Chapter 9

Cox-Type Proportional Hazards Models

Jianwen Cai, Donglin Zeng and Yu Deng

9.1 Introduction

The Cox proportional hazards model, which is also referred to as Cox regression, proportional hazards regression, or relative-risk regression, is a regression procedure in the study of univariate failure times that may be censored. It was originally proposed by Cox [1]. It has become a standard method for dealing with censored failure time data and has been widely used in clinical trials and other biomedical research. Much methodological work has been motivated by this model, including marginal models developed for multivariate failure time data such as multiple type failure time and clustered survival data.

The aim of this article is to provide an overview on the Cox-type proportional hazards model. We first present the model for univariate failure time in its original form and discuss the interpretation and estimation of the regression parameters. We also present the estimation of the cumulative hazard function and the survival function after a Cox model fit. It is further extended to the stratified models. Then marginal models will be introduced together with the parameter estimates, covariance structures and inferences. Applications to different studies and corresponding SAS/R codes will be presented. We will further discuss some issues in practical use. Approximations for handling tied failure-time data, incorporation of time-dependent covariates, ways to check proportional ...

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