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Estimating heterogeneous treatment effects (HTEs) is crucial for precision medicine. While multiple studies can improve the generalizability of results, leveraging them for estimation is statistically challenging. Existing approaches often assume identical HTEs across studies, but this may be violated due to various sources of between-study heterogeneity, including differences in study design, study populations, and data collection protocols, among others. To this end, we propose a framework for multi-study HTE estimation that accounts for between-study heterogeneity in the nuisance functions and treatment effects. Our approach, the multi-study R-learner, extends the R-learner to obtain principled statistical estimation with machine learning (ML) in the multi-study setting. It involves a data-adaptive objective function that links study-specific treatment effects with nuisance functions through membership probabilities, which enable information to be borrowed across potentially heterogeneous studies. The multi-study R-learner framework can combine data from randomized controlled trials, observational studies, or a combination of both. It's easy to implement and flexible in its ability to incorporate ML for estimating HTEs, nuisance functions, and membership probabilities. In the series estimation framework, we show that the multi-study R-learner is asymptotically normal and more efficient than the R-learner when there is between-study heterogeneity in the propensity score model under homoscedasticity. We illustrate using cancer data that the proposed method performs favorably compared to existing approaches in the presence of between-study heterogeneity.

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.

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 PFs with oracle properties. In particular we show that the the stacking weights are nearly optimal. We also characterize the scenario where the proposed no-data-reuse technique increases prediction accuracy compared to stacking with data reuse in a special case.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.

We investigate the power of censoring techniques, first developed for learning {\em fair representations}, to address domain generalization. We examine {\em adversarial} censoring techniques for learning invariant representations from multiple "studies" (or domains), where each study is drawn according to a distribution on domains. The mapping is used at test time to classify instances from a new domain. In many contexts, such as medical forecasting, domain generalization from studies in populous areas (where data are plentiful), to geographically remote populations (for which no training data exist) provides fairness of a different flavor, not anticipated in previous work on algorithmic fairness. We study an adversarial loss function for $k$ domains and precisely characterize its limiting behavior as $k$ grows, formalizing and proving the intuition, backed by experiments, that observing data from a larger number of domains helps. The limiting results are accompanied by non-asymptotic learning-theoretic bounds. Furthermore, we obtain sufficient conditions for good worst-case prediction performance of our algorithm on previously unseen domains. Finally, we decompose our mappings into two components and provide a complete characterization of invariance in terms of this decomposition. To our knowledge, our results provide the first formal guarantees of these kinds for adversarial invariant domain generalization.

A critical decision point when training predictors using multiple studies is whether these studies should be combined or treated separately. We compare two multi-study learning approaches in the presence of potential heterogeneity in predictor-outcome relationships across datasets. We consider 1) merging all of the datasets and training a single learner, and 2) multi-study ensembling, which involves training a separate learner on each dataset and combining the predictions resulting from each learner. In a linear regression setting, we show analytically and confirm via simulation that merging yields lower prediction error than ensembling when the predictor-outcome relationships are relatively homogeneous across studies. However, as cross-study heterogeneity increases, there exists a transition point beyond which ensembling outperforms merging. We provide analytic expressions for the transition point in various scenarios, study asymptotic properties, and illustrate how transition point theory can be used for deciding when studies should be combined with an application from metabolomics.

A recent study of the replicability of key psychological findings is a major contribution toward understanding the human side of the scientific process. Despite the careful and nuanced analysis reported in the paper, mass and social media adhered to the simple narrative that only 36% of the studies replicated their original results. Here we show that 77% of the replication effect sizes reported were within a prediction interval based on the original effect size. In this light, the results of Reproducibility Project: Psychology can be viewed as a positive result for the scientific process., Comment: 6 pages, 3 figures