Bayesian Inference for Medical Screening Tests: Approximations Useful for the Analysis of Acquired Immune Deficiency Syndrome

Large sample Bayesian methods for assessing the accuracy of screening tests that are used to detect antibodies to the human immunodeficiency virus in donated blood, and for assessment the prevalence of the disease in the population sampled from are developed.

Abstract

SUMMARY In this paper, we develop large sample Bayesian methods for assessing the accuracy of screening tests that are used to detect antibodies to the human immunodeficiency virus in donated blood, and for assessing the prevalence of the disease in the population sampled from. We obtain approximate joint and marginal posterior distributions for the predictive values positive and negative of a test and, additionally, we obtain approximate predictive distributions for the number of future individuals that will test positively or be truly positive out of a new sample or population of interest. We illustrate our methods with data from Canada and the UK.