Privacy-Protected Causal Survival Analysis Under Distribution Shift

Causal inference across multiple data sources can improve the generalizability and reproducibility of scientific findings. However, for time-to-event outcomes, data integration methods remain underdeveloped, especially when populations are heterogeneous and privacy constraints prevent direct data pooling. We propose a federated learning method for estimating target site-specific causal effects in multi-source survival settings. Our approach dynamically re-weights source contributions to correct for distributional shifts, while preserving privacy. Leveraging semiparametric efficiency theory under a site-specific exchangeability assumption}, data-adaptive weighting and flexible machine learning, the method achieves double robustness, and it improves efficiency {if at least one source site provides a consistent estimate. Through simulations and two real data applications: (i) multi-site randomized trials of monoclonal antibodies for HIV-1 prevention among cisgender men and transgender persons in the United States, Brazil, Peru, and Switzerland, as well as women in sub-Saharan Africa, and (ii) an analysis of sex disparities across biomarker groups for all-cause mortality using the ``flchain'' dataset, we demonstrate the validity, efficiency gains, and practical utility of the approach. Our findings highlight the promise of federated methods for efficient, privacy-preserving causal survival analysis under distribution shift.