Data were combined in the original Science publications [10]–[13] using a fixed effects (Mantel-Haenszel) model. Fixed effects assume that the genetic effects are the same across the combined investigations and all differences are due to chance [1], [2]. While this assumption is true occasionally, it may not be generalizable to all genetic associations. Genetic effects may vary across different populations for various reasons, including both genuine differences and differential biases and errors across studies [14], [15]. In meta-analyses, fixed effects may give more narrow confidence intervals and more impressively low p-values compared with models that accommodate potential diversity of effects (heterogeneity) [1], [2], [5], [16], [17]. We have re-analyzed the meta-analyses of the three teams with random effects calculations [1], [2]. Random effects calculations assume that due to genuine differences and or different biases, the estimates of the genetic effects may vary across different investigations. Random effects thus try to estimate the population average and the extent of dispersion in these different effect sizes. The presented random effects calculations use the DerSimonian and Laird estimator of the between-study variance [18].
