Proportional Hazards Regression Models

Abstract

The proportional hazards model plays an important role in analyzing data with survival outcomes. This chapter provides a summary of different aspects of this very popular model. The first part gives the definition of the model and shows how to estimate the regression parameters for survival data with or without ties. Hypothesis testing can be built based on these estimates. Formulas to estimate the cumulative hazard function and the survival function are also provided. Modified models for stratified data and data with time-dependent covariates are also discussed. The second part of the chapter talks about goodness-of-fit and model checking techniques. These include testing for proportionality assumptions, testing for function forms for a particular covariate and testing for overall fitting. The third part of the chapter extends the model to accommodate more complicated data structures. Several extended models such as models with random effects, nonproportional models, and models for data with multivariate survival outcomes are introduced. In the last part a real example is given. This serves as an illustration of the implementation of the methods and procedures discussed in this chapter.