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

Elena Kulinskaya; Michael B. Dollinger

doi:10.1186/s12874-015-0034-x

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

Elena Kulinskaya, Michael B. Dollinger

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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 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.

Original language	English
Article number	49
Journal	BMC Medical Research Methodology
Volume	15
DOIs	https://doi.org/10.1186/s12874-015-0034-x
Publication status	Published - 10 Jun 2015

Keywords

meta-analysis
2x 2 tables
heterogeneity test
interaction test
fixed effects model
random effects model

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10.1186/s12874-015-0034-xLicence: CC BY

OR second bmc cFinal published version, 819 KBLicence: CC BY

Elena Kulinskaya
- E.Kulinskayauea.acuk
- School of Computing Sciences - Emeritus Professor
- Norwich Epidemiology Centre - Member
Person: Honorary, Research Group Member

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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 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. ",

keywords = "meta-analysis, 2x 2 tables, heterogeneity test, interaction test, fixed effects model, random effects model ",

author = "Elena Kulinskaya and Dollinger, {Michael B.}",

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AU - Kulinskaya, Elena

AU - Dollinger, Michael B.

N1 - © Kulinskaya and Dollinger. 2015 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), 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 (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

PY - 2015/6/10

Y1 - 2015/6/10

N2 - 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.

AB - 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.

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KW - 2x 2 tables

KW - heterogeneity test

KW - interaction test

KW - fixed effects model

KW - random effects model

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DO - 10.1186/s12874-015-0034-x

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JO - BMC Medical Research Methodology

JF - BMC Medical Research Methodology

SN - 1471-2288

M1 - 49

ER -

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

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Elena Kulinskaya

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