Covariate selection for the nonparametric estimation of an average treatment effect

Observational studies in which the effect of a nonrandomized treatment on an outcome of interest is estimated are common in domains such as labour economics and epidemiology. Such studies often rely on an assumption of unconfounded treatment when controlling for a given set of observed pre-treatment...

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Bibliographic Details
Published in:Biometrika 2011-12, Vol.98 (4), p.861-875
Main Authors: DE LUNA, XAVIER, WAERNBAUM, INGEBORG, RICHARDSON, THOMAS S.
Format: Article
Language:English
Subjects:
Applications
Biology, psychology, social sciences
Cardinality
Directed acyclic graphs
Estimating techniques
Estimation bias
Estimators
Exact sciences and technology
General topics
Inference
Logical givens
Mathematical minima
Mathematical models
Mathematics
Nonparametric inference
Observational studies
Optimization algorithms
Parametric inference
Probability and statistics
Random variables
Sciences and techniques of general use
Statistics
Studies
Vertices
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Summary:Observational studies in which the effect of a nonrandomized treatment on an outcome of interest is estimated are common in domains such as labour economics and epidemiology. Such studies often rely on an assumption of unconfounded treatment when controlling for a given set of observed pre-treatment covariates. The choice of covariates to control in order to guarantee unconfoundedness should primarily be based on subject matter theories, although the latter typically give only partial guidance. It is tempting to include many covariates in the controlling set to try to make the assumption of an unconfounded treatment realistic. Including unnecessary covariates is suboptimal when the effect of a binary treatment is estimated nonparametrically. For instance, when using a n 1/2 -consistent estimator, a loss of efficiency may result from using covariates that are irrelevant for the unconfoundedness assumption. Moreover, bias may dominate the variance when many covariates are used. Embracing the Neyman—Rubin model typically used in conjunction with nonparametric estimators of treatment effects, we characterize subsets from the original reservoir of covariates that are minimal in the sense that the treatment ceases to be unconfounded given any proper subset of these minimal sets. These subsets of covariates are shown to be identified under mild assumptions. These results lead us to propose data-driven algorithms for the selection of minimal sets of covariates.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asr041