An alternative pseudolikelihood method for multivariate random-effects meta-analysis

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.