title: An accurate test for homogeneity of odds ratios based on Cochran's Q-statistic.
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.
authors.affiliation: School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, UK. e.kulinskaya@uea.ac.uk.
authors.forename: Elena
authors.initials: E
authors.lastname: Kulinskaya
authors.affiliation: Department of Mathematics, Pacific Lutheran University, Tacoma, 98447, USA, WA. dollinmb@plu.edu.
authors.forename: Michael B
authors.initials: MB
authors.lastname: Dollinger
mesh_terms: D000465:Algorithms; D001699:Biometry / Q000379:methods*; D016009:Chi-Square Distribution; D003198:Computer Simulation; D006801:Humans; D015201:Meta-Analysis as Topic; D016017:Odds Ratio; D015203:Reproducibility of Results; D012984:Software