Natural direct and indirect effects are mediational estimands that decompose the average treatment effect and describe how outcomes would be affected by contrasting levels of a treatment through changes induced in mediator values (in the case of the indirect effect) or not through induced changes in the mediator values (in the case of the direct effect). Natural direct and indirect effects are not generally point-identifiable in the presence of a treatment-induced confounder, however they may still be identified if one is willing to assume monotonicity between a treatment and the treatment-induced confounder. We argue that this assumption may be reasonable in the relatively common encouragement-design trial setting where intervention is randomized treatment assignment and the treatment-induced confounder is whether or not treatment was actually taken/adhered to. We develop efficiency theory for the natural direct and indirect effects under this monotonicity assumption, and use it to propose a nonparametric, multiply robust estimator. We demonstrate the finite sample properties of this estimator using a simulation study, and apply it to data from the Moving to Opportunity Study to estimate the natural direct and indirect effects of being randomly assigned to receive a Section 8 housing voucher -- the most common form of federal housing assistance -- on risk developing any mood or externalizing disorder among adolescent boys, possibly operating through various school and community characteristics.

翻译：自然的直接和间接影响是调解性估计效应,它分解了平均治疗效果,并描述了通过调解价值的变化(间接影响),而不是通过调解价值的诱导变化(直接影响)对治疗水平的对比,结果将如何受到影响。 自然的直接和间接影响一般在治疗引起的混淆者在场的情况下是无法辨别的,但如果人们愿意在治疗和治疗引起的混乱者之间承担单一性,那么仍然可以辨别这些影响。我们争辩说,在相对常见的鼓励-设计审判环境中,这一假设可能是合理的,因为在相对常见的鼓励-设计审判环境中,干预是随机的治疗任务,而治疗引起的融合者是是否实际接受/接受治疗。 我们为这一单一假设下的自然直接和间接影响制定效率理论,并利用这一理论提出一个非参数性、倍强力的估算。我们利用模拟研究来证明这一估计者有限的抽样性质,并将这一假设应用于从“机会研究”到估计联邦援助的自然和间接影响 -- -- 通过可能任意分配的学校共同病理学系特征,通过学校的外部病理学系,获得一种可能发展各种住房的普通病理学系。