Doubly robust estimation of monotonic survival curves for time-varying treatments in observational studies

Doubly robust estimators of the longitudinal g-computation formula enhance robustness against model misspecification, offering an improvement over the standard inverse probability weighted estimators. However, existing doubly robust estimators for discrete-time survival outcomes do not necessarily guarantee that the estimated survival curves remain monotonic. In this manuscript, we propose a novel estimator of the g-computation formula specifically designed for discrete-time survival outcomes, ensuring that the resulting estimated survival curves are monotonic in the presence of treatment-confounder feedback and simultaneously guaranteeing double robustness at all time points. We establish theoretical properties of this estimator and compare its performance with existing estimators that do not impose monotonicity constraints. Through simulation studies, we compare our proposed approach with existing methodologies in terms of bias, efficiency, and robustness under various model misspecifications, and demonstrate its application using an illustrative real-world dataset.