Stochastic Control for Organ Donations: A Review

Abstract

We review the literature on individual patient organ acceptance decision making by presenting a Markov Decision Process (MDP) model to formulate the organ acceptance decision process as a stochastic control problem. Under the umbrella of the MDP framework, we classify and summarize the major research streams and contributions. In particular, we focus on control limit-type policies, which are shown to be optimal under certain conditions and easy to implement in practice. Finally, we briefly discuss open problems and directions for future research.

Figures (4)

• Figure 1: Assume an optimal policy for an MDP model with ${\mathcal{A}}=\{W,T\}$ is depicted above. Then the corresponding patient-based optimal policy is a control limit policy, but the corresponding organ-based policy is not a control limit policy. For example, for fixed $h_1\in S_H$, action $W$ is specified in two disjoint intervals $[0,k_1]$ and $[k_2,\infty)$.
• Figure 2: For an MDP model with ${\mathcal{A}}=\{W,T\}$, if both patient-based and organ-based control limit optimal policies exist, then there exists an optimal policy such that states for which optimal actions are $W$ and $T$ are contained in two disjoint connected subsets.
• Figure 3: For an MDP model with $|{\mathcal{A}}|= 3$, suppose that its unique optimal policy is depicted above. Both patient-based and organ-based control limit optimal policies exist. However, action $a_3$ is optimal in a disconnected region.
• Figure 5: An example of an AM3R policy that allows ${\mathbb{R}}_+^2$ plane to be partitioned into three connected decision regions.

Theorems & Definitions (8)

• Remark 1
• Remark 2
• Remark 3
• Definition 1
• Definition 2
• Definition 3
• Remark 4
• Remark 5