Abstract
The most widely applied semiparametric model is the proportional hazards model proposed by D. R. Cox, or, as stated in the literature, the Cox model. The Cox model has been used widely, although the proportionality assumption restricts its range of possible empirical applications. This chapter explains the partial likelihood estimation of the model. It discusses the use of time-dependent covariates based on partial likelihood estimation, and how to use the method of episode splitting with Cox models. The chapter describes some methods for testing the proportionality assumption that is required in Cox models. It shows how to estimate stratified Cox models in order to cope with the proportionality requirement. The chapter examines how to estimate rate and survivor functions for the Cox model. Cox models offer an easy way to include time-dependent covariates. The partial likelihood method gives estimates of the parameters of a Cox model, but no direct estimate of the underlying baseline rate.
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