Generating survival times to simulate Cox proportional hazards models

TLDR

Simulation studies are essential for evaluating statistical models, and the Cox proportional hazards model is a key tool in medical research, while non‑exponential distributions are required to explore baseline hazard effects in non‑standard situations. The paper presents methods for generating survival times in simulation studies of Cox proportional hazards models. The authors derive a general hazard–survival relationship and show how exponential, Weibull, and Gompertz distributions, as well as custom distributions, can be used to generate survival times for Cox model simulations. A simulation study on the German Uranium Miners Cohort demonstrates the impact of measurement errors and underscores the need for careful baseline hazard modeling in Cox analyses. © 2005 John Wiley & Sons, Ltd.

Abstract

Abstract Simulation studies present an important statistical tool to investigate the performance, properties and adequacy of statistical models in pre‐specified situations. One of the most important statistical models in medical research is the proportional hazards model of Cox. In this paper, techniques to generate survival times for simulation studies regarding Cox proportional hazards models are presented. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived, which is useful in simulation studies. It is shown how the exponential, the Weibull and the Gompertz distribution can be applied to generate appropriate survival times for simulation studies. Additionally, the general relation between hazard and survival time can be used to develop own distributions for special situations and to handle flexibly parameterized proportional hazards models. The use of distributions other than the exponential distribution is indispensable to investigate the characteristics of the Cox proportional hazards model, especially in non‐standard situations, where the partial likelihood depends on the baseline hazard. A simulation study investigating the effect of measurement errors in the German Uranium Miners Cohort Study is considered to illustrate the proposed simulation techniques and to emphasize the importance of a careful modelling of the baseline hazard in Cox models. Copyright © 2005 John Wiley & Sons, Ltd.