Deconfounded-Debiased Distributed Estimation for High-Dimensional Multi-Site Data with Heterogeneous Pervasive Hidden Confounders

In observational studies, high-dimensional multi-site data are subject to heterogeneous pervasive hidden confounders across sites, leading to substantial bias in distributed estimation.To address this challenge, we propose a deconfounded-debiased distributed estimation method, which integrates majority voting for variable selection and the privacy-preserving aggregation of local deconfoundeddebiased estimators at the central site.This approach corrects biases from both heterogeneous pervasive hidden confounders and high-dimensional estimation, while also accommodating site-specific heteroscedasticity in the random errors.Theoretically, we prove that local deconfounded-debiased estimators are asymptotically normal, and local individual hypothesis tests are asymptotically valid with an asymptotic lower bound on their power.Furthermore, we establish variable selection consistency and asymptotic normality for the proposed distributed estimator.We also provide finite-sample guarantees for variable selection, including an upper bound on the expected false positive rate and a lower bound on the expected true positive rate.Simulation experiments and an application to a protein dataset from the UK Biobank demonstrate our method's superior finite-sample performance.