Zrinka Duvnjak 1,2, Niklas Hartung 3, João A. Abrantes 4, Wilhelm Huisinga 2,3, Robin Michelet 1, Charlotte Kloft 1,2
1 Freie Universität Berlin, Institute of Pharmacy, Department of Clinical Pharmacy and Biochemistry (Berlin, Germany), 2 PharMetrX, Graduate Research Training Program (Berlin/Potsdam, Germany), 3 Universität Potsdam, Institute of Mathematics (Potsdam, Germany), 4 Roche Innovation Center Basel, Roche Pharma Research and Early Development, Pharmaceutical Sciences (Basel, Switzerland)
Introduction:
In clinical practice, missing covariate data (e.g., genetic test, stool biomarker) often limits the use of model-informed precision dosing (MIPD). When a covariate from the utilised model (where covariates are modelled as fixed effects) is missing, its typical value is commonly assumed. This can lead to both (i) biased a priori predictions (other covariate effect coefficients in the model are conditioned on the presence of the missing covariate [1]), and (ii) biased a posteriori predictions (underrepresented inter-individual variability (IIV)). In full random-effects models (FREM), covariates are modelled as random effects together with pharmacokinetic parameters and treated as observations [2,3]. Consequently, utilisation of FREM for MIPD could overcome missing-data issues by their implicit handling. Additionally, developing FREM allows the inclusion of multiple highly correlated covariates, increasing the chance that some of them will be available in clinical practice.
Objectives:
This simulation study aimed to determine whether, and under which conditions, utilising FREM offers predictive advantages over fixed-effects models within an MIPD framework, when a covariate is missing.
Methods:
For each simulated scenario, the starting model was a one-compartment FREM with linear elimination and two covariates (COV) where model parameters were described by a four-dimensional distribution: clearance (CL) and volume of distribution (Vc)) log-normally, while COV1 and COV2 normally distributed. True concentration-time profiles following once-daily intravenous bolus dosing were simulated from a model with the derived three-dimensional (CL, Vc, COV1) parameter distribution conditioned on a predefined value of COV2, which was subsequently treated as missing in the test dataset (COV2 identical for all patients within the scenario). The starting FREM and the corresponding full fixed-effects model (FFEM) (the latter assuming COV2 median value) were then used to predict the next minimum concentration (Cmin) using Bayesian estimation, given a test dataset containing the COV1 value and zero (a priori predictions), one, or two Cmin observations (a posteriori predictions). The two main evaluation metrics were: a) patient-specific differences in Cmin prediction bias between FFEM and FREM, summarised as the median difference per scenario, with positive values indicating improvement in predictions with FREM over FFEM; and b) the percentage of patients with less biased FREM Cmin predictions (i.e. “%improved”).
Overall, >200 simulated scenarios (1000 patients per scenario) were tested. These explored: (i) varying values of the missing covariate (COV2: from mean-2sd to mean+2sd); (ii) magnitude of correlation between covariates (COV1_COV2_corr: from -0.7 to 0.7); (iii) covariate effect sizes (COV2-CL_corr: from 0.1 to 0.8); (iv) total CL IIV (IIV_total_CL_CV: from 10% to 120%); (v) residual unexplained variability (RUV) (RUV_CV: from 5% to 80%), and their combinations.
Results:
FREM decreased a priori median bias by 11.0% points compared to FFEM (%improved: 82.8%), with its advantage decreasing as empirical observations were incorporated (2.04% and 0.71% point improvement for one and two Cmin provided, respectively), for the reference scenario (COV2: mean-2sd, COV1_COV2_corr: -0.5, COV2-CL_corr: 0.7, IIV_total_CL_CV: 80%, RUV_CV: 20%).
(i) Improvement depended heavily on the missing covariate’s true value. For missing COV2 values less extreme (mean-1sd) than in the reference scenario, median improvement dropped to 3.70%; At the population median, FFEM outperformed FREM, as its COV2-median-value assumption was more accurate than FREM’s COV1-based estimation. Univariate alterations from the reference scenario showed smaller FFEM-FREM differences for: (ii) weaker covariate correlations (3.03% point improvement for COV1_COV2_corr: -0.3) and (iii) weaker effect sizes (0.75% point improvement for COV2-CL_corr: 0.3).
For extreme missing covariates, (iv) lower IIV (IIV_total_CL_CV: 30%) reduced the improvement to 6.02%. Finally, while (v) higher RUV increased bias in both models in a posteriori sub-scenarios, FREM was less negatively affected, ultimately increasing superiority over FFEM (e.g., 4.42% improvement at 50% RUV_CV, for one Cmin available).
Conclusions:
These results are in line with theoretical expectations and suggest that FREM may be a robust alternative for MIPD when covariate data are often missing. The highest benefit laid in optimising dosing for patients with extreme missing covariate values—the population potentially benefiting most from individualised dosing—and particularly for first-dose optimisation and drugs characterised by high: COV effect sizes, correlation between covariates, IIV, and RUV. Nevertheless, given that patients with less extreme covariates are more common, and the magnitudes of FREM benefit are model-/drug-specific, further assessments using real-world data are needed to demonstrate potential clinical relevance.
References:
[1] Jonsson EN, Jönsson S, Hansson E, Nyberg J. Conditional versus unconditional covariate effects in pharmacometric models: implications for interpretation, communication, and reporting. CPT Pharmacometrics Syst Pharmacol. 2026;15(2):e70203. doi:10.1002/psp4.70203
[2] Yngman G, Nyberg HB, Nyberg J, Jonsson EN, Karlsson MO. An introduction to the full random effects model. CPT Pharmacometrics Syst Pharmacol. 2022;11(2):149-160. doi:10.1002/psp4.12741
[3] Jonsson EN, Nyberg J. Full random effects models (FREM): a practical usage guide. CPT Pharmacometrics Syst Pharmacol. 2024;13(9):1297-1308. doi:10.1002/psp4.13190
Reference: PAGE 34 (2026) Abstr 11870 [www.page-meeting.org/?abstract=11870]
Poster: Methodology - Covariate/Variability Models