Lucie Fayette (1,2), Karl Brendel (2), France Mentré (1)
(1) Université Paris Cité, INSERM, IAME, UMR 1137, Paris, France, (2) Pharmacometrics, Ipsen Innovation, Les Ulis, France
Objectives:
One of the aims of pharmacokinetic (PK) and pharmacodynamic (PD) analysis is to identify and quantify the covariates that explain inter-individual variability (IIV). The effect of a covariate is evaluated by the ratio of change it causes in the PKPD parameters for given values or categories of the covariates and relatively to a reference value, and the associated confidence interval (CI). Those ratios are represented on forest plots [1]. An effect is deemed statistically significant if the CI on its ratio does not contain the value 0 and clinically relevant if its CI is outside a predetermined interval (often [0.8, 1.2]). Methods based on Fisher Information Matrix (FIM) that predict the power of a test to detect whether a discrete covariate effect is statistically significant and then optimize the design to achieve the desired confidence level have already been proposed [2,3].
The goals of this work were thus to extend power computation to continuous covariate and to relevance test.
Methods:
FIM calculation was extended to the case of continuous covariates by calculating its expectation on the joint distribution of the covariates. To this end, three methods were proposed: using a provided sample of covariate vectors, simulating covariate vectors, based on provided independent distributions or on a provided copula, as the benefits of using copulas in pharmacometrics have already been demonstrate [4]. Thus, for a given design and covariate effects, the FIM can be evaluated and the confidence intervals on the ratios can be calculated from it, making it possible to predict the forest plot. The power of a clinical relevance test on covariate effect was also computed analytically.
A simulation study was performed on a toy example, inspired by a case study from the University of Maryland [5]. The model was a one compartment model with IV bolus and linear elimination population PK model, with random effect on volume V and clearance Cl and a combined error model. Effects from weight and sex on V, and creatinine clearance (ClCR) on Cl were also included. Concentrations after a single dose were simulated in 4 different scenarios, combining:
-Design:
- Design 1: N=100, 16 time points from 0 to 24h post dose
- Design 2: N=24, 3 time points at 1, 4 and 12h post dose
-IIV:
- True Omega
- High Omega, obtained by doubling the standard deviations of the random effects
For each, 200 datasets were simulated and parameters were estimated using Monolix 2023R1 [6]. Standard errors (SE) were calculated from the FIM computed by linearization. Estimated ratio and their CI were derived and both statistical significance and relevance tests were performed. Results were compared to PFIM’s predictions using the three different methods.
Results:
The methods were implemented in a working version of the R package PFIM6 [7], also extended to include discrete and continuous covariates and to calculate the power of statistical significance tests.
The three methods for taking covariates into account in FIM give similar results, and SE and powers are overall well predicted. For instance, the power of relevance test on the effect of the 10th percentile of the ClCR distribution on Cl, both estimated on 200 simulations [95%CI] and predicted in the 4 scenarios are
- Design 1 – True Omega: Estimated: 1 [0.98; 1] – PFIM: 1
- Design 2 – True Omega: Estimated: 0.70 [0.63; 0.76] – PFIM: 0.72
- Design 1 – High Omega: Estimated: 0.94 [0.9; 0.97] – PFIM: 0.97
- Design 2 – High Omega: Estimated: 0.49 [0.42; 0.56] – PFIM: 0.44
If the asymptotic conditions are not reached or if the IIV is high on the parameter on which there is an effect, the SE tends to be slightly underpredicted by PFIM and therefore the power of the tests slightly overpredicted.
Conclusions:
When asymptotic conditions are met and if IIV is limited, PFIM accurately predicts uncertainty on covariate effects and the power of both significance and relevance tests. This tool can therefore be used to study changes in the power of tests as a function of sample size, IIV, effect size or sampling design.
The results of the three methods for FIM computation were the same in our example, but their respective impact should be further explored in complex cases.
These promising results suggest that the method should be more widely implemented in the PFIM package. This work opens the prospect of optimizing the design of clinical trials with the aim of maximizing power of relevance tests.
References:
[1] Marier JF, Teuscher N and Mouksassi MS. “Evaluation of covariate effects using forest plots and introduction to the coveffectsplot R package”. CPT: Pharmacometrics & Systems Pharmacology 11.10 (2022), pp. 1283–1293.
[2] Retout S et al. “Design in nonlinear mixed effects models: optimization using the Fedorov–Wynn algorithm and power of the Wald test for binary covariates”. Statistics in Medicine 26.28 (2007), pp. 5162–5179.
[3] Nguyen TT, Bazzoli C and Mentré F. “Design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models”. Statistics in Medicine 31.11-12 (2012), pp. 1043–1058.
[4] Zwep L et al. “Virtual patient simulation using copula modeling”. Clinical Pharmacology & Therapeutics (2022).
[5] BEGINNER’S TUTORIAL Case Study 1. https://ctm.umaryland.edu/#/ms-pharma/model/bgt/cs.
[6] Monolix 2023R1, Lixoft SAS, a Simulations Plus company.
[7] Leroux R et al. “Design evaluation and optimisation in nonlinear mixed effects models with the R package PFIM 6.0”. PAGE (2023).
Reference: PAGE 32 (2024) Abstr 10956 [www.page-meeting.org/?abstract=10956]
Poster: Methodology - New Modelling Approaches