title: Individual participant data meta-analysis for a binary outcome: one-stage or two-stage?
abstract: BACKGROUND
  A fundamental aspect of epidemiological studies concerns the estimation of factor-outcome associations to identify risk factors, prognostic factors and potential causal factors. Because reliable estimates for these associations are important, there is a growing interest in methods for combining the results from multiple studies in individual participant data meta-analyses (IPD-MA). When there is substantial heterogeneity across studies, various random-effects meta-analysis models are possible that employ a one-stage or two-stage method. These are generally thought to produce similar results, but empirical comparisons are few.
  
  
  OBJECTIVE
  We describe and compare several one- and two-stage random-effects IPD-MA methods for estimating factor-outcome associations from multiple risk-factor or predictor finding studies with a binary outcome. One-stage methods use the IPD of each study and meta-analyse using the exact binomial distribution, whereas two-stage methods reduce evidence to the aggregated level (e.g. odds ratios) and then meta-analyse assuming approximate normality. We compare the methods in an empirical dataset for unadjusted and adjusted risk-factor estimates.
  
  
  RESULTS
  Though often similar, on occasion the one-stage and two-stage methods provide different parameter estimates and different conclusions. For example, the effect of erythema and its statistical significance was different for a one-stage (OR = 1.35, [Formula: see text]) and univariate two-stage (OR = 1.55, [Formula: see text]). Estimation issues can also arise: two-stage models suffer unstable estimates when zero cell counts occur and one-stage models do not always converge.
  
  
  CONCLUSIONS
  When planning an IPD-MA, the choice and implementation (e.g. univariate or multivariate) of a one-stage or two-stage method should be prespecified in the protocol as occasionally they lead to different conclusions about which factors are associated with outcome. Though both approaches can suffer from estimation challenges, we recommend employing the one-stage method, as it uses a more exact statistical approach and accounts for parameter correlation.
authors.affiliation: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, The Netherlands. T.Debray@umcutrecht.nl
authors.forename: Thomas P A
authors.initials: TP
authors.lastname: Debray
authors.forename: Karel G M
authors.initials: KG
authors.lastname: Moons
authors.forename: Ghada Mohammed Abdallah
authors.initials: GM
authors.lastname: Abo-Zaid
authors.forename: Hendrik
authors.initials: H
authors.lastname: Koffijberg
authors.forename: Richard David
authors.initials: RD
authors.lastname: Riley
mesh_terms: D000465:Algorithms; D006801:Humans; D015233:Models, Statistical; D016017:Odds Ratio; D012044:Regression Analysis; D012307:Risk Factors; D016896:Treatment Outcome; D020246:Venous Thrombosis / Q000175:diagnosis* / Q000601:surgery / Q000628:therapy