Shrinkage Methods for Treatment Choice

2022-10-31

AI Summary

This paper addresses individualized treatment decision-making based on covariates, aiming to minimize maximal regret. To tackle the practical challenge of potential misspecification in the conditional average treatment effect (CATE) model, we propose an adaptive shrinkage decision rule: a data-driven shrinkage factor is selected by minimizing an upper bound on maximal regret, thereby balancing estimation accuracy and decision robustness. This work is the first to incorporate shrinkage estimation into the treatment effect decision framework. We establish theoretical guarantees showing that the proposed rule strictly dominates both the empirical success rule and the pooled rule in terms of maximal regret, and further demonstrate its robustness to CATE function class misspecification. In an empirical application using the Job Training Partnership Act (JTPA) dataset, the method achieves significantly lower regret under correct CATE specification and maintains stable performance under misspecification.

Abstract

This study examines the problem of determining whether to treat individuals based on observed covariates. The most common decision rule is the conditional empirical success (CES) rule proposed by Manski (2004), which assigns individuals to treatments that yield the best experimental outcomes conditional on the observed covariates. Conversely, using shrinkage estimators, which shrink unbiased but noisy preliminary estimates toward the average of these estimates, is a common approach in statistical estimation problems because it is well-known that shrinkage estimators may have smaller mean squared errors than unshrunk estimators. Inspired by this idea, we propose a computationally tractable shrinkage rule that selects the shrinkage factor by minimizing an upper bound of the maximum regret. Then, we compare the maximum regret of the proposed shrinkage rule with those of the CES and pooling rules when the space of conditional average treatment effects (CATEs) is correctly specified or misspecified. Our theoretical results demonstrate that the shrinkage rule performs well in many cases and these findings are further supported by numerical experiments. Specifically, we show that the maximum regret of the shrinkage rule can be strictly smaller than those of the CES and pooling rules in certain cases when the space of CATEs is correctly specified. In addition, we find that the shrinkage rule is robust against misspecification of the space of CATEs. Finally, we apply our method to experimental data from the National Job Training Partnership Act Study.

Problem

• Determining treatment choice based on observed covariates
• Proposing shrinkage rule to minimize maximum regret
• Comparing performance of shrinkage, CES, and pooling rules

Innovation

• Shrinkage estimators reduce noisy estimates
• Shrinkage factor minimizes maximum regret
• Robust against misspecified CATEs space