Principal stratification with U-statistics under principal ignorability
arxiv(2024)
摘要
Principal stratification is a popular framework for causal inference in the
presence of an intermediate outcome. While the principal average treatment
effects have traditionally been the default target of inference, it may not be
sufficient when the interest lies in the relative favorability of one potential
outcome over the other within the principal stratum. We thus introduce the
principal generalized causal effect estimands, which extend the principal
average causal effects to accommodate nonlinear contrast functions. Under
principal ignorability, we expand the theoretical results in Jiang et. al.
(2022) to a much wider class of causal estimands in the presence of a binary
intermediate variable. We develop identification formulas and derive the
efficient influence functions of the generalized estimands for principal
stratification analyses. These efficient influence functions motivate a set of
multiply robust estimators and lay the ground for obtaining efficient debiased
machine learning estimators via cross-fitting based on U-statistics. The
proposed methods are illustrated through simulations and the analysis of a data
example.
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