Abstract
Background: A frequently used statistic for testing homogeneity in a metaanalysis of K independent studies is Cochran's Q. For a standard test of homogeneity the Q statistic is referred to a chisquare distribution with K  1 degrees of freedom. For the situation in which the effects of the studies are logarithms of odds ratios, the chisquare 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 chisquare distribution for Q should eliminate inaccurate inferences in assessing homogeneity in a metaanalysis. (A computer program for implementing this test is provided.) This hypothesis test is competitive with the BreslowDay test both in accuracy of level and in power.
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 chisquare distribution for Q should eliminate inaccurate inferences in assessing homogeneity in a metaanalysis. (A computer program for implementing this test is provided.) This hypothesis test is competitive with the BreslowDay test both in accuracy of level and in power.
Original language  English 

Article number  49 
Journal  BMC Medical Research Methodology 
Volume  15 
DOIs  
Publication status  Published  10 Jun 2015 
Keywords
 metaanalysis
 2x 2 tables
 heterogeneity test
 interaction test
 fixed effects model
 random effects model
Profiles

Elena Kulinskaya
 School of Computing Sciences  Professor in Statistics (AVIVA)
 Business and Local Government Data Research Centre  Member
 Norwich Epidemiology Centre  Member
 Data Science and Statistics  Member
Person: Research Group Member, Research Centre Member, Academic, Teaching & Research