Meta-Analysis of Heterogeneous Data: Integrative Sparse Regression in High-Dimensions

Abstract

We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical. To borrow strength across such heterogeneous datasets, we introduce a global parameter that emphasizes interpretability and statistical efficiency in the presence of heterogeneity. We also propose a one-shot estimator of the global parameter that preserves the anonymity of the data sources and converges at a rate that depends on the size of the combined dataset. For high-dimensional linear model settings, we demonstrate the superiority of our identification restrictions in adapting to a previously seen data distribution as well as predicting for a new/unseen data distribution. Finally, we demonstrate the benefits of our approach on a large-scale drug treatment dataset involving several different cancer cell-lines.