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.