Estimating Optimal Site-Specific Individualized Treatment Rules with Limited Data Sharing.

Estimation of optimal individualized treatment rules (ITRs) tailored to patient characteristics is a crucial component of precision medicine. When such problems arise in multicenter randomized trials with known treatment assignment probabilities, the optimal ITR may vary across sites because of site-level heterogeneity, and directly pooling data across centers can lead to biased ITR estimation. Meanwhile, privacy constraints often prevent investigators from accessing individual-level data from all centers. We therefore propose Heterogeneous Distributed Learning (HD-learning) to estimate optimal site-specific ITRs using only summary-level data from each site in a single communication round. The method uses a distributed mixed-effects model to accommodate common fixed effects and site-specific random effects. We further develop Shrinkage HD-learning (SHD-learning) for moderate- or high-dimensional covariates. Under suitable conditions, we establish asymptotic properties of the proposed estimators. Simulations show that our methods are lossless relative to the corresponding pooled estimator and outperform methods that ignore heterogeneity. We illustrate the proposed methods using the acute upper respiratory tract infections (AURTIs) study and the opioid withdrawal study.