Using Bayesian p-values in a 2 x 2 table of matched pairs with incompletely classified data

Altham proposed Bayesian p-values for the analysis of a 2x2 contingency table that is formed from matched pairs. Using the same Bayesian perspective, we develop an extension of Altham's Bayesian p-values to a 2x2 table from matched pairs with missing data that are missing at random. The approach is applied to a rater agreement study, in which two surgeon-reviewers rated whether or not there was a communication breakdown in malpractice cases. We also use a simulation study to explore the power and type I error rate of the Bayesian p-values.