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Beta-binomial model for meta-analysis of odds ratios.

Ilyas Bakbergenuly1, Elena Kulinskaya1

  • 1School of Computing Sciences, University of East Anglia, Norwich, U.K.

Statistics in Medicine
|January 27, 2017
PubMed
Summary

This study introduces new methods for meta-analysis of odds ratios (ORs) using beta-binomial models to account for heterogeneity. The gamma-based intra-class correlation (ICC) estimator is best for small samples, while Breslow-Day is best for larger ones.

Keywords:
Intra-cluster correlationbeta-binomial distributionfixed-effect modelheterogeneityodds ratiooverdispersionrandom-effects model

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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Meta-Analysis

Background:

  • Meta-analysis commonly uses additive random effects models (REM) for odds ratios (ORs), but multiplicative REMs with overdispersion offer an alternative.
  • The overdispersion model (ODM) parameter can be interpreted as an intra-class correlation (ICC), relevant when event probabilities follow beta-distributions, leading to beta-binomial distributions.

Purpose of the Study:

  • To propose and evaluate new estimators for the intra-class correlation (ICC) parameter within the beta-binomial meta-analysis framework.
  • To assess the performance of various ICC estimators regarding bias and coverage through simulation studies.
  • To extend the Mantel-Haenszel approach for OR estimation to the beta-binomial model and evaluate combined OR estimation methods.

Main Methods:

  • Development of two novel ICC estimators: one based on the inverted Breslow-Day test and another using an improved gamma approximation to Cochran's Q distribution.
  • Simulation studies to compare the bias and coverage of proposed ICC estimators against existing methods.
  • Extension of the Mantel-Haenszel method for OR estimation under the beta-binomial model and evaluation of its performance alongside the inverse-variance method.

Main Results:

  • The improved gamma-based ICC estimator demonstrates superior performance for small sample sizes, while the Breslow-Day-based estimator is optimal for sample sizes of 100 or greater.
  • The Mantel-Haenszel estimator for ORs within the beta-binomial model is found to be significantly biased and is not recommended for use.
  • The inverse-variance approach for combining ORs shows some bias when ORs differ from 1, though this bias is generally not substantial in practical applications.

Conclusions:

  • The beta-binomial model, supported by the developed ICC estimators and feasible R programs, presents a viable alternative to standard random effects models for meta-analysis of odds ratios.
  • The choice of ICC estimator is crucial and depends on sample size, with distinct recommendations for small versus large studies.
  • Careful consideration of OR estimation methods is necessary, as the Mantel-Haenszel approach is unreliable, and the inverse-variance method has limitations.