Flexible Parametric Alternatives to the Cox Model, and more

Abstract

Since its introduction to a wondering public in 1972, the Cox proportional hazards regression model has become an overwhelmingly popular tool in the analysis of censored survival data. However, some features of the Cox model may cause problems for the analyst or an interpreter of the data. They include the restrictive assumption of proportional hazards for covariate effects, and “loss” (non-estimation) of the baseline hazard function induced by conditioning on event times. In medicine, the hazard function is often of fundamental interest since it represents an important aspect of the time course of the disease in question. In the present article, the Stata implementation of a class of flexible parametric survival models recently proposed by Royston and Parmar (2001) will be described. The models start by assuming either proportional hazards or proportional odds (user-selected option). The baseline distribution function is modeled by restricted cubic regression spline in log time, and parameter estimation is by maximum likelihood. Model selection and choice of knots for the spline function are discussed. Interval-censored data and models in which one or more covariates have nonproportional effects are also supported by the software. Examples based on a study of prognostic factors in breast cancer are given.