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.

翻译：主分层是处理存在中间结局时因果推断的流行框架。虽然主平均处理效应传统上被默认为推断目标，但当研究关注主层内潜在结局相对优劣关系时，该目标可能不够充分。为此，我们引入主广义因果效应估计量，将主平均因果效应扩展至可容纳非线性对比函数。在主可忽略性假设下，我们将Jiang等（2022）的理论结果推广至存在二元中间变量时更广泛的因果估计量类别。我们推导了主分层分析中广义估计量的识别公式及有效影响函数。这些有效影响函数启示了多重稳健估计量族，并为基于交叉拟合的U统计量高效去偏机器学习估计量奠定基础。通过模拟实验和数据分析实例对所提方法进行了验证。