Cross-study learning for generalist and specialist predictions

The integration and use of data from multiple studies, for the development of prediction models is an important task in several scientific fields. We propose a framework for generalist and specialist predictions that leverages multiple datasets, with potential differences in the relationships between predictors and outcomes. Our framework uses stacking, and it includes three major components: 1) an ensemble of prediction models trained on one or more datasets, 2) task-specific utility functions and 3) a no-data-reuse technique for estimating stacking weights. We illustrate that under mild regularity conditions the framework produces stacked prediction functions with oracle properties. In particular we show that the the stacking weights are nearly optimal. We also provide sufficient conditions under which the proposed no-data-reuse technique increases prediction accuracy compared to stacking with data reuse. We perform a simulation study to illustrate these results. We apply our framework to predict mortality using a collection of datasets on long-term exposure to air pollutants.