When can Multi-Site Datasets be Pooled for Regression? Hypothesis Tests, $\ell_2$-consistency and Neuroscience Applications
This addresses the challenge for biomedical researchers with small sample sizes to decide when pooling data across sites is effective, though it is incremental as it builds on existing statistical machine learning literature.
The paper tackles the problem of determining when pooling multi-site datasets for regression is beneficial, presenting a hypothesis test to identify regimes where pooling improves statistical power, with empirical results in Alzheimer's disease studies showing enhanced power in suggested regimes.
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.