Abstract
Multivariate random effects meta-analysis (MRMA) is an appropriate way for synthesizing data from studies reporting multiple correlated outcomes. In a Bayesian framework, it has great potential for integrating evidence from a variety of sources. In this paper, we propose a Bayesian model for MRMA of mixed outcomes, which extends previously developed bivariate models to the trivariate case and also allows for combination of multiple outcomes that are both continuous and binary. We have constructed informative prior distributions for the correlations by using external evidence. Prior distributions for the within-study correlations were constructed by employing external individual patent data and using a double bootstrap method to obtain the correlations between mixed outcomes. The between-study model of MRMA was parameterized in the form of a product of a series of univariate conditional normal distributions. This allowed us to place explicit prior distributions on the between-study correlations, which were constructed using external summary data. Traditionally, independent ‘vague’ prior distributions are placed on all parameters of the model. In contrast to this approach, we constructed prior distributions for the between-study model parameters in a way that takes into account the inter-relationship between them. This is a flexible method that can be extended to incorporate mixed outcomes other than continuous and binary and beyond the trivariate case. We have applied this model to a motivating example in rheumatoid arthritis with the aim of incorporating all available evidence in the synthesis and potentially reducing uncertainty around the estimate of interest. © 2013 The Authors. Statistics inMedicine Published by John Wiley & Sons, Ltd.
Highlights
When the synthesis of data from studies reporting multiple outcomes is required, multivariate random effects meta-analysis (MRMA) can be used instead of performing meta-analyses on each outcome separately, which has an advantage of taking into account the correlations between the outcomes
We have applied the trivariate random-effects meta-analysis (TRMA) model to the Lloyd data to simultaneously model data on the Health Assessment Questionnaire (HAQ), DAS-28, and ACR20
In the Lloyd data, the HAQ and DAS-28 estimates represent the mean change from baseline of the outcomes, and ACR20 is a proportion of responders, which is transformed to log odds of response to be able to follow the normal distribution in TRMA
Summary
When the synthesis of data from studies reporting multiple outcomes is required, multivariate random effects meta-analysis (MRMA) can be used instead of performing meta-analyses on each outcome separately, which has an advantage of taking into account the correlations between the outcomes. Methods for MRMA have been developed for a number of purposes, for example, to estimate multiple outcomes from clinical trials [1], to model relationships between surrogate endpoints [2], or to evaluate diagnostic tests [3]. Jackson et al [5] describe advances in the development of the methodology of multivariate meta-analysis and discuss the advantages and disadvantages of the use of these methods. One of the advantages of integrating data on multiple outcomes.
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