  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.
