Multiply robust estimators of causal effects for survival outcomes

Multiply robust estimators of the longitudinal g‐formula have recently been proposed to protect against model misspecification better than the standard augmented inverse probability weighted estimator (Rotnitzky et al., 2017; Luedtke et al., 2018). These multiply robust estimators ensure consistency if one of the models for the treatment process or outcome process is correctly specified at each time point. We study the multiply robust estimators of Rotnitzky et al. (2017) in the context of a survival outcome. Specifically, we compare various estimators of the g‐formula for survival outcomes in order to (1) understand how the estimators may be related to one another, (2) understand each estimator's robustness to model misspecification, and (3) construct estimators that can be more efficient than others in certain model misspecification scenarios. We propose a modification of the multiply robust estimators to gain efficiency under misspecification of the outcome model by using calibrated propensity scores over non‐calibrated propensity scores at each time point. Theoretical results are confirmed via simulation studies, and a practical comparison of these estimators is conducted through an application to the US Veterans Aging Cohort Study.