High-dimensional inference for the average treatment effect under model misspecification using penalized bias-reduced double-robust estimation

Abstract

The presence of confounding by high-dimensional variables complicates the estimation of the average effect of a point treatment. On the one hand, it necessitates the use of variable selection strategies or more general high-dimensional statistical methods. On the other hand, the use of such techniques tends to result in biased estimators with a non-standard asymptotic behavior. Double-robust estimators are useful for offering a resolution because they possess a so-called small bias property. This property has been exploited to achieve valid (uniform) inference of the average causal effect when data-adaptive estimators of the propensity score and conditional outcome mean both converge to their respective truths at sufficiently fast rate. In this article, we extend this work in order to retain valid (uniform) inference when one of these estimators does not converge to the truth, regardless of which. This is done by generalizing prior work for low-dimensional settings by [Vermeulen K, Vansteelandt S. Bias-reduced doubly robust estimation. Am Stat Assoc. 2015;110(511):1024–1036.] to incorporate regularization. The proposed penalized bias-reduced double-robust estimation strategy exhibits promising performance in simulation studies and a data analysis, relative to competing proposals.

Keywords:

• Confounding
• debiasing
• double robustness
• high-dimensional inference
• model misspecification
• penalized estimating equations

Acknowledgments

This research is supported by FWO Research Project G016116N.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by FWO (Fonds Wetenschappelijk Onderzoek) Research Project G016116N.

Notes on contributors

Vahe Avagyan

Vahe Avagyan is Assistant Professor in Mathematical and Statistical Methods Group (Biometris) at Wageningen University and Research, The Netherlands.

Stijn Vansteelandt

Stijn Vansteelandt is Professor of Statistics in the Department of Applied Mathematics, Computer Science and Statistics at Ghent University (Belgium) and Professor of Statistical Methodology in the Department of Medical Statistics at the London School of Hygiene and Tropical Medicine (UK).