Review of bayesian analysis in additive hazards model

Abstract

In Survival Analysis, the focus of interest is a time $T^*$ until the occurrence of some event. A set of explanatory variables (denoted by a vector $Z$) is considered to analyze if there is a relationship between any of them and $T^*$. Accordingly, the ``hazard function´´ is defined: [ lambda(t,z) := lim_{Delta downarrow 0} rac{P[Tleq t+ Delta ert T >t,Z=z]}{Delta} .] Several models are defined based on this, as is the case of the additive model (among others). Bayesian techniques allow to incorporate previous knowledge or presumption information about the parameters into the model. This area grows extensively since the computationally techniques increase, giving rise to powerful Markov Chain Monte Carlo (MCMC) methods, which allow to generate random samples from the desired distributions. The purpose of this article is to offer a summary of the research developed in Bayesian techniques to approach the additive hazard models.