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      Multivariate meta-analysis for non-linear and other multi-parameter associations

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          Abstract

          In this paper, we formalize the application of multivariate meta-analysis and meta-regression to synthesize estimates of multi-parameter associations obtained from different studies. This modelling approach extends the standard two-stage analysis used to combine results across different sub-groups or populations. The most straightforward application is for the meta-analysis of non-linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta-analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two-stage analysis for investigating the non-linear exposure–response relationship between temperature and non-accidental mortality using time-series data from multiple cities. Multivariate meta-analysis represents a useful analytical tool for studying complex associations through a two-stage procedure. Copyright © 2012 John Wiley & Sons, Ltd.

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          Most cited references60

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          R: a language and environment for statistical computing

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            Regression Modeling Strategies

            Springer Series in Statistics
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              Small sample inference for fixed effects from restricted maximum likelihood.

              Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T2 type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different REML analyses and the methods are illustrated using three examples.
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                Author and article information

                Journal
                Stat Med
                Stat Med
                sim
                Statistics in Medicine
                Blackwell Publishing Ltd
                0277-6715
                1097-0258
                20 December 2012
                16 July 2012
                : 31
                : 29
                : 3821-3839
                Affiliations
                [a ]Department of Medical Statistics, London School of Hygiene and Tropical Medicine London, U.K.
                [b ]Department of Social and Environmental Health Research, London School of Hygiene and Tropical Medicine London, U.K.
                Author notes
                *Correspondence to: Antonio Gasparrini, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, U.K.
                Article
                10.1002/sim.5471
                3546395
                22807043
                b898fb0e-0ff7-4df8-bdad-bbd30ab9f2a4
                Copyright © 2012 John Wiley & Sons, Ltd.

                Re-use of this article is permitted in accordance with the Creative Commons Deed, Attribution 2.5, which does not permit commercial exploitation.

                History
                : 09 August 2011
                : 11 May 2012
                Categories
                Research Articles

                Biostatistics
                meta-analysis,multivariate analysis,multivariate meta-analysis,non-linear,splines
                Biostatistics
                meta-analysis, multivariate analysis, multivariate meta-analysis, non-linear, splines

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