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

Department of Epidemiology & Biostatistics, Schulich School of Medicine & Dentistry, University of Western Ontario, London, Ontario, Canada; Robarts Clinical Trials, Robarts Research Institute, London, Ontario, Canada

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.

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