The inverse probability weighted Cox model is frequently used to estimate marginal hazard ratios. Its validity requires a crucial condition that the propensity score model is correctly specified. To provide protection against misspecification of the propensity score model, we propose a weighted estimation method rooted in empirical likelihood theory. The proposed estimator is multiply robust in that it is guaranteed to be consistent when a set of postulated propensity score models contains a correctly specified model. Our simulation studies demonstrate satisfactory finite sample performance of the proposed method in terms of consistency and efficiency. We apply the proposed method to compare the risk of postoperative hospitalization between sleeve gastrectomy and Roux-en-Y gastric bypass using data from a large medical claims and billing database.We further extend the development to multi-site studies to enable each site to postulate multiple site-specific propensity score models.



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