A time-dependent stopping problem with application to live organ transplants

Area of Science:

• Operations Research
• Stochastic Processes
• Medical Decision Making

Background:

• Organ transplantation involves complex, time-sensitive decisions regarding offer acceptance.
• The value of organ offers and recipient lifetime are stochastic processes.
• Optimizing transplant allocation requires dynamic decision policies.

Purpose of the Study:

• To develop and analyze a time-dependent stopping problem for live organ transplant decisions.
• To identify optimal control-limit policies that maximize expected rewards.
• To apply the model to real-world kidney transplant data.

Main Methods:

• Formulated a sequential decision problem with time-dependent offer arrivals and recipient lifetimes.
• Analyzed control-limit policies under conditions of increasing failure rate and renewal processes.
• Derived and solved a differential equation for the control-limit function under specific arrival and lifetime distributions.

Main Results:

• Demonstrated that an optimal control-limit policy is a nonincreasing function of time.
• Derived a first-order differential equation governing the control-limit function for non-homogeneous Poisson arrivals.
• Explicitly solved this equation for discrete offers, homogeneous Poisson arrivals, and Gamma lifetime distributions.

Conclusions:

• The developed model provides a framework for optimizing organ transplant allocation strategies.
• The nonincreasing control-limit policy offers a practical approach to maximizing transplant success.
• Numerical analysis using kidney transplant data validates the model's applicability and effectiveness.