As research in causal inference has sought to address more complex scientific questions, the number of specialized estimands in the field has proliferated. Recognition that many of these estimands share a common linear form has generated interest in simplifying estimation procedures using Riesz representers. In this work, we construct a targeted minimum loss-based estimation procedure for nested linear functionals, leveraging Riesz representers of a general recursive form. The proposed method unifies asymptotically efficient estimation for a variety of statistical estimands that originate in causal inference, including the effects of time-varying treatments under treatment-confounder feedback and direct and indirect effects from causal mediation analysis. We demonstrate how our proposal reduces the need for laborious and technically challenging mathematical derivations when constructing estimators of common statistical estimands under complex forms of censoring and sampling. We investigate and validate the properties of the proposed procedures in numerical experiments, discuss open-source software facilitating their implementation, and illustrate their application in a re-analysis of data from an HIV vaccine efficacy trial.

翻译：随着因果推断研究试图解答更复杂的科学问题，该领域中专用的估计量数量激增。认识到许多估计量共享相同的线性形式后，利用Riesz表示者简化估计程序的方法引起了广泛关注。本文针对嵌套线性泛函构建了一种基于Riesz表示者的目标最小损失估计程序，并采用一般递归形式的Riesz表示者。所提出的方法统一了源自因果推断的多种统计估计量的渐近有效估计，包括治疗-混杂反馈下的时变治疗效果以及因果中介分析中的直接与间接效应。我们展示了该方法如何在复杂删失与抽样形式下减少构建常见统计估计量时所必需的繁琐且技术性强的数学推导。通过数值实验验证了所提出程序的性质，讨论了促进其实现的开源软件，并通过重新分析一项HIV疫苗效力试验的数据说明了其应用。