ABSTRACT
Parametric models based on a probability distribution for survival times depend on just one or two unknown parameters. They then have a limited ability to capture the underlying form of a baseline hazard function. This chapter describes some parametric models that have the flexibility of a Cox regression model in a parametric framework. The chapter begins with a summary of the piecewise exponential model, which can be regarded as a parametric version of the Cox model. Spline functions are then introduced, and it is shown how these can be used in modelling the survival data. Possible models include a B-spline model for the log-hazard function and a restricted cubic spline model for the log-cumulative hazard function, also known as the Royston-Parmar model. This chapter shows how the number of knots required in a spline model can be determined, and how the hazard and survivor functions for particular individuals can be estimated. Flexible proportional odds models are also described.
