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A tutorial on Bayesian bivariate meta-analysis of mixed binary-continuous outcomes with missing treatment effects.

Olga Gajic-Veljanoski1,2, Angela M Cheung1,3,4,5, Ahmed M Bayoumi3,4,6

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Statistics in Medicine
|November 11, 2015
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Bivariate random-effects meta-analysis (BVMA) provides more precise estimates than univariate methods, especially for mixed continuous-binary outcomes with missing data. This tutorial details Bayesian BVMA for handling incompletely reported treatment effects.

Keywords:
Bayesian approachbivariate random-effects meta-analysisincomplete datamixed binary-continuous outcomestutorial

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Medical Research Methodology

Background:

  • Bivariate random-effects meta-analysis (BVMA) synthesizes data from studies with two outcomes, offering improved precision over univariate approaches.
  • Existing tutorials primarily address BVMA for single data types (continuous or categorical), with limited guidance for mixed outcomes or incomplete reporting.

Purpose of the Study:

  • To provide a tutorial on Bayesian bivariate random-effects meta-analysis (BVMA) for handling incompletely reported treatment effects on mixed bivariate outcomes.
  • To offer a practical, step-by-step guide for methodologists familiar with Bayesian meta-analysis seeking to fit bivariate models.
  • To demonstrate the application using real-world data and provide accompanying WinBUGS code.

Main Methods:

  • A tutorial approach using Bayesian bivariate random-effects meta-analysis (BVMA).
  • Modeling of incompletely reported treatment effects on mixed continuous-binary outcomes.
  • Application using aggregate data from published trials on vitamin K and bisphosphonates, focusing on fracture and bone mineral density.

Main Results:

  • Bayesian BVMA offers a robust method for synthesizing evidence from trials with mixed bivariate outcomes and missing data.
  • The approach yields more precise estimates of treatment effects and predicted values compared to separate univariate analyses.
  • Demonstrated the estimation of treatment effects on correlated bone outcomes (fracture, bone mineral density) using partially complete datasets.

Conclusions:

  • Bayesian BVMA is advantageous for addressing bias from incomplete outcome reporting in meta-analyses of mixed bivariate outcomes.
  • The presented step-by-step method and code facilitate the application of BVMA for complex data scenarios.
  • Comparison with univariate meta-analyses highlights the gains in precision and handling of missing data offered by BVMA.