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Medical Decision Making
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Bayesian Approaches to Meta-analysi of ROC Curves

Martin Hellmich

Keith R. Abrams, PhD

Alex J. Sutton, MSc

A comparative review of important classic and Bayesian approaches to fixed-effects and random-effects meta-analysis of binormal ROC curves and areas underneath them is presented. The ROC analyses results of seven evaluation studies concerning the dexamethasone suppression test provide the basis for a worked example. Particular attention is given to fully Bayesian inference, a novelty in the ROC context, based on Gibbs samples from posterior distributions of hierarchical model parameters and re lated quantities. Fully Bayesian meta-analysis may properly account for the uncertainty associated with the model parameters, possibly incorporating prior knowledge and beliefs, and allows clinically intuitive predictions of unobserved study effects via cal culation of posterior predictive densities. The effects of various different prior specifi cations (six noninformative as well as one informative) on the posterior estimates are investigated (sensitivity-analysis). Recommendations and suggestions for further re search are made. Computer code for the more advanced methods may either be downloaded via the Internet or be found elsewhere. Key words : Bayesian methods; random effects; meta-analysis; ROC curve; diagnostic test; hierarchical models; Mar kov-chain Monte Carlo technique; Gibbs sampling; maximum likelihood; method of moments. (Med Decis Making 1999; 19:252-264)

Medical Decision Making, Vol. 19, No. 3, 252-264 (1999)
DOI: 10.1177/0272989X9901900304
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