Bayesian Nonparametric Survival Analysis

Abstract This article considers a Bayesian nonparametric approach to a (right) censored data problem. Although the results are applicable to a wide variety of such problems, including reliability analysis, the discussion centers on medical survival studies. We extend the posterior distribution of percentiles given by Hill (1968) to obtain predictive posterior probabilities for the survival of one or more new patients, using data from other individuals having the same disease and given the same treatment. The analysis hinges on three assumptions: (a) The new patients and the previous sample patients are all deemed to be exchangeable with regard to survival time. (b) The posterior prediction rule, in the case of no censoring or ties among (say n) observed survival times, assigns equal probability of 1/(n + 1) to each of the n + 1 open intervals determined by these values. (c) The censoring mechanisms are “noninformative.” Detailed discussion of these assumptions is presented from a Bayesian point of view. I...

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