One relative risk versus two odds ratios: implications for meta-analyses involving paired and unpaired binary data

BACKGROUND: There are debates on whether the conditional odds ratio or marginal odds ratio should be used in meta-analysis involving both paired and unpaired binary data. Although statistically sound, both approaches result in overall odds ratios which are known to be less meaningful to consumers. PURPOSE: To show that while two odds ratios can be calculated in a pair-matched study, there is only one relative risk for such design, and to discuss the implications for meta-analysis involving both paired and unpaired binary data. METHODS: Algebra and an example, along with standard software for implementing relative risk regression models. RESULTS: The choice of relative risk as the effect measure in pair-matched design not only simplifies analysis and interpretation for individual studies, but makes mata-analysis involving both paired and unpaired studies straightforward. Pooling marginal odds ratios in a meta-analysis of diabetic retinopathy treatment resulted in a summarized odds ratio of 2.25 (95% CI 1.83-2.75), compared with that of 2.44 (95% CI 1.95-3.04) from pooling conditional odds ratios. In contrast, summarizing relative risks resulted in an overall effect measure of 1.09 (95% CI 1.06-1.11), implying the treatment reduces visual deterioration rate by 9%. CONCLUSION: Relative risk may be the first consideration in measuring effect for analyzing prospective studies with binary outcomes.