Kulinskaya E, Dollinger MB. An accurate test for homogeneity of odds ratios based on Cochran's Q-statistic.
BMC Med Res Methodol 2015;
15:49. [PMID:
26054650 PMCID:
PMC4531442 DOI:
10.1186/s12874-015-0034-x]
[Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2014] [Accepted: 04/15/2015] [Indexed: 11/25/2022] Open
Abstract
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 fit 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.
Electronic supplementary material
The online version of this article (doi:10.1186/s12874-015-0034-x) contains supplementary material, which is available to authorized users.
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