Some contributions to survival analysis with change-point and decreasing hazard rate

The study of change-point in a hazard rate was initiated in Matthews and Farwell (1982) to model the relapse rate of leukemia patients and further developed in Nguyen, Rogers and Walker (1984), Basu, Ghosh and Joshi (1988), and Ghosh, Joshi and Mukhopadhyay (1993). We introduce to this area Bayesian sequential procedures for a, b, and $\tau$, where the hazard rate h(t) of a lifetime random variable is assumed to be a constant equal to a up to time $\tau$ and another constant equal to b thereafter. The stopping time is defined as the first time the corresponding posterior variance falls below a chosen threshold. Nonparametric Bayesian approaches to decreasing hazard rate and their applications to change-point problem are obtained with the decreased extended gamma process prior, and other choices of prior. Computation of the posteriors with Dykstra-Laud (1981) prior and decreasing hazard rate priors is accomplished by Monte Carlo simulation through an important Polya Urn scheme. A new formula for exact bias and variance of the Kaplan-Meier Product Limit estimator was developed and computation is accomplished by Monte Carlo simulation. A Bayesian life table analysis to Lindley\u27s (1979) model with decreasing hazard rate and its comparison with Thompson\u27s (1977) model is initiated and extended to some extent