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

Game theoretical analysis of Kidney Exchange Programs

The goal of a kidney exchange program (KEP) is to maximize number of transplants within a pool of incompatible patient-donor pairs by exchanging donors. A KEP can be modelled as a maximum matching problem in a graph. A KEP between incompatible patient-donor from pools of several hospitals, regions or countries has the potential to increase the number of transplants. These entities aim is to maximize the transplant benefit for their patients, which can lead to strategic behaviours. Recently, this was formulated as a non-cooperative two-player game and the game solutions (equilibria) were characterized when the entities objective function is the number of their patients receiving a kidney. In this paper, we generalize these results for $N$-players and discuss the impact in the game solutions when transplant information quality is introduced. Furthermore, the game theory model is analyzed through computational experiments on instances generated through the Canada Kidney Paired Donation Program. These experiments highlighting the importance of using the concept of Nash equilibrium, as well as, the anticipation of the necessity to further research for supporting police makers once measures on transplant quality are available

{MDL4BMF}: Minimum Description Length for Boolean Matrix Factorization

Matrix factorizations—where a given data matrix is approximated by a prod- uct of two or more factor matrices—are powerful data mining tools. Among other tasks, matrix factorizations are often used to separate global structure from noise. This, however, requires solving the ‘model order selection problem’ of determining where fine-grained structure stops, and noise starts, i.e., what is the proper size of the factor matrices. Boolean matrix factorization (BMF)—where data, factors, and matrix product are Boolean—has received increased attention from the data mining community in recent years. The technique has desirable properties, such as high interpretability and natural sparsity. However, so far no method for selecting the correct model order for BMF has been available. In this paper we propose to use the Minimum Description Length (MDL) principle for this task. Besides solving the problem, this well-founded approach has numerous benefits, e.g., it is automatic, does not require a likelihood function, is fast, and, as experiments show, is highly accurate. We formulate the description length function for BMF in general—making it applicable for any BMF algorithm. We discuss how to construct an appropriate encoding, starting from a simple and intuitive approach, we arrive at a highly efficient data-to-model based encoding for BMF. We extend an existing algorithm for BMF to use MDL to identify the best Boolean matrix factorization, analyze the complexity of the problem, and perform an extensive experimental evaluation to study its behavior

Cross-modal and synaesthetic perception in music and vision

This thesis is concerned with the cross-modal and synaesthetic perception of musical and visual stimuli. Each of these types of perception has been researched separately, and a hypothesis is presented here that accounts for both cross-modal matching and the development of synaesthesia. This hypothesis claims that sensory information can be evaluated in another modality by using a scale of comparison in that modality. The first set of experiments examines normal subjects performing cross-modal matching with coloured circles and auditory stimuli that vary in complexity. It is shown that subjects use a variety of scales of comparison from both visual and auditory modalities to form matches. As the stimuli increase in complexity, the individual variation in cross-modal matching also increases. The second set of experiments examines matching performance using higher order stimuli, by having subjects evaluate fragments of melodies and complete melodies on affective and descriptive adjective scales. Melodies were also matched with landscape scenes to examine if subjects could form matches between two highly complex sets of stimuli. The final experiments examine synaesthetic associations with colour, evoked from music, letters, numbers, and other categorical information. Common features of synaesthesia from a population of synaesthetes are identified, and experiments performed to test the interference of the synaesthetic associations. Additional experiments are presented that explore the superior short-term memory of one synaesthete, and the role of his associations as a mnemonic device

Operational research applied to regional healthcare system

In this thesis we focus on optimization and simulation techniques applied to solve strategic, tactical and operational problems rising in the healthcare sector. At first we present three applications to Emilia-Romagna Public Health System (SSR) developed in collaboration with Agenzia Sanitaria e Sociale dell'Emilia-Romagna (ASSR), a regional center for innovation and improvement in health. Agenzia launched a strategic campaign aimed at introducing Operations Research techniques as decision making tools to support technological and organizational innovations. The three applications focus on forecast and fund allocation of medical specialty positions, breast screening program extension and operating theater planning. The case studies exploit the potential of combinatorial optimization, discrete event simulation and system dynamics techniques to solve resource constrained problem arising within Emilia-Romagna territory. We then present an application in collaboration with Dipartimento di Epidemiologia del Lazio that focuses on population demand of service allocation to regional emergency departments. Finally, a simulation-optimization approach, developed in collaboration with INESC TECH center of Porto, to evaluate matching policies for the kidney exchange problem is discussed