Multiply robust estimator for the difference in survival functions using pseudo-observations

BACKGROUND: When estimating the causal effect on survival outcomes in observational studies, it is necessary to adjust confounding factors due to unbalanced covariates between treatment and control groups. There is no study on multiple robust method for estimating the difference in survival functions. In this study, we propose a multiply robust (MR) estimator, allowing multiple propensity score models and outcome regression models, to provide multiple protection. METHOD: Based on the previous MR estimator (Han 2014) and pseudo-observation approach, we proposed a new MR estimator for estimating the difference in survival functions. The proposed MR estimator based on the pseudo-observation approach has several advantages. First, the proposed estimator has a small bias when any PS and OR models were correctly specified. Second, the proposed estimator considers the advantage pf the pseudo-observation approach, which avoids proportional hazards assumption. A Monte Carlo simulation study was performed to evaluate the performance of the proposed estimator. And the proposed estimator was used to estimate the effect of chemotherapy on triple-negative breast cancer (TNBC) in real data. RESULTS: The simulation studies showed that the bias of the proposed estimator was small, and the coverage rate was close to 95% when any model for propensity score or outcome regression is correctly specified regardless of whether the proportional hazard assumption holds, finite sample size and censoring rate. And the simulation results also showed that even though the propensity score models are misspecified, the bias of the proposed estimator was still small when there is a correct model in candidate outcome regression models. And we applied the proposed estimator in real data, finding that chemotherapy could improve the prognosis of TNBC. CONCLUSIONS: The proposed estimator, allowing multiple propensity score and outcome regression models, provides multiple protection for estimating the difference in survival functions. The proposed estimator provided a new choice when researchers have a "difficult time" choosing only one model for their studies. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-023-02065-6.