A simple confidence interval for meta‐analysis

By Kurex Sidik, Jeffrey N. Jonkman. Statistics in Medicine, 2002

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The Hartung-Knapp-Sidik-Jonkman method for random effects meta-analysis is straightforward and considerably outperforms the standard DerSimonian-Laird method (2014, methodology): “In contrast, the Hartung, Knapp, Sidik and Jonkman method estimates the variance of ŷr by varHKSJ ¼ X wτi yi−ŷrð Þ2 k−1ð Þ X wτi and uses the t-distribution with k-1 degrees of freedom to derive P-values and confidence intervals, with k the number of studies in the meta-analysis.”
Simple heterogeneity variance estimation for meta‐analysis (2005, methodology): “For details of the approach, see Hartung (1999) and Sidik and Jonkman (2002, 2003).”
A comparison of heterogeneity variance estimators in simulated random‐effects meta‐analyses (2018, methodology): “This method is equivalent to the t-distribution method above, but its variance is multiplied by 217 a scaling factor ∑ ai k i=1 (θi − θ) 2 (k − 1) ⁄ (Sidik and Jonkman, 2002; Wiksten et al., 2016).”
On Constructing Confidence Intervals for a Standardized Mean Difference in Meta-analysis (2003, background): “…i¼1 ŵi : ð2:10Þ Here V̂S is an alternative variance estimate for ̂, and can be viewed as the weighted extension of the usual sample variance estimate for ̂, based on the sample effect measures d1, . . . , dk in the random effects model (Sidik and Jonkman, 2002; Hartung and Knapp, 2001a, 2001b).”