title: A tutorial on Bayesian bivariate meta-analysis of mixed binary-continuous outcomes with missing treatment effects.
abstract: Bivariate random-effects meta-analysis (BVMA) is a method of data synthesis that accounts for treatment effects measured on two outcomes. BVMA gives more precise estimates of the population mean and predicted values than two univariate random-effects meta-analyses (UVMAs). BVMA also addresses bias from incomplete reporting of outcomes. A few tutorials have covered technical details of BVMA of categorical or continuous outcomes. Limited guidance is available on how to analyze datasets that include trials with mixed continuous-binary outcomes where treatment effects on one outcome or the other are not reported. Given the advantages of Bayesian BVMA for handling missing outcomes, we present a tutorial for Bayesian BVMA of incompletely reported treatment effects on mixed bivariate outcomes. This step-by-step approach can serve as a model for our intended audience, the methodologist familiar with Bayesian meta-analysis, looking for practical advice on fitting bivariate models. To facilitate application of the proposed methods, we include our WinBUGS code. As an example, we use aggregate-level data from published trials to demonstrate the estimation of the effects of vitamin K and bisphosphonates on two correlated bone outcomes, fracture, and bone mineral density. We present datasets where reporting of the pairs of treatment effects on both outcomes was 'partially' complete (i.e., pairs completely reported in some trials), and we outline steps for modeling the incompletely reported data. To assess what is gained from the additional work required by BVMA, we compare the resulting estimates to those from separate UVMAs. We discuss methodological findings and make four recommendations. Copyright © 2015 John Wiley & Sons, Ltd.
authors.affiliation: Osteoporosis Program, University Health Network, Toronto, ON, Canada.|Toronto Health Economics and Technology Assessment (THETA) Collaborative, University of Toronto, Toronto, ON, Canada.
authors.forename: Olga
authors.initials: O
authors.lastname: Gajic-Veljanoski
authors.affiliation: Osteoporosis Program, University Health Network, Toronto, ON, Canada.|Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, ON, Canada.|Department of Medicine, University of Toronto, Toronto, ON, Canada.|Dalla Lana School of Public Health, University of Toronto, Toronto, ON, Canada.
authors.forename: Angela M
authors.initials: AM
authors.lastname: Cheung
authors.affiliation: Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, ON, Canada.|Department of Medicine, University of Toronto, Toronto, ON, Canada.|Centre for Research on Inner City Health in the Li Ka Shing Knowledge Institute and Division of General Internal Medicine, St. Michael's Hospital, Toronto, ON, Canada.
authors.forename: Ahmed M
authors.initials: AM
authors.lastname: Bayoumi
authors.affiliation: Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, ON, Canada.|Department of Medicine, University of Toronto, Toronto, ON, Canada.|Dalla Lana School of Public Health, University of Toronto, Toronto, ON, Canada.
authors.forename: George
authors.initials: G
authors.lastname: Tomlinson
mesh_terms: D001499:Bayes Theorem; D015519:Bone Density / Q000187:drug effects; D050071:Bone Density Conservation Agents / Q000627:therapeutic use; D004164:Diphosphonates / Q000627:therapeutic use; D005260:Female; D006801:Humans; D016014:Linear Models; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D015663:Osteoporosis, Postmenopausal / Q000517:prevention & control; D011336:Probability; D016896:Treatment Outcome; D014812:Vitamin K / Q000627:therapeutic use
chemical_list: D050071:Bone Density Conservation Agents; D004164:Diphosphonates; D014812:Vitamin K
keywords: Bayesian approach; bivariate random-effects meta-analysis; incomplete data; mixed binary-continuous outcomes; tutorial