A method for the meta‐analysis of mutually exclusive binary outcomes

Meta-analyses of multiple outcomes need to take into account the within-study correlation across the different outcomes. Here we focus on the meta-analysis of dichotomous outcomes that are mutually exclusive and exhaustive. Correlations between effect sizes for mutually exclusive outcomes are negative and can be obtained from data already available. We present both fixed-effects and random-effects methods that account for the negative correlations and yield correct simultaneous confidence intervals for both the marginal outcome-specific effect sizes and the relative effect sizes between outcomes. Formulae for the odds ratio, risk ratio, risk difference, and the differences in the arcsin-transformed risks are provided. An example of a meta-analysis of randomized trials of radiotherapy and mastectomy with axillary lymph node clearance versus only mastectomy with axillary clearance for early breast cancer is presented. The mutually exclusive outcomes of breast cancer deaths and deaths secondary to other causes are examined in separate meta-analyses, and also by taking the between-outcome correlation into account. We argue that mutually exclusive outcomes in the meta-analyses of binary data are optimally analyzed in a multinomial setting. This may also be applicable when a meta-analysis examines only one out of several mutually exclusive outcomes. For large sample sizes and/or low event counts, the covariances between outcome-specific effect sizes are small, and either ignoring them or accounting for them would result in similar estimates for any practical purpose. However, meta-analysts should explore the robustness of the findings from individual meta-analyses when mutually exclusive outcomes are assessed.