Designing the Liver Allocation Hierarchy: Incorporating Equity and Uncertainty

Liver transplantation is the only available therapy for any acute or chronic condition resulting in irreversible liver dysfunction. The liver allocation system in the U.S. is administered by the United Network for Organ Sharing (UNOS), a scientific and educational nonprofit organization. The main components of the organ procurement and transplant network are Organ Procurement Organizations (OPOs), which are collections of transplant centers responsible for maintaining local waiting lists, harvesting donated organs and carrying out transplants. Currently in the U.S., OPOs are grouped into 11 regions to facilitate organ allocation, and a three-tier mechanism is utilized that aims to reduce organ preservation time and transport distance to maintain organ quality, while giving sicker patients higher priority. Livers are scarce and perishable resources that rapidly lose viability, which makes their transport distance a crucial factor in transplant outcomes. When a liver becomes available, it is matched with patients on the waiting list according to a complex mechanism that gives priority to patients within the harvesting OPO and region. Transplants at the regional level accounted for more than 50% of all transplants since 2000.This dissertation focuses on the design of regions for liver allocation hierarchy, and includes optimization models that incorporate geographic equity as well as uncertainty throughout the analysis. We employ multi-objective optimization algorithms that involve solving parametric integer programs to balance two possibly conflicting objectives in the system: maximizing efficiency, as measured by the number of viability adjusted transplants, and maximizing geographic equity, as measured by the minimum rate of organ flow into individual OPOs from outside of their own local area. Our results show that efficiency improvements of up to 6% or equity gains of about 70% can be achieved when compared to the current performance of the system by redesigning the regional configuration for the national liver allocation hierarchy.We also introduce a stochastic programming framework to capture the uncertainty of the system by considering scenarios that correspond to different snapshots of the national waiting list and maximize the expected benefit from liver transplants under this stochastic view of the system. We explore many algorithmic and computational strategies including sampling methods, column generation strategies, branching and integer-solution generation procedures, to aid the solution process of the resulting large-scale integer programs. We also explore an OPO-based extension to our two-stage stochastic programming framework that lends itself to more extensive computational testing. The regional configurations obtained using these models are estimated to increase expected life-time gained per transplant operation by up to 7% when compared to the current system.This dissertation also focuses on the general question of designing efficient algorithms that combine column and cut generation to solve large-scale two-stage stochastic linear programs. We introduce a flexible method to combine column generation and the L-shaped method for two-stage stochastic linear programming. We explore the performance of various algorithm designs that employ stabilization subroutines for strengthening both column and cut generation to effectively avoid degeneracy. We study two-stage stochastic versions of the cutting stock and multi-commodity network flow problems to analyze the performances of algorithms in this context

IMPROVING HEALTHCARE DELIVERY: LIVER HEALTH UPDATING AND SURGICAL PATIENT ROUTING

Growing healthcare expenditures in the United States require improved healthcare delivery practices. Organ allocation has been one of the most controversial subjects in healthcare due to the scarcity of donated human organs and various ethical concerns. The design of efficient surgical suites management systems and rural healthcare delivery are long-standing efforts to improve the quality of care. In this dissertation, we consider practical models in both domains with the goal of improving the quality of their services. In the United States, the liver allocation system prioritizes among patients on the waiting list based on the patients' geographical locations and their medical urgency. The prioritization policy within a given geographic area is based on the most recently reported health status of the patients, although blood type compatibility and waiting time on the list are used to break ties. Accordingly, the system imposes a health-status updating scheme, which requires patients to update their health status within a timeframe that depends on their last reported health. However, the patients' ability to update their health status at any time point within this timeframe induces information asymmetry in the system. We study the problem of mitigating this information asymmetry in the liver allocation system. Specifically, we consider a joint patient and societal perspective to determine a set of Pareto-optimal updating schemes that minimize information asymmetry and data-processing burden. This approach combines three methodologies: multi-objective optimization, stochastic programming and Markov decision processes (MDPs). Using the structural properties of our proposed modeling approach, an efficient decomposition algorithm is presented to identify the exact efficient frontier of the Pareto-optimal updating schemes within any given degree of accuracy. Many medical centers offer transportation to eligible patients. However, patients' transportation considerations are often ignored in the scheduling of medical appointments. In this dissertation, we propose an integrated approach that simultaneously considers routing and scheduling decisions of a set of elective outpatient surgery requests in the available operating rooms (ORs) of a hospital. The objective is to minimize the total service cost that incorporates transportation and hospital waiting times for all patients. Focusing on the need of specialty or low-volume hospitals, we propose a computationally tractable model formulated as a set partitioning based problem. We present a branch-and-price algorithm to solve this problem, and discuss several algorithmic strategies to enhance the efficiency of the solution method. An extensive computational test using clinical data demonstrates the efficiency of our proposed solution method. This also shows the value of integrating routing and scheduling decisions, indicating that the healthcare providers can substantially improve the quality of their services under this unified framework

