On Robustness of Individualized Decision Rules

Abstract

With the emergence of precision medicine, estimating optimal individualized decision rules (IDRs) has attracted tremendous attention in many scientific areas. Most existing literature has focused on finding optimal IDRs that can maximize the expected outcome for each individual. Motivated by complex individualized decision making procedures and the popular conditional value at risk (CVaR) measure, we propose a new robust criterion to estimate optimal IDRs in order to control the average lower tail of the individuals’ outcomes. In addition to improving the individualized expected outcome, our proposed criterion takes risks into consideration, and thus the resulting IDRs can prevent adverse events. The optimal IDR under our criterion can be interpreted as the decision rule that maximizes the “worst-case” scenario of the individualized outcome when the underlying distribution is perturbed within a constrained set. An efficient non-convex optimization algorithm is proposed with convergence guarantees. We investigate theoretical properties for our estimated optimal IDRs under the proposed criterion such as consistency and finite sample error bounds. Simulation studies and a real data application are used to further demonstrate the robust performance of our methods. Several extensions of the proposed method are also discussed. Supplementary materials for this article are available online.

KEYWORDS:

• Conditional value at risk
• Individualized decision rules
• Nonconvex optimization
• Robustness
• Tail controls

Acknowledgments

The authors would like to thank the Editor, the Associate Editor, and reviewers, whose helpful comments and suggestions led to a much improved presentation. Yufeng Liu’s research was supported in part by NSF grants DMS-1821231 and DMS-2100729, and NIH grant R01GM126550.