Mathematics
Permanent URI for this communityhttp://hdl.handle.net/1903/2261
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Item Application of Mathematical and Computational Models to Mitigate the Overutilization of Healthcare Systems(2017) Hu, Xia; Golden, Bruce; Barnes, Sean; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The overutilization of the healthcare system has been a significant issue financially and politically, placing burdens on the government, patients, providers and individual payers. In this dissertation, we study how mathematical models and computational models can be utilized to support healthcare decision-making and generate effective interventions for healthcare overcrowding. We focus on applying operations research and data mining methods to mitigate the overutilization of emergency department and inpatient services in four scenarios. Firstly, we systematically review research articles that apply analytical queueing models to the study of the emergency department, with an additional focus on comparing simulation models with queueing models when applied to similar research questions. Secondly, we present an agent-based simulation model of epidemic and bioterrorism transmission, and develop a prediction scheme to differentiate the simulated transmission patterns during the initial stage of the event. Thirdly, we develop a machine learning framework for effectively selecting enrollees for case management based on Medicaid claims data, and demonstrate the importance of enrolling current infrequent users whose utilization of emergency visits might increase significantly in the future. Lastly, we study the role of temporal features in predicting future health outcomes for diabetes patients, and identify the levels to which the aggregation can be most informative.Item Applications of parametric and semi-parametric models for longitudinal data analysis(2014) Talukder, Hisham; Corrada Bravo, Héctor; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A wide range of scientific applications involve analyses of longitudinal data. Whether it is time or location, careful considerations need to be made when applying different statistical tools. One such challenge is to correctly estimate variance components in observed data. In this dissertation, I apply statistical tools to solve problems involving longitudinal data in the field of Biology, Healthcare and Networks. In the second chapter, I apply SSANOVA models to find regions in the genome that have a specific biological trait. We introduce a direct approach of estimating genomic longitudinal data of two different biological groups. Using SSANOVA we then produce a novel method to estimate the difference between the two groups and find regions (location or time) where this difference is biologically significant. In the third chapter, we analyze longitudinal network data using an overdispersed Poisson model. We build a network of musical writers yearly for a 42 year period. Using statistical models, we predict network level topology changes and find covariates that explain these changes. Network level characteristics used for this chapter include average node degree, clustering coefficient and network density. We also build a visualization tool using R-Shiny. The fourth chapter uses data partitioning to study the difference between insured patients and uninsured patients in health outcomes. There is a disparity in health outcomes depending on an individual's type of insurance. The level of risk for an injury is the longitudinal aspect of this dataset. We partition the data into four pre-defined risk categories and evaluate the disparity between insured and uninsured patients using logistic regression models.