Diagnostic testing: a simple approximate interval for the positive predictive value

In diagnostic testing, given specificity, sensitivity and prevalence, Bayes' rule gives the so-called positive predictive value. Generally there are two potential pitfalls that have been identified previously. First, it is incorrect to estimate prevalence from the usual 2x2 table if the data are from a case control study. Second, it would usually seem inadequate to only use point estimates, without considering uncertainty. In relation to these pitfalls, it is shown that if in fact the prevalence suggested by the 2x2 table is reasonable, in a Bayesian context a simple beta distribution may be adopted to obtain a credible interval for the positive predictive value, as an approximation of an existing objective Bayesian solution based on Monte Carlo simulation.