ABSTRACT
In practice, the gamma process is used in conjunction with a Cox proportional hazards model, Cox (1972), writing the probability that the ith individual survives at least to times as Pr(T; ~ s) = exp{ -g(s) exp(xTP) }. Here g is referred to a the baseline cumulative hazard. Modeling g through the gamma process adds a nonparametric component to the hazard along with the parametric linear regression aspect associated with the covariate contribution. Kalbfleisch (1978) presents an elegant argument which shows that, with a flat prior on p and the gamma process specification for the r1, when c is near 0 (i.e., small precision for g about g0 ) the marginal posterior density for p is essentially proportional to the customary partial likelihood, Cox (1975), used for making inference about p, ignoring g.
