Integration of Time-Varying Pharmacometric Modeling With Cox Regression for Time-to-Event Analysis in NONMEM

Although time-varying Cox regression modeling approaches have been developed, exposure-response analyses for time-to-event (TTE) endpoints often rely on static exposure covariates and may overlook the real-world dosing variability and drug concentration fluctuations over time. To better characterize pharmacokinetic (PK) or pharmacodynamic (PD) effects on TTE endpoints, a methodology was proposed to integrate time-varying pharmacometric models with Cox regression in the non-linear mixed effects modeling software, NONMEM. Clinical trial simulations were conducted with different sample sizes and dose levels, employing a one-compartment PK model, a bathtub-shaped function for event hazard, and an I_max model for concentration-hazard relationships. Model parameters were estimated based on partial likelihood using the first order approximation method in NONMEM, and results were compared to those obtained from parametric methods under different baseline hazard assumptions. The performance of the models using static and time-varying exposure metrics was also assessed. In the absence of a pre-specified baseline hazard, the proposed semi-parametric approach delivered robust parameter estimates and aligned with the parametric method with the correct baseline hazard assumption. The semi-parametric method outperforms other parametric approaches with incorrect baseline hazard assumptions. Furthermore, the semi-parametric method using time-varying exposure metrics outperforms those using static exposure metrics. The proposed methodology successfully integrates time-varying PK effects on TTE endpoints in the simulation study. It offers a flexible framework in NONMEM and can be extended to include other pharmacometric models with ordinary differential equations, thus enhancing model-informed decision-making for assessing TTE endpoints in drug development.