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Abstract:
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There is a fast-growing literature on estimating optimal decision rules based on randomized trials or observational studies under a key identifying condition of no unmeasured confounding. Because confounding by unmeasured factors cannot generally be ruled out with certainty in observational studies or randomized trials subject to noncompliance, we propose a robust classification-based instrumental variable approach to learning optimal decision rules under endogeneity. Furthermore, we consider the problem of individualized decision rules under sign and partial identification. In the former case, i) we provide a necessary and sufficient identification condition of optimal decision rules with an instrumental variable; ii) we establish the somewhat surprising result that complier optimal rules can be consistently estimated without directly collecting compliance information and therefore without the complier average causal effect itself being identified. In the latter case, we establish a formal link between individualized decision making under partial identification and classical decision theory under uncertainty through a unified lower bound perspective.
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