Parametric g-formula implementations for causal survival analyses

The g-formula can be used to estimate the survival curve under a sustained treatment strategy. Two available estimators of the g-formula are noniterative conditional expectation and iterative conditional expectation. We propose a version of the iterative conditional expectation estimator and describe its procedures for deterministic and random treatment strategies. Also, because little is known about the comparative performance of noniterative and iterative conditional expectation estimators, we explore their relative efficiency via simulation studies. Our simulations show that, in the absence of model misspecification and unmeasured confounding, our proposed iterative conditional expectation estimator and the noniterative conditional expectation estimator are similarly efficient, and that both are at least as efficient as the classical iterative conditional expectation estimator. We describe an application of both noniterative and iterative conditional expectation to answer "when to start" treatment questions using data from the HIV-CAUSAL Collaboration.