Modelling risk when binary outcomes are subject to error

We present methods for binomial regression when the outcome is determined using the results of a single diagnostic test with imperfect sensitivity and specificity. We present our model, illustrate it with the analysis of real data, and provide an example of WinBUGS program code for performing such an analysis. Conditional means priors are used in order to allow for inclusion of prior data and expert opinion in the estimation of odds ratios, probabilities, risk ratios, risk differences, and diagnostic test sensitivity and specificity. A simple method of obtaining Bayes factors for link selection is presented. Methods are illustrated and compared with Bayesian ordinary binary regression using data from a study of the effectiveness of a smoking cessation program among pregnant women. Regression coefficient estimates are shown to change noticeably when expert prior knowledge and imperfect sensitivity and specificity are incorporated into the model.