Department of Biostatistics, Boston University School of Public Health, 801 Massachusetts Avenue, Boston, MA 02118, U.S.A. Program in Medical and Population Genetics, Broad Institute, 7 Cambridge Center, Cambridge, MA 02142, U.S.A. Department of Molecular Biology, Massachusetts General Hospital, 185 Cambridge St, Boston, MA 02114, U.S.A. Department of Genetics, Harvard Medical School, 77 Avenue Louis Pasteur, Boston, MA 02115, U.S.A.
Meta-analysis is a powerful approach to combine evidence from multiple studies to make inference about one or more parameters of interest, such as regression coefficients. The validity of the fixed effect model meta-analysis depends on the underlying assumption that all studies in the meta-analysis share the same effect size. In the presence of heterogeneity, the fixed effect model incorrectly ignores the between-study variance and may yield false positive results. The random effect model takes into account both within-study and between-study variances. It is more conservative than the fixed effect model and should be favored in the presence of heterogeneity. In this paper, we develop a noniterative method of moments estimator for the between-study covariance matrix in the random effect model multivariate meta-analysis. To our knowledge, it is the first such method of moments estimator in the matrix form. We show that our estimator is a multivariate extension of DerSimonian and Laird's univariate method of moments estimator, and it is invariant to linear transformations. In the simulation study, our method performs well when compared to existing random effect model multivariate meta-analysis approaches. We also apply our method in the analysis of a real data example.
[Show abstract][Hide abstract] ABSTRACT: Multivariate meta-analysis is becoming more commonly used. Methods for fitting the multivariate random effects model include maximum likelihood, restricted maximum likelihood, Bayesian estimation and multivariate generalisations of the standard univariate method of moments. Here, we provide a new multivariate method of moments for estimating the between-study covariance matrix with the properties that (1) it allows for either complete or incomplete outcomes and (2) it allows for covariates through meta-regression. Further, for complete data, it is invariant to linear transformations. Our method reduces to the usual univariate method of moments, proposed by DerSimonian and Laird, in a single dimension. We illustrate our method and compare it with some of the alternatives using a simulation study and a real example.
[Show abstract][Hide abstract] ABSTRACT: A fundamental aspect of epidemiological studies concerns the estimation of factor-outcome associations to identify risk factors, prognostic factors and potential causal factors. Because reliable estimates for these associations are important, there is a growing interest in methods for combining the results from multiple studies in individual participant data meta-analyses (IPD-MA). When there is substantial heterogeneity across studies, various random-effects meta-analysis models are possible that employ a one-stage or two-stage method. These are generally thought to produce similar results, but empirical comparisons are few.
We describe and compare several one- and two-stage random-effects IPD-MA methods for estimating factor-outcome associations from multiple risk-factor or predictor finding studies with a binary outcome. One-stage methods use the IPD of each study and meta-analyse using the exact binomial distribution, whereas two-stage methods reduce evidence to the aggregated level (e.g. odds ratios) and then meta-analyse assuming approximate normality. We compare the methods in an empirical dataset for unadjusted and adjusted risk-factor estimates.
Though often similar, on occasion the one-stage and two-stage methods provide different parameter estimates and different conclusions. For example, the effect of erythema and its statistical significance was different for a one-stage (OR = 1.35, [Formula: see text]) and univariate two-stage (OR = 1.55, [Formula: see text]). Estimation issues can also arise: two-stage models suffer unstable estimates when zero cell counts occur and one-stage models do not always converge.
When planning an IPD-MA, the choice and implementation (e.g. univariate or multivariate) of a one-stage or two-stage method should be prespecified in the protocol as occasionally they lead to different conclusions about which factors are associated with outcome. Though both approaches can suffer from estimation challenges, we recommend employing the one-stage method, as it uses a more exact statistical approach and accounts for parameter correlation.
PLoS ONE 04/2013; 8(4):e60650. DOI:10.1371/journal.pone.0060650 · 3.23 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The combination of evidence from independent studies has a curious history. The origins reach back at least to the beginning of the 20th century. Since the mid-1970s, meta-analysis has become popular in several fields, among them medical statistics and the behavioural sciences. The most widely used procedures were perfected in early papers, and subsequently, a kind of groupthink has taken hold of meta-analysis. This explains the need for a review in a statistics journal, destined for a statistical audience. Meta-analysis is not a hot research topic among graduate students in statistics, and by writing this article, we hope to change this. We wish to point out the shortcomings of the mainstream view and exhibit some of the open problems that await the attention of statistical researchers.A host of competent reviews of meta-analysis have been published, and several book-length treatments are also available. We have listed many of these in the bibliography but cannot guarantee completeness.
International Statistical Review 02/2014; 82(2). DOI:10.1111/insr.12037 · 1.20 Impact Factor
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