Department of Population and Quantitative Health Sciences
Epidemiology | Statistics and Probability
Cochran's Q statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value is also used in several popular estimators of the between-study variance, tau 2 . Those applications generally have not considered the implications of its use of estimated variances in the inverse-variance weights. Importantly, those weights make approximating the distribution of Q (more explicitly, Q IV ) rather complicated. As an alternative, we investigate a new Q statistic, Q F , whose constant weights use only the studies' effective sample sizes. For the standardized mean difference as the measure of effect, we study, by simulation, approximations to distributions of Q IV and Q F , as the basis for tests of heterogeneity and for new point and interval estimators of tau 2 . These include new DerSimonian-Kacker-type moment estimators based on the first moment of Q F , and novel median-unbiased estimators. The results show that: an approximation based on an algorithm of Farebrother follows both the null and the alternative distributions of Q F reasonably well, whereas the usual chi-squared approximation for the null distribution of Q IV and the Biggerstaff-Jackson approximation to its alternative distribution are poor; in estimating tau 2 , our moment estimator based on Q F is almost unbiased, the Mandel - Paule estimator has some negative bias in some situations, and the DerSimonian-Laird and restricted maximum likelihood estimators have considerable negative bias; and all 95% interval estimators have coverage that is too high when tau 2 = 0 , but otherwise the Q-profile interval performs very well.
effective sample sizes, heterogeneity, inverse-variance weights, random effects
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DOI of Published Version
Bakbergenuly I, Hoaglin DC, Kulinskaya E. On the Q statistic with constant weights for standardized mean difference. Br J Math Stat Psychol. 2022 Jan 30. doi: 10.1111/bmsp.12263. Epub ahead of print. PMID: 35094381. Link to article on publisher's site
The British journal of mathematical and statistical psychology
Bakbergenuly I, Hoaglin DC, Kulinskaya E. (2022). On the Q statistic with constant weights for standardized mean difference. Population and Quantitative Health Sciences Publications. https://doi.org/10.1111/bmsp.12263. Retrieved from https://escholarship.umassmed.edu/qhs_pp/1470
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