Physical Sciences and Mathematics Commons^™

Approaches To Detecting And Modeling Over-And Underdispersion In Alternative Count Data Distributions And An Application Of Logistic Regression And Random Forest Modeling To Improve Screening Tools For Tic Disorders In Children, Rebecca C. Wardrop

Theses and Dissertations

This dissertation focuses on theory and application of discrete data methods, particularly approaches to over- and underdispersion relative to the Poisson distribution and an application of random forest and logistic regression modeling. The first chapter derives a score test for over- and underdispersion in the heaped generalized Poisson distribution. Equi-, over-, and underdispersed heaped generalized Poisson and heaped negative binomial data are simulated to evaluate the performance of the score test by comparing the power it achieves to that of Wald and likelihood ratio tests. We find that the score test we derive performs comparably to both the Wald and …

A Bayesian Spatial Scan Statistic For Normal Data, Laasya Velamakanni

Theses and Dissertations

Scan statistics are useful methods for detecting spatial clustering. While they were initially developed to detect regions with an excess of binomial or Poisson events, spatial scan statistics have been extended to detect hotspots in other types of data including continuous data. They have many applications in different fields such as epidemiology (e.g. detecting disease outbreaks), sociology (e.g. detecting crime hotspots), and environmental health (e.g. detecting high-pollution areas). Spatial scan statistics identify a ‘most likely cluster’ and then use a likelihood ratio test to determine if this cluster is statistically significant. Spatial scan statistics have been extended to the Bayesian …

Statistical Methods For Single Cell Sequencing Data Analysis, Fei Qin

Theses and Dissertations

The recent emergence of single cell sequencing (SCS) technology has provided us with single-cell DNA or RNA sequencing (scDNA/RNA-seq) information to investigate cellular evolutionary relationships. Despite many analysis methods have been developed to infer intra-tumor genetic heterogeneity, cluster cellular subclones, detect genetic mutations, and investigate spatially variable (SV) genes, exploring SCS data remains statistically challenging due to its noisy nature.

To identify subclones with scDNA-seq data, many existing studies use an independent statistical model to detect copy number profile in the first step, followed by classical clustering methods for subclone identification in downstream analyses. However, spurious results might be generated …

Moral Injury To Inform Analysis Of Post-Traumatic Stress Disorder, Amanda Julia Manea

Senior Theses

Post-traumatic stress disorder (PTSD) is a mental health condition that almost one out of ten veterans struggle with. Although the National Center for PTSD has made extensive progress in characterizing and developing new treatments for PTSD, most veterans still experience symptoms of PTSD following treatment. Novel avenues of investigation, such as developing algorithms to review electronic health record (EHR) data and better understanding moral injury, are being pursued to address the gap that still exists when it comes to treating veterans. Moral injury is the individual evaluation of exposure to a potentially morally injurious event (PMIE) and can lead to …

That’S My Deity: An Examination Of Online Lokean Cultures Through Log-Linear Modeling, Mary Bernstein

Senior Theses

A rise in online religious communities and the growth of so-called ‘Old World’ religions are reflected in the internet’s subcultures of Neopaganism, a growing religious movement that has been documented in America since the 1960s. The religions under this umbrella movement vary drastically and include belief systems such as Wicca, Druidry, and deity worship. Belief systems under this movement lack the traditional hierarchy found in structured religion and lack a singular sacred text. As such, believers usually find and support one another not through a physical sacred place of meeting, but through an online community that acts as sacred space. …

Advancements In Parametric Modal Regression, Qingyang Liu

Theses and Dissertations

This dissertation considers statistical inference methods for parametric modal regression models. In Chapter 1, we motivate the mode as the measure of central tendency instead of the median or the mean with an example. Following the motivational example, we include an overview of existing modal regression models. Later, in the same chapter, we explain advantages of the parametric modal regression models over existing nonparametric modal regression models. In Chapter 2, we address issues in statistical inference brought in by data contaminated with measurement error. With measurement error in covariates, statistical inference methods designed for modal regression models with error-free covariates …

Modeling The Probability Of A Successful Stolen Base Attempt In Major League Baseball, Cade Stanley

Senior Theses

In Major League Baseball (MLB), the outcome of a stolen base attempt has important implications. Success moves the runner closer to scoring, while failure records an out and removes the runner from the basepaths altogether. Therefore, it is important that the decision by a coach or player to steal a base is well-informed. In this thesis, I explore a statistical approach to making this decision. I train logistic regression and random forest models, using data about the game situation and about the runner, pitcher, and catcher involved in the stolen base attempt, to estimate the probability that a stolen base …

Wernicke's Encephalopathy: Mapping The Risk Factors Throughout The State Of South Carolina, Shannon M. Rychener

