Lendle Samuel D, Subbaraman Meenakshi S, van der Laan Mark J
Division of Biostatistics, University of California, Berkeley, CA, USA.
Biometrics. 2013 Jun;69(2):310-7. doi: 10.1111/biom.12022. Epub 2013 Apr 23.
The natural direct effect (NDE), or the effect of an exposure on an outcome if an intermediate variable was set to the level it would have been in the absence of the exposure, is often of interest to investigators. In general, the statistical parameter associated with the NDE is difficult to estimate in the non-parametric model, particularly when the intermediate variable is continuous or high dimensional. In this article, we introduce a new causal parameter called the natural direct effect among the untreated, discuss identifiability assumptions, propose a sensitivity analysis for some of the assumptions, and show that this new parameter is equivalent to the NDE in a randomized controlled trial. We also present a targeted minimum loss estimator (TMLE), a locally efficient, double robust substitution estimator for the statistical parameter associated with this causal parameter. The TMLE can be applied to problems with continuous and high dimensional intermediate variables, and can be used to estimate the NDE in a randomized controlled trial with such data. Additionally, we define and discuss the estimation of three related causal parameters: the natural direct effect among the treated, the indirect effect among the untreated and the indirect effect among the treated.
自然直接效应（NDE），即如果将中间变量设定为在未暴露情况下本应处于的水平时，暴露对结局的效应，通常是研究者感兴趣的。一般来说，在非参数模型中，与NDE相关的统计参数很难估计，尤其是当中间变量是连续的或高维的时候。在本文中，我们引入了一个新的因果参数，称为未治疗者中的自然直接效应，讨论了可识别性假设，针对其中一些假设提出了敏感性分析，并表明在随机对照试验中这个新参数等同于NDE。我们还提出了一个目标最小损失估计量（TMLE），这是一个针对与该因果参数相关的统计参数的局部有效、双重稳健的替代估计量。TMLE可应用于具有连续和高维中间变量的问题，并且可用于估计具有此类数据的随机对照试验中的NDE。此外，我们定义并讨论了三个相关因果参数的估计：治疗者中的自然直接效应、未治疗者中的间接效应以及治疗者中的间接效应。
