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 patient's 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.medical decision making, Markov decision processes, control-limit policy, organ transplantation, liver transplantation, service operations

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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 patientstate-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.

Questions regarding the relative value and frequency of mammography screening for premenopausal women versus postmenopausal women remain open due to the conflicting age-based dynamics of both the disease (increasing incidence, decreasing aggression) and the accuracy of the test results (increasing sensitivity and specificity). To investigate these questions, we formulate a partially observed Markov chain model that captures several of these age-based dynamics not previously considered simultaneously. Using sample-path enumeration, we evaluate a broad range of policies to generate the set of “efficient” policies, as measured by a lifetime breast cancer mortality risk metric and an expected mammogram count, from which a patient may select a policy based on individual circumstance. We demonstrate robustness with respect to small changes in the input data and conclude that, in general, to efficiently achieve a lifetime risk comparable to the current risk among U.S. women, screening should start relatively early in life and continue relatively late in life regardless of the screening interval(s) adopted. The frontier also exhibits interesting patterns with respect to policy type, where policy type is defined by the relationship between the screening interval prescribed in younger years and that prescribed later in life.

Background and objectiveThe composition of human milk varies widely and impacts the ability to meet nutrient requirements for preterm infants. The purpose of this study is to use a large dataset of milk composition from donors to a milk bank to: (1) describe the macronutrient variability in human milk and how it contributes to the ability to meet the protein and calorie targets for the preterm infant using fortification with commercially available multi-nutrient fortifiers; (2) assess how temporal versus subject effects explain macronutrient variability; (3) determine how macronutrient variability contributes to the nutrient distribution in pooled donor milk.MethodsThis is a retrospective, observational study that analyzes the macronutrient data of 1,119 human milk samples from 443 individual donors to a milk bank. We test fortification strategies with potential basic, intermediate, and high protein and calorie commercial fortifiers. Additionally, we simulate the random pooling of multiple donors to model the impact of macronutrient variability on pooled donor milk.ResultsFat was the most variable nutrient and accounted for 80% of the difference in calories. A subject-effect predicted more of the variability after 4 weeks postpartum in all macronutrients (R2 > = 0.50) than a time-effect (R2 < = 0.28). When pooling multiple donors, variability was reduced by increasing the number of donors randomly selected for a pool or targeted pooling based on macronutrient analysis of donor pools. Over 75% of mature milk samples fortified with a basic protein fortifier did not meet daily protein targets of 3.5 g/kg without exceeding volumes of 160 ml/kg/day.ConclusionThere is a strong individual signature to human milk that impacts the pooling of donor milk, and the ability to meet protein and energy requirements for the preterm infant with basic and intermediate protein and calorie fortifiers.

Failure of many engineering systems usually results from a gradual and irreversible accumulation of damage, a degradation process. Most degradation processes can be monitored using sensor technology. The resulting degradation signals are usually correlated with the degradation process. A system is considered to have failed once its degradation signal reaches a prespecified failure threshold. This paper considers a replacement problem for components whose degradation process can be monitored using dedicated sensors. First, we present a stochastic degradation modeling framework that characterizes, in real time, the path of a component's degradation signal. These signals are used to predict the evolution of the component's degradation state. Next, we formulate a single-unit replacement problem as a Markov decision process and utilize the real-time signal observations to determine a replacement policy. We focus on exponentially increasing degradation signals and show that the optimal replacement policy for this class of problems is a monotonically nondecreasing control limit policy. Finally, the model is used to determine an optimal replacement policy by utilizing vibration-based degradation signals from a rotating machinery application.

The only therapy for a patient with end-stage liver disease (ESLD) is liver transplantation, which is performed by using either a cadaveric liver from a deceased donor or a portion of a living-donor's liver. This study addresses the following decision problem for an ESLD patient with an available living donor. Should she have a transplantation now or wait? If she decides to have the transplantation now, should she use her living-donor liver or a cadaveric liver for transplantation? We formulate this problem as a discrete-time, infinite-horizon Markov decision process model and solve it using clinical data. Because living donors are typically related to the recipient, we incorporate a disutility associated with using the living-donor liver as opposed to using a cadaveric liver. We perform a structural analysis of the model, including a set of intuitive conditions that ensure the existence of structured policies such as an at-most-three-region (AM3R) optimal policy. Our computational experiments confirm that the optimal policy is typically of AM3R type.medical decision making, Markov decision processes, control-limit policy, health-care applications, organ transplantation, service operations, optimal stopping, dynamic programming

In the United States, patients with end-stage liver disease must join a waiting list to be eligible for cadaveric liver transplantation. Due to privacy concerns, the details of the composition of this waiting list are not publicly available. This paper considers the benefits associated with creating a more transparent waiting list. We study these benefits by modeling the organ accept/reject decision faced by these patients as a Markov decision process in which the state of the process is described by patient health, quality of the offered liver, and a measure of the rank of the patient in the waiting list. We prove conditions under which there exist structured optimal solutions, such as monotone value functions and control-limit optimal policies. We define the concept of the patient's price of privacy, namely, the number of expected life days lost due to the lack of complete waiting list information. We conduct extensive numerical studies based on clinical data, which indicate that this price of privacy is typically on the order of 5% of the optimal solution value.Subject classifications: dynamic programming/optimal control: applications, Markov; health care: treatment.