A study on the optimal aircraft location for human organ transportation activities

Abstract The donation-transplant network's complexity lies in the need to reconcile standardized processes and high levels of urgency and uncertainty due to organs' perishability and location. Both punctuality and reliability of air transportation service are crucial to ensure the safe outcome of the transplant. To this scope, an Integer Linear Programming (ILP) model is here proposed to determine the optimal distribution of aircraft in a given set of hubs and under the demand extracted from the Italian transplant database. This is an application of uncapacitated facility location problems, where aircraft are facilities to be located and organ transportation requests represent the demand. Two scenarios (two hubs versus three hubs) are tested under the performance point of view and over different time periods to assess the influence of variations in demand pattern and time period length on the solution

A DATA ANALYTICAL FRAMEWORK FOR IMPROVING REAL-TIME, DECISION SUPPORT SYSTEMS IN HEALTHCARE

In this dissertation we develop a framework that combines data mining, statistics and operations research methods for improving real-time decision support systems in healthcare. Our approach consists of three main concepts: data gathering and preprocessing, modeling, and deployment. We introduce the notion of offline and semi-offline modeling to differentiate between models that are based on known baseline behavior and those based on a baseline with missing information. We apply and illustrate the framework in the context of two important healthcare contexts: biosurveillance and kidney allocation. In the biosurveillance context, we address the problem of early detection of disease outbreaks. We discuss integer programming-based univariate monitoring and statistical and operations research-based multivariate monitoring approaches. We assess method performance on authentic biosurveillance data. In the kidney allocation context, we present a two-phase model that combines an integer programming-based learning phase and a data-analytical based real-time phase. We examine and evaluate our method on the current Organ Procurement and Transplantation Network (OPTN) waiting list. In both contexts, we show that our framework produces significant improvements over existing methods

Analysis of Allocation Rules for Heart Transplantation

In this dissertation, we utilize several mathematical, optimization, and simulation techniques to improve the outcomes of organ transplantation allocation systems. Specifically, in Chapter 1, we build a Monte Carlo simulation model of the heart transplantation system in the United States that can be used to compare the performance of different allocation policies and predict the future of allocation systems. In Chapter 2, we develop a constrained Markov Decision model of the transplant queuing system and investigate optimal allocation rules for heart transplantation in the presence of certain fairness constraints. In Chapter 3, we introduce a new measure of fairness in the organ transplantation queuing systems. We show that this measure helps improve the performance loss of incorporating fairness considerations in organ transplantation systems, and decrease the price of fairness

MARKOV DECISION PROCESS MODELS FOR IMPROVING EQUITY IN LIVER ALLOCATION

In the United States, end-stage liver disease (ESLD) patients are prioritized primarily by their Model for End-stage Liver Disease score (MELD) to receive organ offers. Therefore, patients are required to update their MELD score at predefined frequencies that depend on the patient's last reported score. One aim of this dissertation is to mitigate inequities that stem from patients' flexibility regarding MELD score updates. We develop a Markov decision process (MDP) model to examine the degree to which an individual patient can benefit from the updating flexibility, and provide a menu of updating requirements that balance inequity and data processing more efficiently than the current updating requirements. We also derive sufficient conditions under which a structured optimal updating policy exists. As the coordinator of the harvesting Organ Procurement Organization (OPO) extends offers according to MELD score prioritization, the organ becomes less desirable. To avoid not placing the organ, the OPO coordinator can initiate an expedited placement, i.e., offer the organ to a transplant center, which can then allocate it to any of its patients. A second aim of this dissertation is to mitigate inequities induced by the OPO coordinator's premature departure from the prioritized list of patients via an expedited placement. As a preliminary step to studying the inequity induced by expedited liver placement, we conduct an extensive analysis of the current expedited liver placement practice based on recent data. We investigate different aspects of extending offers, e.g., the number of offers extended concurrently, and patients' response characteristics. Several of the results from this analysis serve as inputs for a second MDP model that examines how many concurrent offers the OPO coordinator should extend and when the coordinator should initiate an expedited placement. Numerical experimentation reveals a structured optimal policy, and we test the sensitivity of the model outcomes with respect to changes in model inputs. Lastly, we examine how our model outputs compare to the analogous measures observed in current practice and how they can be used to improve current practice

An Operations Management Framework to Improve Geographic Equity in Liver Transplantation

