A Bayesian Proportional-Hazards Model In Survival Analysis

Let δi = 1 if the i time Yi is an observed death and δi = 0 if it was a right-censored event: That is, the individual was alive at time Yi, but was last seen at that time. If Ti (1 ≤ i ≤ n) are the true survival or failure times, then Yi = Ti if δi = 1 and Yi < Ti if δi = 0, in which case the true failure time Ti is unknown. We also assume d-dimensional covariate vectors X1, X2, . . . , Xn for the n individuals in (1.1). The components of Xi might be age, income status, etc. The basic data for (1.1) is the set of triples (Yi, δi, Xi) for 1 ≤ i ≤ n. The most important statistical questions are connected with estimating the effect of the covariates Xi on the true survival times Ti. Let Ỹ1 < Ỹ2 < . . . < Ỹm (1.2)