Cox Proportional Hazards Model

The Cox proportional hazards model is the most widely used model for analyzing survival data. Its semiparametric nature, focusing on the effect of covariates while leaving the baseline hazard function unspecified, offers a more robust modeling approach compared with parametric models. Furthermore, inference based on the partial likelihood provides simple, robust, and efficient analysis. This chapter discusses the model and inference procedures, including stratified analysis for nonproportional hazards. Moreover, pseudo-likelihood estimation, nonparametric maximum likelihood estimation, and generalized rank estimators are presented. These methods provide alternative approaches that are intuitive. They also have natural extensions to other models or scenarios where the partial likelihood method may be difficult to implement. A section is also devoted to the comparison between timeto- event analysis and binomial approximation. It is shown that the latter method is prone to distortion by differences in the censoring distributions between the two comparison groups, while the former is often much more robust against the influence of censoring.