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Abstract:
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Individualized treatment rules (ITRs) are regarded as a promising recipe to deliver better policy interventions. One key ingredient in optimal ITR estimation problems is to estimate conditional average treatment effect, which is challenging in observational studies due to the concern of unmeasured confounding. Instrumental variables (IVs) are widely-used to infer treatment effect when there is unmeasured confounding between the treatment and outcome. In this work, we propose a general framework to approach the ITR estimation problem with a valid IV by recasting it into a semi-supervised classification problem consisting of a supervised and an unsupervised part. The unsupervised part stems from the partial identification nature of an IV in identifying the treatment effect. We define a new notion of optimality called ``IV-optimality''. A treatment rule is said to be IV-optimal if it minimizes the maximum risk with respect to the IV and IV identification assumptions. We propose a statistical learning method that estimates such an IV-optimal rule, design computationally-efficient algorithms, prove theoretical guarantees, and apply it to a neonatal intensive care unit (NICU) study.
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