Multivariate meta-analysis with a robustified diagonal likelihood function

Multivariate meta-analysis is an efficient tool to analyze multivariate outcomes from independent studies, with the advantage of accounting for correlations between these outcomes. However, existing methods are sensitive to outliers in the data. In this paper, we propose new robust estimation methods for multivariate meta-analysis. In practice, within-study correlations are frequently not reported in studies, conventional robust multivariate methods using modified estimation equations may not be applicable. To address this challenge, we utilize robust functions to create new log-likelihood functions, by only using the diagonal components of the full covariance matrices. This approach bypasses the need for within-study correlations and also avoids the singularity problem of covariance matrices in the computation. Furthermore, the asymptotic distributions can automatically account for the missing correlations between multiple outcomes, enabling valid confidence intervals on functions of parameter estimates. Simulation studies and two real-data analyses are also carried out to demonstrate the advantages of our new robust estimation methods. Our primary focus is on bivariate meta-analysis, although the approaches can be applied more generally.