Estimating survival causal effects with multi-site data: integrating global and local propensity score models

{Theoretical analysis, simulations, and empirical studies are used to validate a novel causal inference method for multi-site survival data}. Multi-site survival data are common in medical research, while heterogeneity in the distribution of covariates and treatment assignments among different sites is often unknown in practice. We propose a new multiple robust method for estimating overall hazard ratio with multi-site survival data, which simultaneously integrates a global propensity score (PS) model for the entire population and local PS models within each site to handle the unknown heterogeneity across sites and reduce the root mean squared error (RMSE). We further extend our method to allow multiple global or local PS models to achieve multiple robust estimation, with theoretical properties demonstrated. Our simulations show that the proposed method can achieve a lower RMSE while maintaining low bias, and it is robust to model misspecification. We apply the proposed method to real-world data from the Surveillance, Epidemiology, and End Result (SEER) database.