An accurate test for homogeneity of odds ratios based on Cochran's Q-statistic

Kulinskaya, Elena and Dollinger, Michael B. (2015) An accurate test for homogeneity of odds ratios based on Cochran's Q-statistic. BMC Medical Research Methodology, 15. ISSN 1471-2288

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Background: A frequently used statistic for testing homogeneity in a meta-analysis of K independent studies is Cochran's Q. For a standard test of homogeneity the Q statistic is referred to a chi-square distribution with K - 1 degrees of freedom. For the situation in which the effects of the studies are logarithms of odds ratios, the chi-square distribution is much too conservative for moderate size studies, although it may be asymptotically correct as the individual studies become large. Methods: Using a mixture of theoretical results and simulations, we provide formulas to estimate the shape and scale parameters of a gamma distribution to t the distribution of Q. Results: Simulation studies show that the gamma distribution is a good approximation to the distribution for Q. Conclusions: : Use of the gamma distribution instead of the chi-square distribution for Q should eliminate inaccurate inferences in assessing homogeneity in a meta-analysis. (A computer program for implementing this test is provided.) This hypothesis test is competitive with the Breslow-Day test both in accuracy of level and in power.

Item Type: Article
Additional Information: © Kulinskaya and Dollinger. 2015 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.
Uncontrolled Keywords: meta-analysis,2x 2 tables,heterogeneity test,interaction test,fixed effects model,random effects model
Faculty \ School: Faculty of Science > School of Computing Sciences
UEA Research Groups: Faculty of Science > Research Groups > Data Science and Statistics
Faculty of Medicine and Health Sciences > Research Centres > Business and Local Government Data Research Centre
Faculty of Science > Research Groups > Norwich Epidemiology Centre
Faculty of Medicine and Health Sciences > Research Groups > Norwich Epidemiology Centre
Depositing User: Pure Connector
Date Deposited: 13 Nov 2015 12:00
Last Modified: 19 Apr 2023 00:40
DOI: 10.1186/s12874-015-0034-x

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