In the United States (U.S.), on average three people die every day awaiting a liver transplant for a total of 1,133 lives lost in 2021. While 13,439 patients were added to the waiting list in 2021, only 9,236 patients received liver transplantation. To make matters worse, there is significant geographic disparity across the U.S. in transplant candidate access to deceased donor organs. The U.S. Department of Health and Human Services (HHS) is keen to improve transplant policy to mitigate these disparities. The deceased donor liver allocation policy has been through three major implementations in the last nine years, but yet the issue persists. This dissertation seeks to apply operations management models to (i) understand transplant candidate behavior, and (ii) suggest improvements to transplant policy that mitigate geographic disparity. In the first essay, we focus on reducing disparities in the organ supply to candidate demand (s/d) ratios across transplant centers. We develop a nonlinear integer programming model that allocates organ supply to maximize the minimum s/d ratios across all transplant centers. We focus on circular donation regions that address legal issues raised with earlier organ distribution frameworks. This enables reformulating our model as a set-partitioning problem and our proposal can be viewed as a heterogeneous donor circle policy. Compared to the current Acuity Circles policy that has fixed radius circles around donation locations, the heterogeneous donor circle policy greatly improves both the worst s/d ratio, and the range of s/d ratios. With the fixed radius policy of 500 nautical miles (NM) the s/d ratio ranges from 0.37 to 0.84 at transplant centers, while with the heterogeneous circle policy capped at a maximum radius of 500NM the s/d ratio ranges from 0.55 to 0.60, closely matching the national s/d ratio of 0.5983. Broader sharing of organs is believed to mitigate geographic disparity. Recent policies are moving towards broader sharing in principle. In the second essay, we develop a patient's dynamic choice model to analyze her strategic response to a policy change. First, we study the impact of the Share 35 policy, a variant of broader sharing introduced in 2013, on the behavioral change of patients at the transplant centers (i.e., change in their organ acceptance probability), geographic equity, and efficiency (transplant quality, offer refusals, survival benefit from a transplant, and organ travel distance). We find that sicker patients became more selective in accepting organs (acceptance probability decreased) under the Share 35 policy. Second, we study the current Acuity Circles policy and conclude that it would result in lower efficiency (more offer refusals and a lower transplant benefit) than the previous Share 35 policy. Finally, we show that broader sharing in its current form may not be the best strategy to balance geographic equity and efficiency. The intuition is that by indiscriminately enlarging the pool of supply locations from where patients can receive offers, they tend to become more selective, resulting in more offer rejections and less efficiency. We illustrate that the heterogeneous donor circles policy that equalizes the s/d ratios across geographies is better than Acuity Circles in achieving geographic equity at the lowest trade-off on efficiency metrics. The previous two essays demonstrate the benefit of equalizing the s/d ratios across geographies. In December 2018 the Organ Procurement and Transplantation Network (OPTN) Board of Directors approved the continuous distribution framework as the desired policy goal for all the organ allocation systems. In this framework, the waiting list candidates will be prioritized based on several factors, each contributing some points towards the total score of a candidate. The factors in consideration are medical severity, expected post-transplant outcome, the efficient management of organ placement, and equity. However, the respective weights for each of these potential factors are not yet decided. In the third essay, we consider two factors, medical severity and the efficient management of organ placement (captured using the distance between the donor hospital and transplant center), and we design an allocation policy that maximizes the geographic equity. We develop a mathematical model to calculate the s/d ratio of deceased-donor organs at a transplant center in a continuous scoring framework of organ allocation policy. We then formulate a set-partitioning optimization problem and test our proposals using simulation. Our experiments suggest that reducing inherent differences in s/d ratios at the transplant centers result in saving lives and reduced geographic disparity

Optimizing the Efficiency of the United States Organ Allocation System through Region Reorganization

