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Sensitivity analysis for stopping criteria with application to organ transplantations

Xingyu Ren, Michael C. Fu, Steven I. Marcus

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.

Sensitivity analysis for stopping criteria with application to organ transplantations

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.

Paper Structure

This paper contains 6 sections, 8 theorems, 42 equations, 1 figure, 1 table.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM SETTING
  3. CONTROL LIMIT POLICY
  4. Smoothed perturbation analysis (SPA) estimator
  5. Simulation example
  6. Summary and future research

Key Result

Lemma 1

The transition kernel $\mathbb{S}$ is strongly continuous, i.e., for every $u\in M_b(\mathcal{S})$, $v(s,a)=\int_{S} u(s')\mathbb{S}(ds'|s,a)$ is continuous and bounded on ${\mathcal{K}}$. $\blacktriangleleft$$\blacktriangleleft$

Figures (1)

  • Figure 1: Simulation results for the sensitivity of the value function $V(\theta)$ and their standard errors (SEs).

Theorems & Definitions (15)

  • Definition 1
  • Lemma 1
  • proof
  • Theorem 1
  • Definition 2
  • Lemma 2
  • Theorem 2
  • Lemma 3
  • proof
  • Theorem 3
  • ...and 5 more