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Identification and Efficient Estimation of the Natural Direct Effect among the Untreated
Author(s) -
Lendle Samuel D.,
Subbaraman Meenakshi S.,
van der Laan Mark J.
Publication year - 2013
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12022
Subject(s) - identifiability , estimator , identification (biology) , statistics , parametric statistics , causal inference , mathematics , estimation theory , randomized experiment , econometrics , variable (mathematics) , computer science , biology , mathematical analysis , botany
Summary 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, discus 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.