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 non-proportional effects are also supported by the
software. Examples based on a study of prognostic factors in breast cancer
are given.
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Patrick Royston
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parametric survival analysis, hazard function, proportional hazards, proportional odds
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