Principal stratification is essential for revealing causal mechanisms involving post-treatment intermediate variables. Principal stratification analysis with continuous intermediate variables is increasingly common but challenging due to the infinite principal strata and the nonidentifiability and nonregularity of principal causal effects. Inspired by recent research, we resolve these challenges by first using a flexible copula-based principal score model to identify principal causal effect under weak principal ignorability. We then target the local functional substitute of principal causal effect, which is statistically regular and can accurately approximate principal causal effect with vanishing bandwidth. We simplify the full efficient influence function of the local functional substitute by considering its oracle-scenario alternative. This leads to a computationally efficient and straightforward estimator for the local functional substitute and principal causal effect with vanishing bandwidth. We prove the double robustness and statistical optimality of our proposed estimator, and derive its asymptotic normality for inferential purposes. We illustrate the appealing statistical performance of our proposed estimator in simulations, and apply it to two real datasets with intriguing scientific discoveries.

翻译：主分层分析对于揭示涉及处理后中间变量的因果机制至关重要。随着连续中间变量的主分层分析日益普遍，由于无限主分层以及主因果效应的不可识别性和非正则性，该分析面临诸多挑战。受近期研究启发，我们首先采用基于灵活Copula的主得分模型，在弱主可忽略性条件下识别主因果效应，从而解决这些挑战。随后，我们以主因果效应的局部函数替代量为目标——该替代量具有统计正则性，且能通过渐消带宽精确逼近主因果效应。通过考虑其理想场景替代形式，我们简化了局部函数替代量的完全有效影响函数，从而构建出计算高效、形式简洁的估计量，适用于渐消带宽下的局部函数替代量与主因果效应。我们证明了所提估计量的双重稳健性与统计最优性，并推导了其用于统计推断的渐近正态性。通过模拟研究展示了所提估计量优越的统计性能，并将其应用于两个具有重要科学发现的实际数据集。