Meta-Analysis of Odds Ratios

Bei‐Hung Chang · David C. Hoaglin

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Meta-analysis and systematic reviews Statistical Methods in Clinical Trials Statistical Methods in Epidemiology

Abstract

BACKGROUND: Many systematic reviews of randomized clinical trials lead to meta-analyses of odds ratios (ORs). The customary methods of estimating an overall OR involve weighted averages of the individual trials' estimates of the logarithm of the OR. That approach, however, has several shortcomings, arising from assumptions and approximations, that render the results unreliable. Although the problems have been documented in the literature for many years, the conventional methods persist in software and applications. A well-developed alternative approach avoids the approximations by working directly with the numbers of subjects and events in the arms of the individual trials. OBJECTIVE: We aim to raise awareness of methods that avoid the conventional approximations, can be applied with widely available software, and produce more-reliable results. METHODS: We summarize the fixed-effect and random-effects approaches to meta-analysis; describe conventional, approximate methods and alternative methods; apply the methods in a meta-analysis of 19 randomized trials of endoscopic sclerotherapy in patients with cirrhosis and esophagogastric varices; and compare the results. We demonstrate the use of SAS, Stata, and R software for the analysis. RESULTS: In the example, point estimates and confidence intervals for the overall log-odds-ratio differ between the conventional and alternative methods, in ways that can affect inferences. Programming is straightforward in the 3 software packages; an appendix, Suppemental Digital Content 1 (http://links.lww.com/MLR/B335) gives the details. CONCLUSIONS: The modest additional programming required should not be an obstacle to adoption of the alternative methods. Because their results are unreliable, use of the conventional methods for meta-analysis of ORs should be discontinued.

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References

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