Primary Submission Category: Policy Learning
Treatment Policy Design in the Presence of Measurement Error
Authors: Chang Liu, Mats Stensrud, AmirEmad Ghassami,
Presenting Author: Chang Liu*
In many applications, the goal is to assign treatments based on unit features, leading to personalized treatment policies. This often involves optimizing an objective function with counterfactual quantities such as the conditional ATE (CATE). However, in most real-world settings, some unit features may be measured with error and overlooking these errors can introduce systematic bias. In this work, we consider such settings with discrete unobserved features. After establishing the non-identifiability of the CATE, we propose two novel frameworks for treatment policy design using partial identification techniques, focusing on the measurement mechanism—the conditional distribution of measurements given the unobserved features. The first framework requires mild invertibility of the measurement mechanism, leading to a conservative treatment policy design based on ideas from proximal causal inference. The second framework further incorporates modeling assumptions on the measurement mechanism. We demonstrate that sharp bounds on the CATE can be obtained in this framework. This approach also leads to a novel characterization for informative measurements. We provide computationally efficient methods for obtaining bounds and quantifying uncertainty. Additionally, we show that integrating natural treatment values can further improve the bounding methods in treatment policy designs. We evaluate our methods through simulations and compare with naive methods that ignore measurement errors.
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