A new multivariate meta-analysis model for many variates and few studies.

Studies often estimate associations between an outcome and multiple variates. For example, studies of diagnostic test accuracy estimate sensitivity and specificity, and studies of prognostic factors typically estimate associations for multiple factors. Meta-analysis is a family of methods for synthesizing estimates across multiple studies. Multivariate models exist that account for within-study correlations and between-study heterogeneity. The number of parameters that must be estimated in existing models is quadratic in the number of variates, which means they may not be usable if data are sparse with many variates and few studies. We propose a new model that addresses this problem by approximating a variance-covariance matrix that models within-study correlation and between-study heterogeneity in a low-dimensional space using random projection. The number of parameters that must be estimated in this model is quadratic in the dimensionality of the low-dimensional space, making estimation more tractable. We demonstrate the method using data from an ongoing systematic review on predictors of pain and function after total knee arthroplasty.