Sensitivity analysis for stopping criteria with application to organ transplantations

TL;DR

This paper models the decision process for organ transplantation timing, establishing optimal control policies and introducing a novel gradient estimation method for policy optimization.

Contribution

It develops a control limit optimal policy framework and proposes a smoothed perturbation analysis estimator for gradient computation in this context.

Findings

Existence of a control limit optimal policy under certain conditions.

Introduction of a SPA estimator that is asymptotically unbiased.

Application of the model to organ 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.