Efficient and Globally Robust Causal Excursion Effect Estimation (2311.16529v3)

Abstract: Causal excursion effect (CEE) characterizes the effect of an intervention under policies that deviate from the experimental policy. It is widely used to study the effect of time-varying interventions that have the potential to be frequently adaptive, such as those delivered through smartphones. We study the semiparametric efficient estimation of CEE and we derive a semiparametric efficiency bound for CEE with identity or log link functions under working assumptions, in the context of micro-randomized trials. We propose a class of two-stage estimators that achieve the efficiency bound and are robust to misspecified nuisance models. In deriving the asymptotic property of the estimators, we establish a general theory for globally robust Z-estimators with either cross-fitted or non-cross-fitted nuisance parameters. We demonstrate substantial efficiency gain of the proposed estimator compared to existing ones through simulations and a real data application using the Drink Less micro-randomized trial.