Simulating survival data with predefined censoring rates for proportional hazards models.

The proportional hazard model is one of the most important statistical models used in medical research involving time-to-event data. Simulation studies are routinely used to evaluate the performance and properties of the model and other alternative statistical models for time-to-event outcomes under a variety of situations. Complex simulations that examine multiple situations with different censoring rates demand approaches that can accommodate this variety. In this paper, we propose a general framework for simulating right-censored survival data for proportional hazards models by simultaneously incorporating a baseline hazard function from a known survival distribution, a known censoring time distribution, and a set of baseline covariates. Specifically, we present scenarios in which time to event is generated from exponential or Weibull distributions and censoring time has a uniform or Weibull distribution. The proposed framework incorporates any combination of covariate distributions. We describe the steps involved in nested numerical integration and using a root-finding algorithm to choose the censoring parameter that achieves predefined censoring rates in simulated survival data. We conducted simulation studies to assess the performance of the proposed framework. We demonstrated the application of the new framework in a comprehensively designed simulation study. We investigated the effect of censoring rate on potential bias in estimating the conditional treatment effect using the proportional hazard model in the presence of unmeasured confounding variables.