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Intervals for Posttest Probabilities: A Comparison of 5 Methods

Division of Forensic Psychiatry, Wright State University School of Medicine, Dayton, Ohio

James O. Berger, PhD

Institute of Statistics and Decision Sciences, Duke University, Durham, North Carolina

Background. Several medical articles discuss methods of constructing confidence intervals for single proportions and the likelihood ratio, but scant attention has been given to the systematic study of intervals for the posterior odds, or the positive predictive value, of a test. Methods. The authors describe 5 methods of constructing confidence intervals for posttest probabilities when estimates of sensitivity, specificity, and the pretest probability of a disorder are derived from empirical data. They then evaluate each method to determine how well the intervals’ coverage properties correspond to their nominal value. Results. When the estimates of pretest probabilities, sensitivity, and specificity are derived from more than 80 subjects and are not close to 0 or 1, all methods generate intervals with appropriate coverage properties. When these conditions are not met, however, the best-performing method is an objective Bayesian approach implemented by a simple simulation using a spreadsheet. Conclusion. Physicians and investigators can generate accurate confidence intervals for posttest probabilities in small-sample situations using the objective Bayesian approach.

Key Words: positive predictive value • Bayes’ theorem • posterior probability • posterior odds • posttest probability • confidence interval • objective Bayesian

Medical Decision Making, Vol. 21, No. 6, 498-507 (2001)
DOI: 10.1177/0272989X0102100608


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