Bayesian estimation of intervention effect with pre- and post-misclassified binomial data

We consider studies in which an enrolled subject tests positive on a fallible test. After an intervention, disease status is re-diagnosed with the same fallible instrument. Potential misclassification in the diagnostic test causes regression to the mean that biases inferences about the true intervention effect. The existing likelihood approach suffers in situations where either sensitivity or specificity is near 1. In such cases, common in many diagnostic tests, confidence interval coverage can often be below nominal for the likelihood approach. Another potential drawback of the maximum likelihood estimator (MLE) method is that it requires validation data to eliminate identification problems. We propose a Bayesian approach that offers improved performance in general, but substantially better performance than the MLE method in the realistic case of a highly accurate diagnostic test. We obtain this superior performance using no more information than that employed in the likelihood method. Our approach is also more flexible, doing without validation data if necessary, but accommodating multiple sources of information, if available, thereby systematically eliminating identification problems. We show via a simulation study that our Bayesian approach outperforms the MLE method, especially when the diagnostic test has high sensitivity, specificity, or both. We also consider a real data example for which the diagnostic test specificity is close to 1 (false positive probability close to 0).