Bayes' theorem and diagnostic tests in neuropsychology: interval estimates for post-test probabilities

Most neuropsychologists are aware that, given the specificity and sensitivity of a test and an estimate of the base rate of a disorder, Bayes' theorem can be used to provide a post-test probability for the presence of the disorder given a positive test result (and a post-test probability for the absence of a disorder given a negative result). However, in the standard application of Bayes' theorem the three quantities (sensitivity, specificity, and the base rate) are all treated as fixed, known quantities. This is very unrealistic as there may be considerable uncertainty over these quantities and therefore even greater uncertainty over the post-test probability. Methods of obtaining interval estimates on the specificity and sensitivity of a test are set out. In addition, drawing and extending upon work by Mossman and Berger (2001), a Monte Carlo method is used to obtain interval estimates for post-test probabilities. All the methods have been implemented in a computer program, which is described and made available (www.abdn.ac.uk/~psy086/dept/BayesPTP.htm). When objective data on the base rate are lacking (or have limited relevance to the case at hand) the program elicits opinion for the pre-test probability.