Multiply Robust Causal Mediation Analysis with Continuous Treatments
- URL: http://arxiv.org/abs/2105.09254v2
- Date: Sat, 3 Feb 2024 18:49:47 GMT
- Title: Multiply Robust Causal Mediation Analysis with Continuous Treatments
- Authors: Numair Sani, Yizhen Xu, AmirEmad Ghassami, Ilya Shpitser
- Abstract summary: We propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimator of Tchetgen Tchetgen and Shpitser (2012)
Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions, and allowing them to be estimated slower rates than the target parameter.
- Score: 13.324203991645629
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In many applications, researchers are interested in the direct and indirect
causal effects of a treatment or exposure on an outcome of interest. Mediation
analysis offers a rigorous framework for identifying and estimating these
causal effects. For binary treatments, efficient estimators for the direct and
indirect effects are presented in Tchetgen Tchetgen and Shpitser (2012) based
on the influence function of the parameter of interest. These estimators
possess desirable properties, such as multiple-robustness and asymptotic
normality, while allowing for slower than root-n rates of convergence for the
nuisance parameters. However, in settings involving continuous treatments,
these influence function-based estimators are not readily applicable without
making strong parametric assumptions. In this work, utilizing a
kernel-smoothing approach, we propose an estimator suitable for settings with
continuous treatments inspired by the influence function-based estimator of
Tchetgen Tchetgen and Shpitser (2012). Our proposed approach employs
cross-fitting, relaxing the smoothness requirements on the nuisance functions,
and allowing them to be estimated at slower rates than the target parameter.
Additionally, similar to influence function-based estimators, our proposed
estimator is multiply robust and asymptotically normal, making it applicable
for inference in settings where a parametric model cannot be assumed.
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