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, treatments are assigned based on unit features, leading to personalized treatment policies. This often involves optimizing objective functions with counterfactual quantities such as the conditional ATE (CATE). In practice, some key features may be measured with error and ignoring such errors can introduce systematic bias. We study how to design personalized treatment policies when some features are latent and only noisy measurements are available. We ask how policies can be constructed when the CATE is not identifiable, and how uncertainty from measurement error can be incorporated into policy learning. We propose two frameworks for treatment policy design based on partial identification, focusing on the measurement mechanism—the conditional distribution of observed measurements given unobserved features. The first framework builds on ideas from proximal causal inference. The second adopts a Bayesian approach, using a reparametrization of the likelihood to obtain the posterior distribution of the parameters of interest. We use data augmentation for latent variables and a Gibbs sampler with Hamiltonian Monte Carlo updates for model parameters. Quantiles of the posterior distribution are used to construct bounds for the CATE. Treatment policies are then derived by comparing the null value of the CATE to these bounds. The proposed methods provide a coherent way to account for measurement error and model uncertainty in personalized treatment policy learning.
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