Abstract
When sample sizes are small, the ability to identify weak (but scientifically interesting) associations between a set of predictors and a response may be enhanced by pooling existing datasets. However, variations in acquisition methods and the distribution of participants or observations between datasets, especially due to the distributional shifts in some predictors, may obfuscate real effects when datasets are combined. We present a rigorous statistical treatment of this problem and identify conditions where we can correct the distributional shift. We also provide an algorithm for the situation where the correction is identifiable. We analyze various properties of the framework for testing model fit, constructing confidence intervals, and evaluating consistency characteristics. Our technical development is motivated by Alzheimer's disease (AD) studies, and we present empirical results showing that our framework enables harmonizing of protein biomarkers, even when the assays across sites differ. Our contribution may, in part, mitigate a bottleneck that researchers face in clinical research when pooling smaller sized datasets and may offer benefits when the subjects of interest are difficult to recruit or when resources prohibit large single-site studies.