Bayesian inference for polyhazard models in the presence of covariates

Abstract

Polyhazard models are a flexible family for fitting lifetime data. Their main advantage over the single hazard models, such as the Weibull and the log-logistic models, is to include a large amount of nonmonotone hazard shapes, as bathtub and multimodal curves. The main goal of this paper is to present a Bayesian inference procedure for the polyhazard models in the presence of covariates, generalizing the Bayesian analysis presented in Berger and Sun (J. Amer. Statist. Assoc. 88 (1993) 1412), Basu et al. (J. Statist. Plan Inference 78 (1999) 255) and Kuo and Yang (Statist. Probab. Lett. 47 (2000) 229). The two most important particular polyhazard models, namely poly-Weibull, poly-log-logistic and a combination of both are studied in detail. The methodology is illustrated in two real medical datasets.