Estimation in the Koziol-Green model using a gamma process prior

In survival analysis we deal with times to occurrence of an event. If a variable of interest X with survival function S is cen-sored from the right by a random variable Y (independent of X) we get the random censorship model. We observe a pair Z =min(X,Y) and I = I[X≤Y], (1) where I is an indicator of noncensored observation. Here we deal with the proportional hazards censorship model of Koziol and Green [7], in which survival function SY of the time censor is moreover assumed to satisfy SY (x) = (S(x))γ, x> 0, (2) with some positive constant γ. Or, using cumulative hazard rate Λ = − lnS of X, the rate of Y equals γΛ. Equivalently, Z and I are independent, in continuous case P(X ≤Y) = (1+γ)−1. See [3] for a review of implications to inference. We work with a random sample of size n from (1) with (2)