Comment: Stabilizing the Doubly-Robust Estimators of the Average Treatment Effect under Positivity Violations

2020 ◽  
Vol 35 (3) ◽  
pp. 503-510
Author(s):  
Fan Li
Keyword(s):  
Treatment Effect ◽  
Average Treatment Effect ◽  
Robust Estimators ◽  
Average Treatment ◽  
Doubly Robust

scholarly journals Doubly robust nonparametric inference on the average treatment effect

Biometrika ◽  
2017 ◽  
Vol 104 (4) ◽  
pp. 863-880 ◽  
Author(s):  
D Benkeser ◽  
M Carone ◽  
M J Van Der Laan ◽  
P B Gilbert
Keyword(s):  
Treatment Effect ◽  
Theoretical Study ◽  
Average Treatment Effect ◽  
Robust Inference ◽  
Nuisance Parameters ◽  
Robust Estimators ◽  
Average Treatment ◽  
Adaptive Estimators ◽  
Data Adaptive ◽  
Doubly Robust

Summary Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average treatment effect when one of the nuisance parameters is inconsistently estimated. We contrast different methods for constructing such estimators and investigate the extent to which they may be modified to also allow doubly robust inference. We find that while targeted minimum loss-based estimation can be used to solve this problem very naturally, common alternative frameworks appear to be inappropriate for this purpose. We provide a theoretical study and a numerical evaluation of the alternatives considered. Our simulations highlight the need for and usefulness of these approaches in practice, while our theoretical developments have broad implications for the construction of estimators that permit doubly robust inference in other problems.

A doubly robust weighting estimator of the average treatment effect on the treated

Stat ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. e205 ◽  
Author(s):  
Erica E. M. Moodie ◽  
Olli Saarela ◽  
David A. Stephens
Keyword(s):  
Treatment Effect ◽  
Average Treatment Effect ◽  
Average Treatment ◽  
Doubly Robust

Estimating the Population Average Treatment Effect in Observational Studies with Choice-Based Sampling

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Zhiwei Zhang ◽  
Zonghui Hu ◽  
Chunling Liu
Keyword(s):  
Observational Study ◽  
Treatment Effect ◽  
Observational Studies ◽  
Average Treatment Effect ◽  
Parametric Models ◽  
Average Treatment ◽  
Population Average ◽  
Doubly Robust ◽  
Asymptotically Efficient ◽  
Semiparametric Theory

AbstractWe consider causal inference in observational studies with choice-based sampling, in which subject enrollment is stratified on treatment choice. Choice-based sampling has been considered mainly in the econometrics literature, but it can be useful for biomedical studies as well, especially when one of the treatments being compared is uncommon. We propose new methods for estimating the population average treatment effect under choice-based sampling, including doubly robust methods motivated by semiparametric theory. A doubly robust, locally efficient estimator may be obtained by replacing nuisance functions in the efficient influence function with estimates based on parametric models. The use of machine learning methods to estimate nuisance functions leads to estimators that are consistent and asymptotically efficient under broader conditions. The methods are compared in simulation experiments and illustrated in the context of a large observational study in obstetrics. We also make suggestions on how to choose the target proportion of treated subjects and the sample size in designing a choice-based observational study.

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