Abstract
Recently, multivariate random-effects meta-analysis models have received a great deal of attention, despite its greater complexity compared to univariate meta-analyses. One of its advantages is its ability to account for the within-study and between-study correlations. However, the standard inference procedures, such as the maximum likelihood or maximum restricted likelihood inference, require the within-study correlations, which are usually unavailable. In addition, the standard inference procedures suffer from the problem of singular estimated covariance matrix. In this paper, we propose a pseudolikelihood method to overcome the aforementioned problems. The pseudolikelihood method does not require within-study correlations and is not prone to singular covariance matrix problem. In addition, it can properly estimate the covariance between pooled estimates for different outcomes, which enables valid inference on functions of pooled estimates, and can be applied to meta-analysis where some studies have outcomes missing completely at random. Simulation studies show that the pseudolikelihood method provides unbiased estimates for functions of pooled estimates, well-estimated standard errors, and confidence intervals with good coverage probability. Furthermore, the pseudolikelihood method is found to maintain high relative efficiency compared to that of the standard inferences with known within-study correlations. We illustrate the proposed method through three meta-analyses for comparison of prostate cancer treatment, for the association between paraoxonase 1 activities and coronary heart disease, and for the association between homocysteine level and coronary heart disease. © 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.
Highlights
The rapid growth of evidence-based medicine has led to dramatically increasing attention to metaanalysis, which combines statistical evidence from multiple studies
One potential drawback of the Pseudo-restricted ML (REML) method when assuming the data are complete or missing completely at random (MCAR) is that because the point estimates of overall effect sizes are the same as that from separate univariate meta-analyses, there is potential efficiency loss compared to the methods accounting for the correlations between dependent outcomes
We find that when the between-study heterogeneity is relatively small, there is a substantial increase in the percentage of singular estimated covariance matrix problem in both REML and Riley methods
Summary
The rapid growth of evidence-based medicine has led to dramatically increasing attention to metaanalysis, which combines statistical evidence from multiple studies. Wei and Higgins [11] recently proposed a practical method for MMA when the within-study correlations are missing They used the information on possible correlations between the underlying outcomes to impute any missing within-study covariances, and conducted the inference by REML estimation. When a working independence assumption is adopted, the pseudolikelihood is called independence likelihood [19], where the covariance between estimates of overall effect sizes can be consistently estimated by the Huber–White standard error estimates, known as ‘sandwich’ variance estimator [20, 21] Another advantage of the pseudolikelihood method is the simplicity of the extension to MMA where more than two outcomes are analyzed, and to missing data situations where some of the multiple outcomes are missing completely at random (MCAR).
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