Identification, Semiparametric Efficiency, and Quadruply Robust Estimation in Mediation Analysis with Treatment-Induced Confounding

Natural mediation effects are often of interest when the goal is to understand a causal mechanism. However, most existing methods and their identification assumptions preclude treatment-induced confounders often present in practice. To address this fundamental limitation, we provide a set of assumptions that identify the natural direct effect in the presence of treatment-induced confounders. Even when some of those assumptions are violated, the estimand still has an interventional direct effect interpretation. We derive the semiparametric efficiency bound for the estimand, which unlike usual expressions, contains conditional densities that are variational dependent. We consider a reparameterization and propose a quadruply robust estimator that remains consistent under four types of possible misspecification and is also locally semiparametric efficient. We use simulation studies to demonstrate the proposed method and study an application to the 2017 Natality data to investigate the effect of prenatal care on preterm birth mediated by preeclampsia with smoking status during pregnancy being a potential treatment-induced confounder.

当研究目标为阐释某一因果机制（causal mechanism）时，自然中介效应（natural mediation effects）往往是学界重点关注的核心议题。然而，现有绝大多数方法及其识别假设均无法容纳实际研究中普遍存在的处理诱导混杂因素（treatment-induced confounders）。为解决这一根本性局限，本文提出一组可在存在处理诱导混杂因素的场景下识别自然直接效应（natural direct effect）的假设。即便部分假设遭到违背，该待估目标仍可被解释为干预型直接效应。本文推导了该待估目标的半参数效率界（semiparametric efficiency bound），与常规表达式不同，该界包含具有变分相依性的条件密度（conditional densities）。本文考虑一种重参数化方式，并提出一种四重稳健估计量（quadruply robust estimator）：该估计量在四类可能的模型误设情形下仍保持一致性，同时具备局部半参数有效性（locally semiparametric efficient）。我们通过模拟研究验证了所提方法的有效性，并将其应用于2017年美国出生登记数据（2017 Natality data），以探究产前保健（prenatal care）对早产（preterm birth）的影响，其中子痫前期（preeclampsia）为中介变量，孕期吸烟状态（smoking status）则为潜在的处理诱导混杂因素。