title: Trial Sequential Analysis in systematic reviews with meta-analysis.
abstract: Most meta-analyses in systematic reviews, including Cochrane ones, do not have sufficient statistical power to detect or refute even large intervention effects. This is why a meta-analysis ought to be regarded as an interim analysis on its way towards a required information size. The results of the meta-analyses should relate the total number of randomised participants to the estimated required meta-analytic information size accounting for statistical diversity. When the number of participants and the corresponding number of trials in a meta-analysis are insufficient, the use of the traditional 95% confidence interval or the 5% statistical significance threshold will lead to too many false positive conclusions (type I errors) and too many false negative conclusions (type II errors).
  
  
  
  We developed a methodology for interpreting meta-analysis results, using generally accepted, valid evidence on how to adjust thresholds for significance in randomised clinical trials when the required sample size has not been reached.
  
  
  
  The Lan-DeMets trial sequential monitoring boundaries in Trial Sequential Analysis offer adjusted confidence intervals and restricted thresholds for statistical significance when the diversity-adjusted required information size and the corresponding number of required trials for the meta-analysis have not been reached. Trial Sequential Analysis provides a frequentistic approach to control both type I and type II errors. We define the required information size and the corresponding number of required trials in a meta-analysis and the diversity (D2) measure of heterogeneity. We explain the reasons for using Trial Sequential Analysis of meta-analysis when the actual information size fails to reach the required information size. We present examples drawn from traditional meta-analyses using unadjusted naïve 95% confidence intervals and 5% thresholds for statistical significance. Spurious conclusions in systematic reviews with traditional meta-analyses can be reduced using Trial Sequential Analysis. Several empirical studies have demonstrated that the Trial Sequential Analysis provides better control of type I errors and of type II errors than the traditional naïve meta-analysis.
  
  
  
  Trial Sequential Analysis represents analysis of meta-analytic data, with transparent assumptions, and better control of type I and type II errors than the traditional meta-analysis using naïve unadjusted confidence intervals.
authors.affiliation: Copenhagen Trial Unit, Centre for Clinial Intervention Research, Dpt. 7812, Rigshospitalet, Copenhagen University Hospital, Blegdamsvej 9, DK-2100, Copenhagen, Denmark. wetterslev@ctu.dk.|Centre for Research in Intensive Care, Rigshospitalet, Copenhagen University Hospital, Blegdamsvej 9, DK-2100, Copenhagen, Denmark. wetterslev@ctu.dk.
authors.forename: Jørn
authors.identifier: 0000-0001-7778-1771
authors.initials: J
authors.lastname: Wetterslev
authors.affiliation: Copenhagen Trial Unit, Centre for Clinial Intervention Research, Dpt. 7812, Rigshospitalet, Copenhagen University Hospital, Blegdamsvej 9, DK-2100, Copenhagen, Denmark.|Centre for Research in Intensive Care, Rigshospitalet, Copenhagen University Hospital, Blegdamsvej 9, DK-2100, Copenhagen, Denmark.|Department of Cardiology, Holbæk Hospital, DK-4300, Holbæk, Denmark.|The Cochrane Hepato-Biliary Group, Copenhagen Trial Unit, Centre for Clinial Intervention Research, Dpt. 7812, Rigshospitalet, Copenhagen University Hospital, Blegdamsvej 9, DK-2100, Copenhagen, Denmark.
authors.forename: Janus Christian
authors.initials: JC
authors.lastname: Jakobsen
authors.affiliation: Copenhagen Trial Unit, Centre for Clinial Intervention Research, Dpt. 7812, Rigshospitalet, Copenhagen University Hospital, Blegdamsvej 9, DK-2100, Copenhagen, Denmark.|The Cochrane Hepato-Biliary Group, Copenhagen Trial Unit, Centre for Clinial Intervention Research, Dpt. 7812, Rigshospitalet, Copenhagen University Hospital, Blegdamsvej 9, DK-2100, Copenhagen, Denmark.
authors.forename: Christian
authors.initials: C
authors.lastname: Gluud
mesh_terms: D006801:Humans; D015201:Meta-Analysis as Topic; D016032:Randomized Controlled Trials as Topic; D012107:Research Design; D018401:Sample Size
keywords: Diversity; Fixed-effect model; Group sequential analysis; Heterogeneity; Information size; Interim analysis; Meta-analysis; Random-effects model; Sample size; Trial sequential analysis