This work focuses on design of experiments for Pharmacokinetic (PK) and Pharmacodynamic (PD) studies. Non-Linear Mixed effects Models (NLMEM) modeling 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 the power of a test to detect statistical significance. A covariate effect on a parameter 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 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 PFIM. 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, PFIM correctly predicted uncertainty, and is therefore suitable for rapidly computing number of subjects needed to achieve given powers.

L.F and K.B. are full-/-part-time employees of Ipsen.

This work was financed by a CIFRE agreement (Conventions Industrielles de Formation par la Recherche) of the ANRT (Association Nationale de la Recherche et de la Technologie). The CIFRE agreement is a partnership between a public laboratory and a company, here the UMR (Unité Mixte de Recherche) 1137 and Ipsen, respectively. The authors would like to thank the entire PFIM group, and in particular Romain Leroux, PFIM6 development manager of PFIM6, for their help in adapting the R code for our use.

I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.

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The details of the IRB/oversight body that provided approval or exemption for the research described are given below:

This work used the same data as "Nguyen, L., Chapel, S., Tran, B. D., & Lacy, S. (2019). Updated population pharmacokinetic model of cabozantinib integrating various cancer types including hepatocellular carcinoma. The Journal of Clinical Pharmacology, 59(11), 1551-1561." The latter pooled data from 10 clinical trials for which all protocols were approved by institutional review boards of participating institutions, and written informed consent was obtained from all HV and patients prior to enrollment.

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Yes

I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).

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The simulated data and the scripts that support the evaluation of the proposed method are openly available online at https://doi.org/10.5281/zenodo.13692989.

https://doi.org/10.5281/zenodo.13692989