Infinitesimal Robustness in Randomized Controlled Trials

M. Zhelonkin

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Department of Econometrics, Erasmus University Rotterdam, Rotterdam, the Netherlands [zhelonkin@ese.eur.nl]

Keywords: Causal effect; Change-of-variance function; Influence function; Randomized controlled trial; Robustness.

1 Abstract

Treatment effect evaluation is one of the central topics in many fields including Biology, Economics, Medicine and Social Sciences. The randomized controlled trials (RCT) are the gold standard for causal effect estimation and inference. The difference-in-means estimator is a simple estimator with well-studied properties. However, in practice, it is advised to use the regression-adjusted estimator, since it is more efficient. In this paper we study the robustness properties of the classical estimators and show that their theoretical properties can be distorted in the presence of data contamination. We derive the influence functions (IF) and the change-of-variance functions (CVF) for the diference-in-means and regression-adjusted estimator. The IF and CVF are not bounded, hence these estimators can possess arbitrary behavior with respect to bias and variance. Therefore we propose the robust alternatives. The theoretical results are illustrated via a simulation study and a real data example.