Privacy-preserving Meta-analysis through Low-Rank Basis Hunting

Abstract

A central challenge of meta-analysis is that the populations underlying existing studies often differ from the target population in unknown ways. We study the problem of predicting function-valued quantities, such as regression and conditional average treatment effect functions, for a new target population using only study-level covariates and study-specific function estimates. We propose MetaHunt, a new meta-analysis methodology based on a shared low-rank structure, in which the true function from each study lies within the convex hull of a small set of latent basis functions. To recover these basis functions, we extend a vertex-hunting procedure called the Successive Projection Algorithm to the functional setting, incorporating a denoised basis-hunting step. We establish consistency of the recovered basis functions under mild regularity conditions. We then model the relationship between study-level covariates and the corresponding mixing weights using flexible semi-parametric or non-parametric methods. MetaHunt is privacy-preserving and enables meta-analytic prediction based on study-level information alone, even when individual-level data are unavailable to analysts. In addition, for each study, functions of interest can be estimated using possibly different machine learning algorithms. For uncertainty quantification, we construct prediction intervals via conformal prediction. We show that, under exchangeability and mild estimation-error conditions, these intervals achieve asymptotically valid marginal coverage. We demonstrate the effectiveness of MetaHunt through both simulation studies and empirical applications. An open-source software package is available for implementing MetaHunt.