Sensitivity analysis for stopping criteria with application to organ transplantations
This work addresses decision-making in organ transplantations for patients, but it is incremental as it applies known methods to a specific domain.
The paper tackles the problem of determining optimal timing for organ transplantation by analyzing a stopping problem, showing that a control limit policy is optimal and proposing a smoothed perturbation analysis estimator for gradient estimation, which is proven to be asymptotically unbiased.
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.