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

Zhang Zhiwei (), Hu Zonghui and Liu Chunling
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Zhang Zhiwei: Department of Statistics, University of California, Riverside, CA, USA
Hu Zonghui: Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Rockville, MD, USA
Liu Chunling: Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China

The International Journal of Biostatistics, 2019, vol. 15, issue 1, 29

Abstract: We 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.

Keywords: causal inference; double robustness; efficient influence function; machine learning; semiparametric theory; super learner (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/ijb-2018-0093

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