Physical Sciences and Mathematics Commons^™

Novel Simulation To Avoid Bias In Measurement Of Hyperpolarized Pyruvate: Demonstrated In Phantom And In Vivo, Christopher M. Walker

Dissertations & Theses (Open Access)

Dynamic nuclear polarization creates a transient hyperpolarized nuclear state that can dramatically increase the signal detected by magnetic resonance imaging. This signal increase allows real-time spectroscopic imaging of specific metabolites in vivo by magnetic resonance. Real-time imaging of both the spatial and chemical fate of hyperpolarized metabolites is showing great promise to meaningfully benefit clinical care of cancer patients. Imaging of hyperpolarized agents will have a larger clinical impact if it can function as a quantitative modality upon which clinical decisions can be made. However, quantitative measurement of hyperpolarized agents is currently difficult due to the restrictions imposed by the …

Simulating The Spread Of The Common Cold, R. Corban Harwood

Faculty Publications - Department of Mathematics

This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential equation model, solve that equation, estimate parameter values by hand and through regression, visually evaluate the consistency of the model with their data, and present their results to the class.

The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares

Department of Math & Statistics Faculty Publications

Antimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and sub-optimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study …

Multicollinearity In Regression Analyses Conducted In Epidemiologic Studies, Kristina Vatcheva, Minjae Lee, Joseph B. Mccormick, Mohammad H. Rahbar

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The adverse impact of ignoring multicollinearity on findings and data interpretation in regression analysis is very well documented in the statistical literature. The failure to identify and report multicollinearity could result in misleading interpretations of the results. A review of epidemiological literature in PubMed from January 2004 to December 2013, illustrated the need for a greater attention to identifying and minimizing the effect of multicollinearity in analysis of data from epidemiologic studies. We used simulated datasets and real life data from the Cameron County Hispanic Cohort to demonstrate the adverse effects of multicollinearity in the regression analysis and encourage researchers …

The Effect Of Ignoring Statistical Interactions In Regression Analyses Conducted In Epidemiologic Studies: An Example With Survival Analysis Using Cox Proportional Hazards Regression Model, Kristina Vatcheva, Joseph B. Mccormick, Mohammad H. Rahbar

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Objective: To demonstrate the adverse impact of ignoring statistical interactions in regression models used in epidemiologic studies.

Study design and setting: Based on different scenarios that involved known values for coefficient of the interaction term in Cox regression models we generated 1000 samples of size 600 each. The simulated samples and a real life data set from the Cameron County Hispanic Cohort were used to evaluate the effect of ignoring statistical interactions in these models.

Results: Compared to correctly specified Cox regression models with interaction terms, misspecified models without interaction terms resulted in up to 8.95 fold bias in estimated …