title: Meta-analyses triggered by previous (false-)significant findings: problems and solutions.
abstract: BACKGROUND
  Meta-analyses are typically triggered by a (potentially false-significant) finding in one of the preceding primary studies. We studied consequences of meta-analysis investigating effects when primary studies that triggered such meta-analysis are also included.
  
  
  METHODS
  We analytically determined the bias of the treatment effect estimates obtained by meta-analysis, conditional on the number of included primary and false-significant studies. The type I error rate and power of the meta-analysis were assessed using simulations. We applied a method for bias-correction, by subtracting an analytically derived bias from the treatment effect estimated in meta-analysis.
  
  
  RESULTS
  Bias in meta-analytical effects and type I error rates increased when increasing numbers of primary studies with false-significant effects were included. When 20% of the primary studies showed false-significant effects, the bias was 0.33 (z-score) instead of 0, and the type I error rate was 23% instead of 5%. After applying a bias-correction, the type I error rate became indeed 5%.
  
  
  CONCLUSIONS
  Inclusion of primary studies with false-significant effects leads to biased effect estimates and inflated type I error rates in the meta-analysis, depending on the number of false-significant studies. This bias can be adjusted for.
authors.affiliation: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Universiteitsweg 100, 3584 CG, Utrecht, The Netherlands. eschuit@stanford.edu.|Department of Obstetrics and Gynecology, Academic Medical Center, Meibergdreef 9, 1105 AZ, Amsterdam, The Netherlands. eschuit@stanford.edu.|Stanford Prevention Research Center, Medical School Office Building, Stanford University, 1265 Welch Road, Stanford, CA, 94305, USA. eschuit@stanford.edu.
authors.forename: Ewoud
authors.initials: E
authors.lastname: Schuit
authors.affiliation: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Universiteitsweg 100, 3584 CG, Utrecht, The Netherlands. k.c.b.roes@umcutrecht.nl.
authors.forename: Kit C B
authors.initials: KC
authors.lastname: Roes
authors.affiliation: The Robinson Institute, School of Reproductive Health and Pediatrics, University of Adelaide, 55 King William Road, North Adelaide, SA, 5006, Australia. ben.mol@adelaide.edu.au.
authors.forename: Ben W J
authors.initials: BW
authors.lastname: Mol
authors.affiliation: Department of Obstetrics and Gynecology, University Medical Center Utrecht, Lundlaan 6, 3584 EA, Utrecht, The Netherlands. a.kwee@umcutrecht.nl.
authors.forename: Anneke
authors.initials: A
authors.lastname: Kwee
authors.affiliation: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Universiteitsweg 100, 3584 CG, Utrecht, The Netherlands. k.g.m.moons@umcutrecht.nl.
authors.forename: Karel G M
authors.initials: KG
authors.lastname: Moons
authors.affiliation: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Universiteitsweg 100, 3584 CG, Utrecht, The Netherlands. r.h.h.groenwold@umcutrecht.nl.
authors.forename: Rolf H H
authors.initials: RH
authors.lastname: Groenwold
mesh_terms: D015982:Bias; D035843:Biomedical Research / Q000706:statistics & numerical data*; D006801:Humans; D015201:Meta-Analysis as Topic; D017594:Publication Bias / Q000706:statistics & numerical data*