Sensitivity of between-study heterogeneity in meta-analysis: proposed metrics and empirical evaluation

Background Several approaches are available for evaluating heterogeneity in meta-analysis. Sensitivity analyses are often used, but these are often implemented in various non-standardized ways. Methods We 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%). Results Both 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). Conclusions The 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.