21 Cox Proportionate Hazards Regression Model
Peter McQuire
21.1 Introduction
In this chapter we will look at one of the most cited statistical models used to analyse survival data – the Cox proportional hazards model (the “Cox model”) developed by Sir David Cox in 1972. The principal objective of the Cox model is to determine the influence of various chosen covariates on the hazard rate, and hence understand the extent of heterogeneity present in a particular investigation.
In contrast with many statistical models we look at in this book, it is not the objective of the Cox model to determine the absolute hazard rate given a particular set of covariates. Instead, here we are interested in the ratio of hazard rates, or the relative effect which a covariate has on the hazard rate. For example we may use the Cox model to measure the efficacy of a trialled drug by comparing survival rates of patients diagnosed with a potentially fatal disease, where patients are given either the drug or a placebo (here the covariate is binary: drug or placebo). Our objective in this example is to compare the mortality rates of patients who were given the drug with those who were given the placebo.
The Cox model could also be used, for example, to address the following questions:
- What is the effect on human mortality rates from exercising, drinking alcohol or smoking cigarettes?
- Do prisoners’ reoffending rates reduce if they receive certain types of education ...