Overall, uncertainty on covariate effects and power of tests were accurately predicted. The method was applied to a population PK model of the drug cabozantinib including 27 covariate relationships. Despite numerous relationships, limited representation of certain covariates, FIM correctly predicted uncertainty, and is therefore suitable for rapidly computing number of subjects needed to achieve given powers.