Alexandra Lavalley-Morelle 1, E. Niclas Jonsson 1
1 Pharmetheus AB (Uppsala, Sweden)
Background: Covariate analysis remains a critical challenge in pharmacometrics. The Full Random Effects Model (FREM) [1] offers a robust solution for covariate modeling, specifically addressing issues of collinearity and missing data by estimating the joint distribution of parameters and covariates. However, while established in NONMEM, this methodology is not currently available in the R environment.
Objective: The objective of this work was to implement a FREM workflow within the open-source saemix package [2] and evaluate its performance against standard Fixed Effects Modeling (FEM) under varying degrees of collinearity in a Repeated Time-to-Event (RTTE) modeling framework.
Methods: We implemented the FREM workflow based on the saemix package extension for multi-response models [3], using the SAEM algorithm [4]. To set up the FREM framework within this environment, patient covariates were incorporated as additional dependent variables alongside the primary clinical outcome. Instead of explicitly estimating fixed covariate effects on the structural parameters, the model estimates a joint multivariate normal distribution, deriving the covariate relationships directly from the full variance-covariance matrix between the random effects and the covariates. A total of 100 datasets of 1000 subjects were simulated for a RTTE outcome, which was defined by a constant baseline hazard with inter-individual variability (IIV). The covariate structure contained 20 variables organized into four correlation blocks: high (Cov 1-5, r ≈ 0.8), medium (Cov 6-10, r ≈ 0.5), weak (Cov 11-15, |r| ≤ 0.3), and negligible (Cov 16-20, |r| ≤ 0.1). Covariates were simulated following a multivariate normal distribution, with low inter-block correlations. The true underlying model was driven by four active covariates (one from each correlation block). To assess the impact of collinearity, we evaluated covariate effects in saemix using standard FEM and FREM by incrementally including 1 to 4 correlated covariates per block into the estimation. The algorithm utilized 10 chains, with 500 iterations for the exploratory phase and 150 for the smoothing phase. Performances were quantified by comparing the estimated individual linear predictor for a typical subject (estimated covariate effects multiplied by covariate means) to the true predictor, summarized using Relative Mean Error (RME) for bias and Relative Root Mean Squared Error (RRMSE) for precision across the 100 replicates.
Results: Both FEM and FREM estimation methods demonstrated good overall performance, maintaining a consistently low bias and high precision (RME ≤ 8% and RRMSE ≤ 30%) regardless of the number of covariates included. FREM yielded estimations with slightly lower RMEs overall. With one covariate per block, FREM showed near-zero bias (RME = 0.3%) compared to FEM (2.2%). When two covariates per block were included, FEM exhibited a RME of 7.2% versus -1.9% for FREM. At the highest level of collinearity (four covariates per block), both methods slightly underestimated the predictor (-6.0% for FEM and -5.3% for FREM). Given the small magnitude of these differences, the predictive performances of FEM and FREM remain comparable for this RTTE outcome. However, by estimating a joint variance-covariance matrix rather than relying on direct parameterization, FREM provides a robust alternative that naturally absorbs collinearity, avoiding the pre-selection covariate process and the iterative procedure typically required in traditional FEM approaches.
Conclusion: This work introduces an implementation of the FREM framework within the R environment using the SAEM algorithm, providing a novel tool for covariate modeling that effectively handles collinearity. As a next step, this framework will be utilized to introduce and evaluate the performance of the SAEM algorithm for both methodologies under various missing data scenarios.
References:
[1] Nyberg et al. Properties of the full random-effect modeling approach with missing covariate data, CPT: Pharmacometrics & Systems Pharmacology, 2023
[2] Comets et al. Parameter Estimation in Nonlinear Mixed Effect Models Using saemix, an R Implementation of the SAEM Algorithm, Journal of Statistical software, 2017
[3] Lavalley-Morelle et al. Extending the code in the open-source saemix package to fit joint models of longitudinal and time-to-event data, Computer Methods and Programs in Biomedicine, 2024
[4] Delyon et al. Convergence of a Stochastic Approximation Version of the EM Algorithm, The Annals of Statistics, 1999
Reference: PAGE 34 (2026) Abstr 12205 [www.page-meeting.org/?abstract=12205]
Poster: Methodology - Covariate/Variability Models