A parametric dynamic survival model applied to breast cancer survival times

Abstract

Much current analysis of cancer registry data uses the semiparametric proportional hazards Cox model. In this paper, the time-dependent effect of various prognostic indicators on breast cancer survival times from the West Midlands Cancer Intelligence Unit are investigated. Using Bayesian methodology and Markov chain Monte Carlo estimation methods, we develop a parametric dynamic survival model which avoids the proportional hazards assumption. The model has close links to that developed by both Gamerman and Sinha and co-workers: the log-base-line hazard and covariate effects are piecewise constant functions, related between intervals by a simple stochastic evolution process. Here this evolution is assigned a parametric distribution, with a variance that is further included as a hyperparameter. To avoid problems of convergence within the Gibbs sampler, we consider using a reparameterization. It is found that, for some of the prognostic indicators considered, the estimated effects change with increasing follow-up time. In general those prognostic indicators which are thought to be representative of the most hazardous groups (late-staged tumour and oldest age group) have a declining effect.