Distributed Semiparametric Inference for Heterogeneous Sites via Single-Round Communication

Distributed inference has proven useful in contexts where data privacy is the central concern. However, privacy constraints often necessitate cumbersome coordination to exchange summary data during distributed learning. Most existing methods require two rounds of data communication, yet excessive communication rounds might discourage participation from local sites. This study develops distributed algorithms that require only a single communication round while maintaining efficiency comparable to existing two-round methods. Under a general heterogeneous semiparametric framework with an increasing number of sites, our objective is to estimate a common Euclidean parameter shared across all sites. We consider two possible coordination schemes, one led by a central server without access to raw data and the other by a designated leading site. We design estimators tailored to each coordination setting by leveraging surrogate criterion construction and approximate one-step calibration. We show theoretically and through comprehensive simulations that the proposed estimators achieve the same or better approximation accuracy to the pooled-data estimator compared with existing two-round methods designed for heterogeneous sites. The advantages of the proposed methods are demonstrated using Cox’s model and logistic regression on two electronic health record datasets from the University of Pennsylvania Health System.