On the Q statistic with constant weights for standardized mean difference.
Br J Math Stat Psychol
; 75(3): 444-465, 2022 11.
Article
en En
| MEDLINE
| ID: mdl-35094381
ABSTRACT
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, τ 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 τ 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 τ 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 τ 2 = 0 , but otherwise the Q-profile interval performs very well.
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Texto completo:
1
Colección:
01-internacional
Base de datos:
MEDLINE
Asunto principal:
Algoritmos
/
Modelos Estadísticos
Tipo de estudio:
Prognostic_studies
/
Risk_factors_studies
/
Systematic_reviews
Idioma:
En
Revista:
Br J Math Stat Psychol
Año:
2022
Tipo del documento:
Article
País de afiliación:
Reino Unido