ABSTRACT
When information on variables such as age, weight and gender is available for individuals in a survival study, a modelling approach is needed to explore the relationship between the observed survival times and the values of these variables. The Cox regression model that is described in this chapter is a model for the dependence of the hazard of an event occurring at a given time on such variables. The form of the model and the fitting process, based on the partial likelihood function, is described, and this is followed by an account of how alternative models can be compared. Variable selection procedures are outlined, including the lasso. The interpretation of a fitted model in terms of estimated hazard ratios and their associated confidence intervals is illustrated and methods for estimating the survivor function of individuals with given characteristics are developed. This chapter also includes techniques for summarising the variation in the survival times that is explained by a fitted model, the concordance between the model and observed data, and the predictive ability of a model at different time points.
