Multivariate meta‐analysis of mixed outcomes: a Bayesian approach

Bujkiewicz, Sylwia; Thompson, John R.; Sutton, Alex J.; Cooper, Nicola J.; Harrison, Mark; Symmons, Deborah; Abrams, Keith R.

doi:10.1002/sim.5831

Cited by 58 publications

(113 citation statements)

References 43 publications

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“…The problem of missing within-study correlations has traditionally hampered the widespread application of multivariate meta-analysis [7,10,15]. In our example, IPD was available from a proportion of the included studies and we have used correlations estimated from the IPD to formulate informative prior distributions for the within-study model.…”

Section: Discussionmentioning

confidence: 99%

Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes

Achana

Cooper

Bujkiewicz

et al. 2014

BMC Med Res Methodol

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BackgroundNetwork meta-analysis (NMA) enables simultaneous comparison of multiple treatments while preserving randomisation. When summarising evidence to inform an economic evaluation, it is important that the analysis accurately reflects the dependency structure within the data, as correlations between outcomes may have implication for estimating the net benefit associated with treatment. A multivariate NMA offers a framework for evaluating multiple treatments across multiple outcome measures while accounting for the correlation structure between outcomes.MethodsThe standard NMA model is extended to multiple outcome settings in two stages. In the first stage, information is borrowed across outcomes as well across studies through modelling the within-study and between-study correlation structure. In the second stage, we make use of the additional assumption that intervention effects are exchangeable between outcomes to predict effect estimates for all outcomes, including effect estimates on outcomes where evidence is either sparse or the treatment had not been considered by any one of the studies included in the analysis. We apply the methods to binary outcome data from a systematic review evaluating the effectiveness of nine home safety interventions on uptake of three poisoning prevention practices (safe storage of medicines, safe storage of other household products, and possession of poison centre control telephone number) in households with children. Analyses are conducted in WinBUGS using Markov Chain Monte Carlo (MCMC) simulations.ResultsUnivariate and the first stage multivariate models produced broadly similar point estimates of intervention effects but the uncertainty around the multivariate estimates varied depending on the prior distribution specified for the between-study covariance structure. The second stage multivariate analyses produced more precise effect estimates while enabling intervention effects to be predicted for all outcomes, including intervention effects on outcomes not directly considered by the studies included in the analysis.ConclusionsAccounting for the dependency between outcomes in a multivariate meta-analysis may or may not improve the precision of effect estimates from a network meta-analysis compared to analysing each outcome separately.

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Section: Discussionmentioning

confidence: 99%

Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes

Achana

Cooper

Bujkiewicz

et al. 2014

BMC Med Res Methodol

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“…We used a trivariate random-effects meta-analysis (TRMA), described in much more detail elsewhere [3], in the following form:

(\begin{matrix} left \\ Δ {HAQ}_{i} \\ Δ {DAS}_{i} \\ ACR 20_{i} \end{matrix}) ~ N ((\begin{matrix} left \\ μ_{H i} \\ μ_{D i} \\ μ_{A i} \end{matrix}), (\begin{matrix} left \\ σ_{H i}^{2} & left σ_{H i} σ_{D i} ρ_{w i}^{H D} & left σ_{H i} σ_{A i} ρ_{w i}^{H A} \\ σ_{H i} σ_{D i} ρ_{w i}^{H D} & left σ_{D i}^{2} & left σ_{D i} σ_{A i} ρ_{w i}^{D A} \\ σ_{H i} σ_{A i} ρ_{w i}^{H A} & left σ_{D i} σ_{A i} ρ_{w i}^{D A} & left σ_{A i}^{2} \end{matrix}))

(\begin{matrix} left \\ μ_{H i} \\ μ_{D i} \\ μ_{A i} \end{matrix}) ~ N ...

