Efficient Estimation of the Causal Effects of Stochastic Interventions

Efficient estimation of the population-level causal effects of stochastic interventions on a continuous-valued exposure. Both one-step and targeted minimum loss estimators are implemented for the counterfactual mean value of an outcome of interest under an additive modified treatment policy, a stochastic intervention that may depend on the natural value of the exposure. To accommodate settings with outcome-dependent two-phase sampling, procedures incorporating inverse probability of censoring weighting are provided to facilitate the construction of inefficient and efficient one-step and targeted minimum loss estimators. The causal parameter and its estimation were first described by Díaz and van der Laan (2013) , while the multiply robust estimation procedure and its application to data from two-phase sampling designs is detailed in NS Hejazi, MJ van der Laan, HE Janes, PB Gilbert, and DC Benkeser (2020) . The software package implementation is described in NS Hejazi and DC Benkeser (2020) . Estimation of nuisance parameters may be enhanced through the Super Learner ensemble model in 'sl3', available for download from GitHub using 'remotes::install_github("tlverse/sl3")'.