Efficient and Globally Robust Causal Excursion Effect Estimation
arxiv(2023)
摘要
Causal excursion effect (CEE) characterizes the effect of an intervention
under policies that deviate from the experimental policy. It is widely used to
study 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. 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.
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