STATISTICS IN MEDICINE, VOL. 4,509-520 (1985) AN APPLICATION OF BAYESIAN ANALYSIS TO MEDICAL FOLLOW-UP DATA zyxw JORGE A. ACHCAR zyxwvu Department of Computer Science and Statistics, Federal University of Sao Carlos, Sao Carlos, Brazil RON BROOKMEYER Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland, U.S.A. AND WILLIAM G. HUNTER Department of Statistics, University of Wisconsin, Madison, Wisconsin, U.S.A. SUMMARY Posterior distributions can provide effective summaries of the main conclusions of medical follow-up studies, In this article, we use Bayesian methods for the analysis of survival data. We describe posterior distributions for various parameters of clinical interest in the presence of arbitrary right censorship. Non-informative reference priors result from transformation of a two-parameter Weibull model into a location-scale family. We suggest an approach for checking adequacy. For illustration, we apply the methods to a well-known acute leukemia data set. zyxwvuts KEY WORDS Bayesian analysis Censoring Medical follow-up study Weibull distribution 1. INTRODUCTION This research seeks to explore the possible usefulness of Bayes’ theorem in the analysis of survival data from medical follow-up studies. Bayesian methods in this context have received little attention, the argument having been that non-parametric methods are more appropriate because of the diffuculty of model specification with clinical data. Clinical data, however, do contain information with respect to model form. If a particular data set contains little information of this kind, a careful Bayesian analysis will reveal this fact, a desirable rather than undesirable feature of the method. We summarize our conclusions from this research as follows: posterior distributions of various parameters of clinical interest can often provide striking and effective summaries of the main conclusions of medical follow-up studies. For instance, one often employs the median survival time to characterize the survival experience of a single treatment group, and the ratio of medians is useful for the comparison of the relative efficacy of two treatments. Posterior distributions for such parameters have ease of interpretation, and they can provide valuable insight. In our experience, medical researchers readily understand the meaning of such posterior distributions. One can supplement posterior distributions for the median with other percentiles of interest, such as the 25th and 75th. Furthermore, one can construct posterior distributions for 0277-6715/85/040509-12SO1.20 zyxwvu 0 1985 by John Wiley zyxwvuts & Sons, Ltd. Received May zy 1984 Revised zyx February 1985