Research Scientist I Metrum Research Group Murray, Utah, United States
Disclosure(s):
Elias Clark: No financial relationships to disclose
Objectives: Disease progression models are widely used in pharmacometrics to quantify the time course of disease status [1,2]. Data supporting these models frequently contain months to years of patient follow-up. Timeframes over which patient factors affect disease progression are likely to change, motivating the use of time-varying covariates. Approaches for handling time-varying continuous covariates in pharmacokinetic models have been extensively explored [3-6]. The objective of this analysis was to evaluate $PRED (analytical solution) and $DES (differential equation) methods in NONMEM (v7.5) for handling time-varying, categorical covariates in a disease progression framework.
Methods: A linear disease progression model was parameterized in terms of baseline disease status, natural progression rate, and time-varying binary treatment effect. This model was used to simulate the data with treatment initiation at a landmark time point. $PRED and $DES methods were implemented to fit the simulated data and evaluated using standard diagnostic plots and visual predictive checks (VPCs). A stochastic simulation and estimation (SSE) procedure was also performed to assess the bias and precision of parameter estimates for both methods. The SSE design mimicked a hypothetical Phase 3 trial evaluating the treatment effect on disease progression. One hundred SSE replicates were performed across three sample sizes of subjects (N = 50, 100, 200) and treatment effects of a 10%, 25%, 50%, 75%, and 90% reduction in the disease progression rate. Parameter estimates were compared to true values across $PRED and $DES methods, sample sizes, and treatment-effect magnitude using accuracy and precision metrics including mean relative prediction error (MRPE) and relative root mean squared error (RRMSE).
Results: Both methods provided adequate fits based on the diagnostic plots and VPCs. However, the $PRED method resulted in significant bias: the treatment effect was overestimated by 12% to 500%, and the natural progression rate was underestimated by 3% to 40%. Bias worsened with larger treatment effects. The $DES method provided more accurate and robust parameter estimates across scenarios (e.g., MRPE and RRMSE were < 22% and < 32%, respectively, at N=200). However, computational speed favored $PRED methods (up to 7 times faster than $DES methods).
Conclusions: For time-varying binary covariates, $DES provided reasonably accurate and precise parameter estimates, whereas $PRED exhibited substantial bias (especially for large treatment effects). Despite longer runtimes, $DES is preferred over $PRED for time-varying categorical covariates in disease progression modeling.
Citations: [1] Mould, D.R. (2012), Models for Disease Progression: New Approaches and Uses. Clinical Pharmacology & Therapeutics, 92: 125-131. https://doi.org/10.1038/clpt.2012.53 [2] Cook SF, Bies RR. Disease Progression Modeling: Key Concepts and Recent Developments. Curr Pharmacol Rep. 2016;2(5):221-230. doi:10.1007/s40495-016-0066-x [3] Brochot, A., Dunne, A., Poggesi, I., Vermeulen A. Specifying Models with Time-Dependent Pharmacokinetic Parameters in NONMEM. PAGE; June 2011; Athens, Greece. [4] Wählby U, Thomson AH, Milligan PA, Karlsson MO. Models for time-varying covariates in population pharmacokinetic-pharmacodynamic analysis. Br J Clin Pharmacol. 2004;58(4):367-377. doi:10.1111/j.1365-2125.2004.02170.x [5] Goulooze SC, Snelder N. Time-varying covariates, overadjustment bias and mediation in pharmacokinetic/pharmacodynamic modeling. CPT Pharmacometrics Syst Pharmacol. 2024; 13: 1285-1288. doi:10.1002/psp4.13200 [6] Sanghavi K, Ribbing J, Rogers JA, et al. Covariate modeling in pharmacometrics: General points for consideration. CPT Pharmacometrics Syst Pharmacol. 2024;13:710-728. doi:10.1002/psp4.13115
Keywords: Time-varying covariates, Disease progression modeling, Stochastic simulation and estimation
