Sensitivity analysis for stopping criteria with application to organ transplantations

2026-04-02

AI Summary

This study addresses the optimal timing decision for organ transplantation in individual patients under dynamic health conditions, formulated as a sequential stopping problem with termination. The authors theoretically establish the existence of a threshold-type optimal policy and, for the first time in this domain, introduce Smoothed Perturbation Analysis (SPA) to construct an SPA-based estimator for the gradient of the total expected discounted reward with respect to threshold policies. This estimator is proven to be asymptotically unbiased. By integrating stochastic dynamic programming with control-limit policy theory, the proposed approach provides an efficient and reliable gradient estimation tool for optimizing critical parameters in transplantation decision-making.

Abstract

We consider a stopping problem and its application to the decision-making process regarding the optimal timing of organ transplantation for individual patients. At each decision period, the patient state is inspected and a decision is made whether to transplant. If the organ is transplanted, the process terminates; otherwise, the process continues until a transplant happens or the patient dies. Under suitable conditions, we show that there exists a control limit optimal policy. We propose a smoothed perturbation analysis (SPA) estimator for the gradient of the total expected discounted reward with respect to the control limit. Moreover, we show that the SPA estimator is asymptotically unbiased.

Problem

• stopping problem
• organ transplantation
• optimal timing
• decision-making
• sensitivity analysis

Innovation

• stopping problem
• control limit policy
• smoothed perturbation analysis
• sensitivity analysis
• organ transplantation