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Studies often estimate associations between an outcome and multiple variates.For example, studies of diagnostic test accuracy estimate sensitivity andspecificity, and studies of predictive and prognostic factors typicallyestimate associations for multiple factors. Meta-analysis is a family ofstatistical methods for synthesizing estimates across multiple studies.Multivariate models exist that account for within-study correlations andbetween-study heterogeneity. The number of parameters that must be estimated inexisting models is quadratic in the number of variates (e.g., risk factors).This means they may not be usable if data are sparse with many variates and fewstudies. We propose a new model that addresses this problem by approximating avariance-covariance matrix that models within-study correlation andbetween-study heterogeneity in a low-dimensional space using random projection.The number of parameters that must be estimated in this model scales linearlyin the number of variates and quadratically in the dimension of theapproximating space, making estimation more tractable. We performed asimulation study to compare coverage, bias, and precision of estimates madeusing the proposed model to those from univariate meta-analyses. We demonstratethe method using data from an ongoing systematic review on predictors of painand function after total knee arthroplasty. Finally, we suggest a decision toolto help analysts choose among available models.

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