Multivariate meta-analysis for data consortia, individual patient meta-analysis, and pooling projects

We discuss maximum likelihood and estimating equations methods for combining results from multiple studies in pooling projects and data consortia using a meta-analysis model, when the multivariate estimates with their covariance matrices are available. The estimates to be combined are typically regression slopes, often from relative risk models in biomedical and epidemiologic applications. We generalize the existing univariate meta-analysis model and investigate the efficiency advantages of the multivariate methods, relative to the univariate ones. We generalize a popular univariate test for between-studies homogeneity to a multivariate test. The methods are applied to a pooled analysis of type of carotenoids in relation to lung cancer incidence from seven prospective studies. In these data, the expected gain in efficiency was evident, sometimes to a large extent. Finally, we study the finite sample properties of the estimators and compare the multivariate ones to their univariate counterparts.