Meta-analysis combining parallel and cross-over clinical trials. II: Binary outcomes

We examine different methods to pool binary outcomes used both in parallel and cross-over trials. Odds ratio (OR) estimators obtained from joint conditional probabilities in cross-over trials, such as the Mantel-Haenszel and Peto methods, are compared to an OR estimator using marginal results of cross-over trials. When there is correlation between the outcomes in the two cross-over periods, joint conditional ORs differ from marginal ORs and cannot be combined with OR estimates from parallel trials. The marginal OR estimate is independent of the between-period correlation and it includes a correction for cross-over correlation in the variance estimate. As its computation is similar in cross-over and parallel trials, it is the method of choice to pool results from parallel and cross-over trials in a combined design meta-analysis.