Bias-adjusted Kaplan-Meier survival curves for marginal treatment effect in observational studies

For time-to-event outcomes, the Kaplan-Meier estimator is commonly used to estimate survival functions of treatment groups and to compute marginal treatment effects, such as the difference in survival rates between treatments at a landmark time. The derived estimates of the marginal treatment effect are uniformly consistent under general conditions when data are from randomized clinical trials. For data from observational studies, however, these statistical quantities are often biased due to treatment-selection bias. Propensity score-based methods estimate the survival function by adjusting for the disparity of propensity scores between treatment groups. Unfortunately, misspecification of the regression model can lead to biased estimates. Using an empirical likelihood (EL) method in which the moments of the covariate distribution of treatment groups are constrained to equality, we obtain consistent estimates of the survival functions and the marginal treatment effect. Equating moments of the covariate distribution between treatment groups simulate the covariate distribution that would have been obtained if the patients had been randomized to these treatment groups. We establish the consistency and the asymptotic limiting distribution of the proposed EL estimators. We demonstrate that the proposed estimator is robust to model misspecification. Simulation is used to study the finite sample properties of the proposed estimator. The proposed estimator is applied to a lung cancer observational study to compare two surgical procedures in treating early-stage lung cancer patients.