Bayesian semiparametric estimation of proportional hazards models

This paper proposes a semiparametric analysis of proportional hazards models. This approach consists in specifying the relation between a duration and explanatory variables, without specifying the data distribution. The parameters involved in this relation are then considered as parameters of interest, and the data distribution is treated as a nuisance parameter. We propose a Bayesian estimation method, the principle of which is to specify a prior distribution on the nuisance parameter. We then obtain semiparametric estimators for the parameters of interest, by computing their posterior distribution, conditional on the data and integrated with respect to the nuisance parameter.