Allocating organs for transplantation has been controversial in the United States for decades. Two main allocation approaches developed in the past are (1) to allocate organs to patients with higher priority at the same locale; (2) to allocate organs to patients with the greatest medical need regardless of their locations. To balance these two allocation preferences, the U.S. organ transplantation and allocation network has lately implemented a three-tier hierarchical allocation system, dividing the U.S. into 11 regions, composed of 59 Organ Procurement Organizations (OPOs). At present, an procured organ is offered first at the local level, and then regionally and nationally. The purpose of allocating organs at the regional level is to increase the likelihood that a donor-recipient match exists, compared to the former allocation approach, and to increase the quality of the match, compared to the latter approach. However, the question of which regional configuration is the most efficient remains unanswered. This dissertation develops several integer programming models to find the most efficient set of regions. Unlike previous efforts, our model addresses efficient region design for the entire hierarchical system given the existing allocation policy. To measure allocation efficiency, we use the intra-regional transplant cardinality. Two estimates are developed in this dissertation. One is a population-based estimate; the other is an estimate based on the situation where there is only one waiting list nationwide. The latter estimate is a refinement of the former one in that it captures the effect of national-level allocation and heterogeneity of clinical and demographic characteristics among donors and patients. To model national-level allocation, we apply a modeling technique similar to spill-and-recapture in the airline fleet assignment problem. A clinically based simulation model is used in this dissertation to estimate several necessary parameters in the analytic model and to verify the optimal regional configuration obtained from the analytic model. The resulting optimal region design problem is a large-scale set-partitioning problem in whichthere are too many columns to handle explicitly. Given this challenge, we adapt branch and price in this dissertation. We develop a mixed-integer programming pricing problem that is both theoretically and practically hard to solve. To alleviate this existing computational difficulty, we apply geographic decomposition to solve many smaller-scale pricing problems based on pre-specified subsets of OPOs instead of a big pricing problem. When solving each smaller-scale pricing problem, we also generate multiple ``promising' regions that are not necessarily optimal to the pricing problem. In addition, we attempt to develop more efficient solutions for the pricing problem by studying alternative formulations and developing strong valid inequalities. The computational studies in this dissertation use clinical data and show that (1) regional reorganization is beneficial; (2) our branch-and-price application is effective in solving the optimal region design problem

Incentives for Optimal Allocation of HIV Prevention Resources

The thesis consists of three main chapters on optimal incentives for a multi-level allocation process of HIV/AIDS prevention funds. HIV/AIDS prevention funds often traverse several levels of distribution. At each level, equity-based heuristics are often used by decision-makers that may lead to sub-optimal allocation. Mathematical programming models may help to allocate prevention funds optimally. Thus, incentives could be given to decision-makers to encourage optimal allocation. Chapter 4 investigates the impact of incentives by developing a model in which an upper-level decision-maker (UD) allocates funds to a single lower-level decision-maker (LD) who then distributes funds to local programs. The UD makes use of an incentive scheme to encourage a LD to allocate optimally. The results demonstrate that under certain conditions an incentive may help the upper-level to encourage optimal allocation at the lower-level. Chapter 5 extends the model developed in Chapter 4 to incorporate information asymmetry. The information about the total infections prevented per dollar and preferences of the LD regarding equity-based allocation is known at the lower-level, but unknown at the upper-level. We examine conditions when loss of efficiency is higher or zero at the upper-level. Chapter 6 evaluates the impact of two types of incentives between and within the two LDs. The UD sets the level of incentives and then the two LDs sets the fraction of the funds to be reserved for proportional allocation and the amounts allocated to the lower-level programs. We analyze each decision-makers’ behaviour at the equilibrium when either or both incentive schemes are incorporated

Dynamic Decision Models for Managing the Major Complications of Diabetes

Diabetes is the sixth-leading cause of death and a major cause of cardiovascular and renal diseases in the U.S. In this dissertation, we consider the major complications of diabetes and develop dynamic decision models for two important timing problems: Transplantation in prearranged paired kidney exchanges (PKEs) and statin initiation. Transplantation is the most viable renal replacement therapy for end-stage renal disease (ESRD) patients, but there is a severe disparity between the demand and supply of kidneys for transplantation. PKE, a cross-exchange of kidneys between incompatible patient-donor pairs, overcomes many difficulties in matching patients with incompatible donors. In a typical PKE, transplantation surgeries take place simultaneously so that no donor may renege after her intended recipient receives the kidney. We consider two autonomous patients with probabilistically evolving health statuses in a PKE, and model their transplant timing decisions as a discrete-time non-zero-sum stochastic game. We explore necessary and sufficient conditions for patients' decisions to form a stationary-perfect equilibrium, and formulate a mixed-integer linear programming (MIP) representation of equilibrium constraints to characterize a socially optimal stationary-perfect equilibrium. We calibrate our model using large scale clinical data. We quantify the social welfare loss due to patient autonomy and demonstrate that the objective of maximizing the number of transplants may be undesirable. Patients with Type 2 diabetes have higher risk of heart attack and stroke, and if not treated these risks are confounded by lipid abnormalities. Statins can be used to treat such abnormalities, but their use may lead to adverse outcomes. We consider the question of when to initiate statin therapy for patients with Type 2 diabetes. We formulate a Markov decision process (MDP) to maximize the patient's quality-adjusted life years (QALYs) prior to the first heart attack or stroke. We derive sufficient conditions for the optimality of control-limit policies with respect to patient's lipid-ratio (LR) levels and age and parameterize our model using clinical data. We compute the optimal treatment policies and illustrate the importance of individualized treatment factors by comparing their performance to those of the guidelines in use in the U.S