• Nikolaos A Patsopoulos, Evangelos Evangelou, and John P A Ioannidis.
• Clinical Trials and Evidence-Based Medicine Unit and Clinical and Molecular Epidemiology Unit, Department of Hygiene and Epidemiology, University of Ioannina School of Medicine, Ioannina 45110, Greece.
• Int J Epidemiol. 2008 Oct 1;37(5):1148-57.

BackgroundSeveral approaches are available for evaluating heterogeneity in meta-analysis. Sensitivity analyses are often used, but these are often implemented in various non-standardized ways.MethodsWe developed and implemented sequential and combinatorial algorithms that evaluate the change in between-study heterogeneity as one or more studies are excluded from the calculations. The algorithms exclude studies aiming to achieve either the maximum or the minimum final I(2) below a desired pre-set threshold. We applied these algorithms in databases of meta-analyses of binary outcome and >/=4 studies from Cochrane Database of Systematic Reviews (Issue 4, 2005, n = 1011) and meta-analyses of genetic associations (n = 50). Two I(2) thresholds were used (50% and 25%).ResultsBoth algorithms have succeeded in achieving the pre-specified final I(2) thresholds. Differences in the number of excluded studies varied from 0% to 6% depending on the database and the heterogeneity threshold, while it was common to exclude different specific studies. Among meta-analyses with initial I(2) > 50%, in the large majority [19 (90.5%) and 208 (85.9%) in genetic and Cochrane meta-analyses, respectively] exclusion of one or two studies sufficed to decrease I(2) < 50%. Similarly, among meta-analyses with initial I(2) > 25%, in most cases [16 (57.1%) and 382 (81.3%), respectively) exclusion of one or two studies sufficed to decrease heterogeneity even <25%. The number of excluded studies correlated modestly with initial estimated I(2) (correlation coefficients 0.52-0.68 depending on algorithm used).ConclusionsThe proposed algorithms can be routinely applied in meta-analyses as standardized sensitivity analyses for heterogeneity. Caution is needed evaluating post hoc which specific studies are responsible for the heterogeneity.

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