  Cross-study replicability is a powerful model evaluation criterion that
emphasizes generalizability of predictions. When training cross-study
replicable prediction models, it is critical to decide between merging and
treating the studies separately. We study boosting algorithms in the presence
of potential heterogeneity in predictor-outcome relationships across studies
and compare two multi-study learning strategies: 1) merging all the studies and
training a single model, and 2) multi-study ensembling, which involves training
a separate model on each study and ensembling the resulting predictions. In the
regression setting, we provide theoretical guidelines based on an analytical
transition point to determine whether it is more beneficial to merge or to
ensemble for boosting with linear learners. In addition, we characterize a
bias-variance decomposition of estimation error for boosting with
component-wise linear learners. We verify the theoretical transition point
result in simulation and illustrate how it can guide the decision on merging
vs. ensembling in an application to breast cancer gene expression data.
