Doubly Robust Transfer Learning Under Sub-group Shift for Cohort-level Missing Indicator Covariates

Modern biomedical research increasingly relies on integrating multiple cohort studies, yet faces a critical challenge: indicator covariates such as smoking status, vaccination records, or diagnostic codes that are entirely absent in some cohorts due to differences in data collection protocols.This cohort-level missingness violates the assumptions underlying traditional missing data methods, as the complete absence of covariates across entire populations fundamentally differs from sporadic individual-level missingness.To address this gap, we develop a doubly robust transfer learning framework based on a novel sub-group shift assumption, which posits that the conditional distribution of the missing indicator given other variables remains stable across cohorts while allowing marginal distributions to vary.Our approach combines importance weighting with imputation in augmented estimating equations, achieving robustness to misspecification of either the density ratio model or the imputation model.We establish