Comparison of $PRED and $DES in NONMEM for time-varying categorical covariates in disease progression modeling.

<p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d611004e67"> <b>Objectives:</b> Disease progression models are widely used in pharmacometrics to quantify the time course of disease status [ <a class="xref-link" href="#r1">1</a>, <a class="xref-link" href="#r2">2</a>]. 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 [ <a class="xref-link" href="#r3">3</a>– <a class="xref-link" href="#r6">6</a>]. 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. <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d611004e84"> <b>Methods:</b> 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). <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d611004e89"> <b>Results:</b> 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 &lt; 22% and &lt; 32%, respectively, at N=200). However, computational speed favored $PRED methods (up to 7 times faster than $DES methods). <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d611004e94"> <b>Conclusions:</b> 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.