Bayesian Interim Analysis of Censored Exponential Observations

by Seymour Geisser
Technical Report No. 563
School of Statistics
University of Minnesota
October, 1991

Introduction

In a previous paper we outlined a procedure that could be useful in certain circumstances in deciding whether or not an experiment should be continued or curtailed, Geisser (1991). The situation envisaged was that an experiment would require a minimum number of observations, say S for concluding the effectiveness of a therapy or drug. One particular case that was dealt with thus was sampling from an exponential distribution in order to test the hypothesis that the mean survival time exceeded a given value. The approach taken was Bayesian and what was required was that after minimum of S observations a posterior probability of at least p was necessary to decide that the mean survival time exceeded a given value a. However an investigator would like to curtail the experiment if the results at a certain time do not appear sufficiently promising. Where he stops to perform an interim analysis will not be preset but will be at any convenient time(s). It is also envisaged that the subjects are put on trial at varying times so that the investigator can decide to discontinue putting new subjects on trial at any time.

In the previous paper we derived algorithms for calculating the predictive probability, after observing N observations, that if the experiment were continued for another M observations we would decide to accept a particular hypothesis. Solutions were obtained for a number of random sampling distributions. Among them was the exponential distribution, but with all observations fully observed. Here we consider the exponential distribution with censoring both with observations lost to follow-up (or that cannot be continued after their being censored) and those that are censored at the interim analysis but can still be observed where the experiment continued.

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