(S-026) Evaluation of Fluctuating Drug Concentration and Pharmacokinetic Effects on Time-to-event Endpoint Using Proportional Hazard Cox Regression in NONMEM

Chih-Wei Lin – Clinical Pharmacology, Modeling and Simulation – Amgen; Po-Wei Chen – Clinical Pharmacology, Modeling and Simulation – Amgen; Sameer Doshi – Clinical Pharmacology, Modeling and Simulation – Amgen; Sandeep Dutta – Clinical Pharmacology, Modeling and Simulation – Amgen

Objectives: Cox regression is an extensively utilized statistical method to assess the influence of covariates on Time-to-event (TTE) endpoints in drug development. When the covariate is time-variant and the proportional hazards assumption is violated, a methodology has been developed in R to evaluate the effects of time-varying covariates on TTE endpoints. Nonetheless, evaluating the impact of fluctuating drug concentration on TTE endpoints using Cox regression within pharmacometrics remains challenging. To better characterize exposure-response relationships for TTE endpoints, a methodology was developed to evaluate time-variant pharmacokinetics (PK) effects on TTE endpoints using Cox regression in the non-linear mixed effects modeling software, NONMEM.

Methods: The methodology was developed using NONMEM. Utilizing the individual's PK parameters, dosing records, and the PK model, the subjects' PK profiles can be projected, and the time-variant PK effect on the hazard of the event can be calculated at all subjects’ event/censoring times. Within the Cox regression framework, the partial likelihood for an event is calculated as the hazard ratio of the event over the sum of hazard ratios from all subjects at risk at the same event time. Simulation datasets with 150 or 1500 subjects were created, including one time-invariant covariate, one time-variant covariate, PK parameters, and dosing records. Simulations assumed a bathtub-like baseline hazard, a 1-compartment PK model, and an Imax exposure-response relationship for the TTE endpoint. The hazard for censoring was presumed constant. Hazard functions corresponding to the covariates and model-predicted PK profiles were generated, followed by the generation of event and censoring times for all subjects according to their hazard functions. Model parameters for time-invariant and time-variant covariates were estimated and compared in NONMEM and R. Additional comparisons using semi-parametric Cox regression and parametric analysis for time-variant PK effects were done in NONMEM.

Results: Estimated coefficients and relative standard errors for the time-invariant and time-variant covariates were nearly identical ( < 1% difference) between NONMEM and R when excluding PK effects from the model. Estimation performance was assessed through Imax and IC50 values using both the proposed semi-parametric method and a parametric approach with the bathtub hazard. Model parameters were well estimated by both methods. Differences in parameter estimates were minimal with a larger sample size (n=1500 vs n=150), indicating that the proposed method can reliably estimate the exposure-response relationship using proportional hazards Cox regression without a baseline hazard assumption.

Conclusions: The developed methodology successfully integrates time-variant pharmacokinetics and assesses the impact of varying drug concentrations on TTE endpoints. This approach can be further extended to include pharmacodynamic model or biomarker data, thus enhancing decision-making processes in the evaluation of TTE endpoints during drug development.

Citations: [1] Zhang, Z. et al. “Time-varying covariates and coefficients in Cox regression models.” Annals of translational medicine vol. 6,7 (2018): 121. doi:10.21037/atm.2018.02.12
[2] Karlsson, KE. Et al. “Estimating a Cox proportional hazard model in NONMEM”. PAGE - Population Approach Group Europe. (2024) https://www.page-meeting.org/pdf_assets/4156-Poster_PAGE%20_2014_COXPH_Kristin_Karlsson.pdf

Keywords: Cox proportional hazards, time-variant covariate, NONMEM