A Communication-Efficient Distributed Algorithm for Learning with Heterogeneous and Structurally Incomplete Multi-Site Data

In multicenter biomedical research, integrating data from multiple decentralized sites provides more robust and generalizable findings due to its larger sample size and the ability to account for the between-site heterogeneity. However, sharing individual-level data across sites is often difficult due to patient privacy concerns and regulatory restrictions. To overcome this challenge, many distributed algorithms, that fit a global model by only communicating aggregated information across sites, have been proposed. A major challenge in applying existing distributed algorithms to real-world data is that their validity often relies on the assumption that data across sites are independently and identically distributed, which is frequently violated in practice. In biomedical applications, data distributions across clinical sites can be heterogeneous. Additionally, the set of covariates available at each site may vary due to different data collection protocols. We propose a distributed inference framework for data integration in the presence of both distribution heterogeneity and data structural heterogeneity. By modeling heterogeneous and structurally missing data using density-tilted generalized method of moments, we developed a general aggregated data-based distributed algorithm that is communication-efficient and heterogeneity-aware. We establish the asymptotic properties of our estimator and demonstrate the validity of our method via simulation studies.