…”

Section: Methodsmentioning

confidence: 99%

Use of Bayesian Multivariate Meta-Analysis to Estimate the HAQ for Mapping Onto the EQ-5D Questionnaire in Rheumatoid Arthritis

et al. 2014

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BackgroundIn health technology assessment, decisions about reimbursement for new health technologies are largely based on effectiveness estimates. Sometimes, however, the target effectiveness estimates are not readily available. This may be because many alternative instruments measuring these outcomes are being used (and not all always reported) or an extended follow-up time of clinical trials is needed to evaluate long-term end points, leading to the limited data on the target clinical outcome. In the areas of highest priority in health care, decisions are required to be made on a short time scale. Therefore, alternative clinical outcomes, including surrogate end points, are increasingly being considered for use in evidence synthesis as part of economic evaluation.ObjectiveTo illustrate the potential effect of reduced uncertainty around the clinical outcome on the utility when estimating it from a multivariate meta-analysis.MethodsBayesian multivariate meta-analysis has been used to synthesize data on correlated outcomes in rheumatoid arthritis and to incorporate external data in the model in the form of informative prior distributions. Estimates of Health Assessment Questionnaire were then mapped onto the health-related quality-of-life measure EuroQol five-dimensional questionnaire, and the effect was compared with mapping the Health Assessment Questionnaire obtained from the univariate approach.ResultsThe use of multivariate meta-analysis can lead to reduced uncertainty around the effectiveness parameter and ultimately uncertainty around the utility.ConclusionsBy allowing all the relevant data to be incorporated in estimating clinical effectiveness outcomes, multivariate meta-analysis can improve the estimation of health utilities estimated through mapping methods. While reduced uncertainty may have an effect on decisions based on economic evaluation of new health technologies, the use of short-term surrogate end points can allow for early decisions. More research is needed to determine the circumstances under which uncertainty is reduced.

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“…Estimation of model (1) is needed to obtain estimates of μ and Σ. Estimation can be achieved by a variety of options (Jackson et al, 2011), including restricted maximum likelihood (REML), method of moments (MM) approaches (Jackson et al, 2010;Jackson et al, 2013;Chen et al, 2012), the U statistic (Ma and Mazumdar, 2011), and a Bayesian approach (Nam et al, 2003;Wei and Higgins, 2013a;Bujkiewicz et al, 2013). In this article, we present results using REML and Bayesian estimation.…”

Section: Estimationmentioning

confidence: 99%

“…Our WinBUGS code for a four outcome multivariate meta-analysis using either decomposition is given in Web Appendix 1. A productnormal specification of Σ is also possible (Spiegelhalter et al, 2000;Bujkiewicz et al, 2013).…”

Section: Estimationmentioning

confidence: 99%

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Multivariate meta‐analysis using individual participant data

et al. 2014

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When combining results across related studies, a multivariate meta-analysis allows the joint synthesis of correlated effect estimates from multiple outcomes. Joint synthesis can improve efficiency over separate univariate syntheses, may reduce selective outcome reporting biases, and enables joint inferences across the outcomes. A common issue is that within-study correlations needed to fit the multivariate model are unknown from published reports. However, provision of individual participant data (IPD) allows them to be calculated directly. Here, we illustrate how to use IPD to estimate within-study correlations, using a joint linear regression for multiple continuous outcomes and bootstrapping methods for binary, survival and mixed outcomes. In a meta-analysis of 10 hypertension trials, we then show how these methods enable multivariate meta-analysis to address novel clinical questions about continuous, survival and binary outcomes; treatment–covariate interactions; adjusted risk/prognostic factor effects; longitudinal data; prognostic and multiparameter models; and multiple treatment comparisons. Both frequentist and Bayesian approaches are applied, with example software code provided to derive within-study correlations and to fit the models.

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Multivariate meta‐analysis of mixed outcomes: a Bayesian approach

Cited by 58 publications

References 43 publications

Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes

Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes

Use of Bayesian Multivariate Meta-Analysis to Estimate the HAQ for Mapping Onto the EQ-5D Questionnaire in Rheumatoid Arthritis

Multivariate meta‐analysis using individual participant data

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