Comparative Bayesian and Traditional Inference for Gamma-Modeled Survival Data

Abstract

Two distinct Bayesian methodologies are developed and compared for inference on .gamma.-scale parameters in 1 and 2 population problems. Both approaches permit concomitant variables and censored observations in the exponential case. The first approach, based on the use of natural-conjugate prior distributions, generalizes and harmonizes and harmonizes with the traditional frequentist analysis in terms of .chi.2 and F distributions. The second method is based on non-continuous-type extensions of the natural conjugate priors, and involves the use of Bayes factors for sharply defined hypotheses. The 2 methods appear to conflict in hypothesis inference problems and to harmonize in interval estimation problems. Inferences from the 2 methods are compared for survival data from a [human] Hodgkin''s disease therapy trial.