Comparison of one-step and two-step meta-analysis models using individual patient data

Thomas Mathew, Kenneth Nordström

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


The problem of combining information from separate trials is a key consideration when performing a meta-analysis or planning a multicentre trial. Although there is a considerable journal literature on meta-analysis based on individual patient data (IPD), i.e. a one-step IPD meta-analysis, versus analysis based on summary data, i.e. a two-step IPD meta-analysis, recent articles in the medical literature indicate that there is still confusion and uncertainty as to the validity of an analysis based on aggregate data. In this study, we address one of the central statistical issues by considering the estimation of a linear function of the mean, based on linear models for summary data and for IPD. The summary data from a trial is assumed to comprise the best linear unbiased estimator, or maximum likelihood estimator of the parameter, along with its covariance matrix. The setup, which allows for the presence of random effects and covariates in the model, is quite general and includes many of the commonly employed models, for example, linear models with fixed treatment effects and fixed or random trial effects. For this general model, we derive a condition under which the one-step and two-step IPD meta-analysis estimators coincide, extending earlier work considerably. The implications of this result for the specific models mentioned above are illustrated in detail, both theoretically and in terms of two real data sets, and the roles of balance and heterogeneity are highlighted. Our analysis also shows that when covariates are present, which is typically the case, the two estimators coincide only under extra simplifying assumptions, which are somewhat unrealistic in practice.

Original languageEnglish
Pages (from-to)271-287
Number of pages17
JournalBiometrical Journal
Issue number2
Publication statusPublished - Apr 1 2010


  • Balance
  • Covariates
  • Fixed effect
  • Random effect
  • Treatment-control difference

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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