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A likelihood approach to meta-analysis with random effects

R J Hardy1, S G Thompson

  • 1Medical Statistics Unit, London School of Hygiene and Tropical Medicine, U.K.

Statistics in Medicine
|March 30, 1996
PubMed
Summary
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This study introduces a likelihood-based method for random effects meta-analysis, improving confidence intervals for treatment effects (theta) and between-trial variance (sigma B2). This approach provides more accurate estimates when heterogeneity is significant.

Area of Science:

  • Biostatistics
  • Clinical Trials Methodology
  • Epidemiology

Background:

  • Meta-analysis is crucial for synthesizing clinical trial data, but estimating overall treatment effects (theta) with confidence intervals is challenging, especially with heterogeneity.
  • The standard DerSimonian and Laird random effects method uses a moment estimator for between-trial variance (sigma B2) but doesn't provide confidence intervals for sigma B2 or account for its estimation in theta's interval.
  • Fixed-effect models produce artificially narrow confidence intervals for theta in the presence of heterogeneity.

Purpose of the Study:

  • To develop and present a likelihood-based method for random effects meta-analysis.
  • To construct accurate confidence intervals for both the overall treatment effect (theta) and the between-trial variance (sigma B2).
  • To address the limitations of the standard DerSimonian and Laird method regarding the estimation of sigma B2 and its impact on theta's confidence interval.

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Main Methods:

  • Utilized a likelihood-based approach, specifically employing profile likelihoods.
  • Constructed likelihood-based confidence intervals for theta and sigma B2.
  • Applied the developed method to a published meta-analysis and a multicentre clinical trial for validation.

Main Results:

  • The likelihood-based method provides appropriately widened confidence intervals for theta compared to the standard random effects method.
  • This approach yields confidence intervals for theta that account for the fact that sigma B2 is estimated from the data.
  • The method successfully provides confidence intervals for sigma B2, which is not offered by the standard approach.

Conclusions:

  • Likelihood-based methods are superior to the standard DerSimonian and Laird method for random effects meta-analysis when sigma B2 significantly influences the estimated treatment effect.
  • The proposed method offers more reliable confidence intervals for treatment effects in the presence of heterogeneity.
  • This approach enhances the accuracy and interpretability of meta-analysis results by providing valid confidence intervals for key parameters.