title: Sensitivity of between-study heterogeneity in meta-analysis: proposed metrics and empirical evaluation.
abstract: 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.
authors.affiliation: 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.
authors.forename: Nikolaos A
authors.initials: NA
authors.lastname: Patsopoulos
authors.forename: Evangelos
authors.initials: E
authors.lastname: Evangelou
authors.forename: John P A
authors.initials: JP
authors.lastname: Ioannidis
mesh_terms: D000465:Algorithms; D030541:Databases, Genetic; D006801:Humans; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D016896:Treatment Outcome