The exact distribution of Cochran's heterogeneity statistic in one-way random effects meta-analysis

Authors

  • Brad J. Biggerstaff,

    Corresponding author
    1. Division of Vector-Borne Infectious Diseases, National Center for Zoonotic, Vector-Borne, and Enteric Diseases, Centers for Disease Control and Prevention, Fort Collins, CO 80521, U.S.A.
    • Division of Vector-Borne Infectious Diseases, National Center for Zoonotic, Vector-Borne, and Enteric Diseases, Centers for Disease Control and Prevention, Fort Collins, CO 80521, U.S.A.
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  • Dan Jackson

    1. MRC Biostatistics Unit, Institute of Public Health, Robinson Way, Cambridge CB2 0SR, U.K.
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  • The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the Centers for Disease Control and Prevention.

  • This article is a U.S. Government work and is in the public domain in the U.S.A.

Abstract

The presence and impact of heterogeneity in the standard one-way random effects model in meta-analysis are often assessed using the Q statistic due to Cochran. We derive the exact distribution of this statistic under the assumptions of the random effects model, and also suggest two moment-based approximations and a saddlepoint approximation for Q. The exact and approximate distributions are then applied to obtain the corresponding distributions of the recently proposed heterogeneity measures I2 and Hmath image, the power of the standard test for the presence of heterogeneity and confidence intervals for the between-study variance parameter when the DerSimonian–Laird or the Hartung–Makambi estimator is used. The methodology is illustrated by revisiting a recent simulation study concerning the heterogeneity measures and applying all the proposed methods to four published meta-analyses. Published in 2008 by John Wiley & Sons, Ltd.

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