ABSTRACT
The Cox regression model is readily extended to incorporate variables whose values change over time, or to allow the coefficient of an explanatory variable to vary with time. Different types of time-dependent variable are summarised, and it is shown how the Cox model can be extended to incorporate them. Estimation of the survivor function, model comparison and validation are all considered. When using computer software to fit models with time-dependent variables, survival data are expressed in counting process format. This is described and the necessary data manipulation illustrated. An alternative to incorporating time-dependent variables in a Cox model is to first develop a model for the dependence of the evolving values of a variable on time. This is then combined with either a Cox regression model, or a parametric model for the survival times, to give a joint model for longitudinal and survival data. Following an introduction to models for longitudinal data, a joint model for the dependence of the hazard of an event occurring on a longitudinal variable is described and illustrated, and some extensions to the basic model are outlined.
