The impact of multiple endpoint dependency on Q and I(2) in meta-analysis

A common assumption in meta-analysis is that effect sizes are independent. When correlated effect sizes are analyzed using traditional univariate techniques, this assumption is violated. This research assesses the impact of dependence arising from treatment-control studies with multiple endpoints on homogeneity measures Q and I(2) in scenarios using the unbiased standardized-mean-difference effect size. Univariate and multivariate meta-analysis methods are examined. Conditions included different overall outcome effects, study sample sizes, numbers of studies, between-outcomes correlations, dependency structures, and ways of computing the correlation. The univariate approach used typical fixed-effects analyses whereas the multivariate approach used generalized least-squares (GLS) estimates of a fixed-effects model, weighted by the inverse variance-covariance matrix. Increased dependence among effect sizes led to increased Type I error rates from univariate models. When effect sizes were strongly dependent, error rates were drastically higher than nominal levels regardless of study sample size and number of studies. In contrast, using GLS estimation to account for multiple-endpoint dependency maintained error rates within nominal levels. Conversely, mean I(2) values were not greatly affected by increased amounts of dependency. Last, we point out that the between-outcomes correlation should be estimated as a pooled within-groups correlation rather than using a full-sample estimator that does not consider treatment/control group membership.