Andrew J. Schaefer

The Optimal Timing of Living-Donor Liver Transplantation

Living donors are a significant and increasing source of livers for transplantation, mainly because of the insufficient supply of cadaveric organs. We consider the problem of optimally timing a living-donor liver transplant to maximize the patients total reward, such as quality-adjusted life expectancy. We formulate a Markov decision process (MDP) model in which the state of the process is described by patient health. We derive structural properties of the MDP model, including a set of intuitive conditions that ensure the existence of a control-limit optimal policy. We use clinical data in our computational experiments, which show that the optimal policy is typically of control-limit type.

Airline Crew Scheduling Under Uncertainty

Airline crew scheduling algorithms widely used in practice assume no disruptions. Because disruptions often occur, the actual cost of the resulting crew schedules is often greater. We consider algorithms for finding crew schedules that perform well in practice. The deterministic crew scheduling model is an approximation of crew scheduling under uncertainty with the assumption that all pairings will operate as planned. We seek better approximate solution methods for crew scheduling under uncertainty that still remain tractable. We give computational results from three fleets that indicate that the crew schedules obtained from our method perform better in a model of operations with disruptions than the crew schedules found via deterministic methods. Under mild assumptions we provide a lower bound on the cost of an optimal crew schedule in operations, and we demonstrate that some of the crew schedules found using our method perform very well relative to this lower bound.

A Stochastic Model of Airline Operations

We present a stochastic model of the daily operations of an airline. Its primary purpose is to evaluate plans, such as crew schedules, as well as recovery policies in a random environment. We describe the structure of the stochastic model, sources of disruptions, recovery policies, and performance measures. Then, we describe SimAir--our simulation implementation of the stochastic model, and we give computational results. Finally, we give future directions for the study of airline recovery policies and planning under uncertainty.

Estimating the impact of alcohol consumption on survival for HIV+ individuals.

Abstract Alcohol consumption is associated with decreased antiretroviral adherence, and decreased adherence results in poorer outcomes. However the magnitude of alcohols impact on survival is unknown. Our objective was to use a calibrated and validated simulation of HIV disease to estimate the impact of alcohol on survival. We incorporated clinical data describing the temporal and dose-response relationships between alcohol consumption and adherence in a large observational cohort (N=2,702). Individuals were categorized as nondrinkers (no alcohol consumption), hazardous drinkers (consume ≥5 standard drinks on drinking days), and nonhazardous drinkers (consume <5 standard drinks on drinking days). Our results showed that nonhazardous alcohol consumption decreased survival by more than 1 year if the frequency of consumption was once per week or greater, and by 3.3 years (from 21.7 years to 18.4 years) with daily consumption. Hazardous alcohol consumption decreased overall survival by more than 3 years if frequency of consumption was once per week or greater, and by 6.4 years (From 16.1 years to 9.7 years) with daily consumption. Our results suggest that alcohol is an underappreciated yet modifiable risk factor for poor survival among individuals with HIV.

Markov Decision Processes: A Tool for Sequential Decision Making under Uncertainty

We provide a tutorial on the construction and evaluation of Markov decision processes (MDPs), which are powerful analytical tools used for sequential decision making under uncertainty that have been widely used in many industrial and manufacturing applications but are underutilized in medical decision making (MDM). We demonstrate the use of an MDP to solve a sequential clinical treatment problem under uncertainty. Markov decision processes generalize standard Markov models in that a decision process is embedded in the model and multiple decisions are made over time. Furthermore, they have significant advantages over standard decision analysis. We compare MDPs to standard Markov-based simulation models by solving the problem of the optimal timing of living-donor liver transplantation using both methods. Both models result in the same optimal transplantation policy and the same total life expectancies for the same patient and living donor. The computation time for solving the MDP model is significantly smaller than that for solving the Markov model. We briefly describe the growing literature of MDPs applied to medical decisions.

A Clinically Based Discrete-Event Simulation of End-Stage Liver Disease and the Organ Allocation Process

Background . The optimal allocation of scarce donor livers is a contentious health care issue requiring careful analysis. The objective of this article was to design a biologically based discrete-event simulation to test proposed changes in allocation policies. Methods . The authors used data from multiple sources to simulate end-stage liver disease and the complex allocation system. To validate the model, they compared simulation output with historical data. Results . Simulation outcomes were within 1% to 2% of actual results for measures such as new candidates, donated livers, and transplants by year. The model overestimated the yearly size of the waiting list by 5% in the last year of the simulation and the total number of pretransplant deaths by 10%. Conclusion . The authors created a discrete-event simulation model that represents the biology of end-stage liver disease and the health care organization of transplantation in the United States.

