Uncertainty in clinical prediction rules: the value of credible intervals

Decision making in physical therapy is increasingly informed by evidence in the form of probabilities. Prior beliefs concerning diagnoses, prognoses, and treatment effects are quantitatively revised by the integration of new information derived from the history, physical examination, and other investigations in a well-recognized application of Bayes' theorem. Clinical prediction rule development studies commonly employ such methodology to produce quantified estimates of the likelihood of patients having certain diagnoses or achieving given outcomes. To date, the physical therapy literature has been limited to the discussion and calculation of the point estimate of such probabilities. The degree of precision associated with the construction of posterior probabilities, which requires consideration of both uncertainty associated with pretest probability and uncertainty associated with test accuracy, remains largely unrecognized and unreported. This paper provides an introduction to the calculation of the uncertainty interval, known as a credible interval, around posterior probability estimates. The method for calculating the credible interval is detailed and illustrated with example data from 2 clinical prediction rule development studies. Two relatively quick and simple methods for approximating the credible interval are also outlined. It is anticipated that knowledge of the credible interval will have practical implications for the incorporation of probabilistic evidence in clinical practice. Consistent with reporting standards for interventional and diagnostic studies, it is equally appropriate that studies reporting posterior probabilities calculate and report the level of precision associated with these point estimates.