When can Multi-Site Datasets be Pooled for Regression? Hypothesis Tests, $\ell_2$-consistency and Neuroscience Applications

TL;DR

This paper develops a hypothesis test to determine when pooling multi-site datasets for regression analysis is beneficial, providing practical checks to guide data integration in biomedical research, especially Alzheimer's studies.

Contribution

It introduces a hypothesis testing framework for assessing the benefits of dataset pooling in regression, applicable to classical and high-dimensional settings, with practical pre-transfer checks.

Findings

Pooling improves power in Alzheimer's studies under certain regimes.

The proposed checks can be performed locally before data sharing.

The method clarifies when multi-site data integration is statistically advantageous.

Abstract

Many studies in biomedical and health sciences involve small sample sizes due to logistic or financial constraints. Often, identifying weak (but scientifically interesting) associations between a set of predictors and a response necessitates pooling datasets from multiple diverse labs or groups. While there is a rich literature in statistical machine learning to address distributional shifts and inference in multi-site datasets, it is less clear ${\it when}$ such pooling is guaranteed to help (and when it does not) -- independent of the inference algorithms we use. In this paper, we present a hypothesis test to answer this question, both for classical and high dimensional linear regression. We precisely identify regimes where pooling datasets across multiple sites is sensible, and how such policy decisions can be made via simple checks executable on each site before any data transfer ever happens. With a focus on Alzheimer's disease studies, we present empirical results showing that in regimes suggested by our analysis, pooling a local dataset with data from an international study improves power.