Bayesian analysis of two dependent 2×2 contingency tables

Bayesian analysis of correlated binary data when individual information is not available is considered. In particular, a binary outcome is measured on the same subjects of two independent groups at two separate occasions (usually time points). The groups are formulated through a binary exposure or a prognostic factor. Interest lies in estimating the association between exposure and outcome over time. Standard methods for this purpose apply on the individual item responses and are insufficient in case these are missing. Moreover it is assumed that the only available information is the marginal 2×2 cross-tabulations between the grouping variable and the response for each occasion. Assuming independent binomial distributions for the two groups, the success probabilities for each occasion as well as the associations between exposure and outcome, based on the corresponding odds ratios, are estimated. In order to deal with the missing information of each item’s response and to estimate the corresponding transition probabilities, a Bayesian procedure is adopted.