Determining the Acceptance of Cadaveric Livers Using an Implicit Model of the Waiting List

The only available therapy for patients with end-stage liver disease is organ transplantation. In the United States, patients with end-stage liver disease are placed on a waiting list and offered livers based on location and waiting time, as well as current and past health. Although there is a shortage of cadaveric livers, 45% of all cadaveric liver offers are declined by the first transplant surgeon and/or patient to whom they are offered. We consider the decision problem faced by these patients: Should an offered organ of a given quality be accepted or declined? We formulate a Markov decision process model in which the state of the process is described by patient state and organ quality. We use a detailed model of patient health to estimate the parameters of our decision model and implicitly consider the effects of the waiting list through our patient-state-dependent definition of the organ arrival probabilities. We derive structural properties of the model, including a set of intuitive conditions that ensure the existence of control-limit optimal policies. We use clinical data in our computational experiments, which confirm that the optimal policy is typically of control-limit type.

Operating Room Pooling and Parallel Surgery Processing Under Uncertainty

Operating room (OR) scheduling is an important operational problem for most hospitals. In this study, we present a novel two-stage stochastic mixed-integer programming model to minimize total expected operating cost given that scheduling decisions are made before the resolution of uncertainty in surgery durations. We use this model to quantify the benefit of pooling ORs as a shared resource and to illustrate the impact of parallel surgery processing on surgery schedules. Decisions in our model include the number of ORs to open each day, the allocation of surgeries to ORs, the sequence of surgeries within each OR, and the start time for each surgeon. Realistic-sized instances of our model are difficult or impossible to solve with standard stochastic programming techniques. Therefore, we exploit several structural properties of the model to achieve computational advantages. Furthermore, we describe a novel set of widely applicable valid inequalities that make it possible to solve practical instances. Based on our results for different resource usage schemes, we conclude that the impact of parallel surgery processing and the benefit of OR pooling are significant. The latter may lead to total cost reductions between 21% and 59% on average.

The Optimal Time to Initiate HIV Therapy Under Ordered Health States

The question of when to initiate HIV treatment is considered the most important question in HIV care today. Benefits of delaying therapy include avoiding the negative side effects and toxicities associated with the drugs, delaying selective pressures that induce the development of resistant strains of the virus, and preserving a limited number of treatment options. On the other hand, the risks of delayed therapy include the possibility of irreversible damage to the immune system, development of AIDS-related complications, and death. We use Markov decision processes to develop the first HIV optimization models that aim to maximize the expected lifetime or quality-adjusted lifetime of a patient. We prove conditions that establish structural properties of the optimal solution and compare them to our data and results. Model solutions, based on clinical data, support a strategy of treating HIV earlier in its course as opposed to recent trends toward treating it later.

Consequences of cold-ischemia time on primary nonfunction and patient and graft survival in liver transplantation: a meta-analysis.

Introduction The ability to preserve organs prior to transplant is essential to the organ allocation process. Objective The purpose of this study is to describe the functional relationship between cold-ischemia time (CIT) and primary nonfunction (PNF), patient and graft survival in liver transplant. Methods To identify relevant articles Medline, EMBASE and the Cochrane database, including the non-English literature identified in these databases, was searched from 1966 to April 2008. Two independent reviewers screened and extracted the data. CIT was analyzed both as a continuous variable and stratified by clinically relevant intervals. Nondichotomous variables were weighted by sample size. Percent variables were weighted by the inverse of the binomial variance. Results Twenty-six studies met criteria. Functionally, PNF% = −6.678281+0.9134701*CIT Mean+0.1250879*(CIT Mean−9.89535)2−0.0067663*(CIT Mean−9.89535)3, r2 = .625, , p<.0001. Mean patient survival: 93 % (1 month), 88 % (3 months), 83 % (6 months) and 83 % (12 months). Mean graft survival: 85.9 % (1 month), 80.5 % (3 months), 78.1 % (6 months) and 76.8 % (12 months). Maximum patient and graft survival occurred with CITs between 7.5–12.5 hrs at each survival interval. PNF was also significantly correlated with ICU time, % first time grafts and % immunologic mismatches. Conclusion The results of this work imply that CIT may be the most important pre-transplant information needed in the decision to accept an organ.