Bayesian nonparametric prediction based on censored data.

This dissertation extends the results of Berliner and Hill (1988) in several directions, including a computational algorithm, the two-sample case, and two simulation studies. The results are applicable for medical survival studies. The fundamental problem of Berliner and Hill is: given death times and censored times, what is the predictive posterior distribution of the death time of the next patient? The nonparametric Bayesian procedure, denoted by $A\sb n$, was proposed by Hill (1968). Berliner and Hill use $A\sb n$, exchangeability, noninformative censoring assumptions, and the Partial Censoring Information (PCI) approximation to solve the problem. This yields a coherent Bayesian procedure. For the same problem, this study proposes a simple algorithm which can derive the predictive probabilities for $K$ new patients. The results are recursive formulas which are efficient for computation. The sequential approach of Genest and Kalbfleisch is discussed. Given two sets of censored data, one may ask for the probability that the death time for the next patient for one group is larger than that for the other group. This problem is solved by adding two more assumptions: continuous distributions and independence between the two groups. The probability is evaluated by spline smoothing and a graphical argument. Comparing the PCI estimator with the Kaplan-Meier (KM) estimator, the simulation studies yield the following results: the PCI estimators for the mean and for the percentiles outperform the corresponding KM estimators except in one of the six populations studied.PhDPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128410/2/9013873.pd