Multivariate random-effects meta-analysis for sparse data using smvmeta

Multivariate meta-analysis is used to synthesize estimates of multi- ple quantities (“effect sizes”), such as risk factors or treatment effects, accounting for correlation and typically also heterogeneity. In the most general case, estima- tion can be intractable if data are sparse (for example, many risk factors but few studies) because the number of model parameters that must be estimated scales quadratically with the number of effect sizes. This article presents a new command, smvmeta, that makes estimation tractable by modeling correlation and heterogene- ity in a low-dimensional space via random projection. This reduces the number of model parameters to be linear in the number of effect sizes. smvmeta is demon- strated in a meta-analysis of 23 risk factors for pain after total knee arthroplasty. Validation experiments show that, compared with meta-regression (a reasonable alternative model that could be used when data are sparse), smvmeta can pro- vide substantially more precise estimates (that is, narrower confidence intervals) at little cost in bias.