Senior Theses

Wernicke’s Encephalopathy is a consistently underrecognized neurodegenerative brain disorder resulting from prolonged thiamine deficiency. Clinical presentation of the disease results from brain lesions attributable to thiamine deficiency. Because these lesions occur in various locations in the cerebral cortex, symptoms can vary significantly. Varied presentation of symptoms, in addition to the lack of a widely accepted biomarker for the disorder cause challenges to clinicians when identifying and diagnosing the disorder. Due to these challenges, healthcare providers must heavily rely on patient history and risk factor prevalence when multiple symptoms of the disorder are present. By mapping the prevalence of the four …

Sparse Partitioned Empirical Bayes Ecm Algorithms For High-Dimensional Linear Mixed Effects And Heteroscedastic Regression, Anja Zgodic

Theses and Dissertations

Variable selection methods in both the frequentist and Bayesian frameworks are powerful techniques that provide prediction and inference in high-dimensional linear regression models. These methods often assume independence between observations and normally distributed errors with the same variance. In practice, these two assumptions are often violated. To mitigate this, we develop efficient and powerful Bayesian approaches for linear mixed modeling and heteroscedastic linear regression. These method offers increased flexibility through the development of empirical Bayes estimators for hyperparameters, with computationally efficient estimation through the Expectation Conditional-Minimization (ECM) algorithm. The novelty of these approaches lies in the partitioning and parameter expansion, …

Quantile Differences In The Age-Related Decline In Cardiorespiratory Fitness Between Sexes In Adults Without Type 2 Diabetes Mellitus In The United States, Andrew Ortaglia, Melissa Stansbury, Michael David Wirth, Xuemei Sui, Matteo Bottai

Faculty Publications

Objective: To comprehensively assess the extent to which the decline in cardiorespiratory fitness (CRF) with age differs between sexes. Participants and Methods: This study used data from the Aerobics Center Longitudinal Study, conducted between September 1974 and August 2006, consisting primarily of White adults from middle-to-upper socioeconomic strata restricted to adults without type 2 diabetes mellitus (33,742 men and 9,415 women). Quantile regression models were used to estimate the differences in age-associated changes in CRF between the sexes, estimated using a maximal treadmill test. Results: For adults aged up to 45 years, significant differences in slopes relating to age and …

Modified Em Algorithm In Smcure Package Based On Proportional Hazards Mixture Cure Model With Offset Terms, Jiaying Yi

Theses and Dissertations

Mixture cure model is a useful method of survival analysis for population including cured proportion and uncured proportion. The R package SMCURE applies EM algorithm to estimate the coefficients of covariates in the mixture cure model. Although an offset term is specified in the SMCURE statement, the offset term is not appropriately handled in the algorithm. This thesis aims to adjust the EM algorithm for the proportional hazards mixture cure model in the SMCURE package. In addition, the offset term can be specified separately in the incidence part or the latency part. The numerical experiments include simulation study and real …

Statistical Methods For Analyzing Dependence Structures With Applications In Single-Cell Experiments, Zhen Yang

Theses and Dissertations

This dissertation focuses on studying methods in dependence structure analysis. In particular, it consists of two topics: (1) modeling dynamic correlation in zero-inflated bivariate count data; and (2) gene co-expression latent factor analysis for cell-type clustering.

In Chapter 2, a zero-inflated negative binomial model for analyzing the dynamic correlation in zero-inflated bivariate count data is proposed. Interactions between biological molecules in a cell are tightly coordinated and often highly dynamic. As a result of these varying signaling activities, changes in gene co-expression patterns could often be observed. The advancements in next-generation sequencing tech-nologies bring new statistical challenges for studying these …

Statistical Methods For Analyzing Multi-Omics Data: Dependence Structure And Missing Values, Wenda Zhang

Theses and Dissertations

The advancements in high-throughput technologies have made it possible to generate a huge number of "omics'' data, including genomics, proteomics, transcriptomics, epigenomics, metabolomics, and microbiomics. Combining multiple data sources and performing joint analyses with all available information and the phenotypic outcome can reflect various aspects in complex biological systems, such as revealing regulation processes, discovering novel associations between biological entities, and identifying relevant biomarkers for certain diseases or phenotypic outcomes. This dissertation focuses on developing statistical models for analyzing multi-omics data. It is comprised of three topics: (1) integrative analysis for multi-omics data with missing observations in intermediate variables; (2) …

Unrestricted Factor Analysis: A Powerful Alternative To Confirmatory Factor Analysis, Jan-Benedict E.M. Steenkamp, Alberto Maydeu-Olivares

Faculty Publications

The gold standard for modeling multiple indicator measurement data is confirmatory factor analysis (CFA), which has many statistical advantages over traditional exploratory factor analysis (EFA). In most CFA applications, items are assumed to be pure indicators of the construct they intend to measure. However, despite our best efforts, this is often not the case. Cross-loadings incorrectly set to zero can only be expressed through the correlations between the factors, leading to biased factor correlations and to biased structural (regression) parameter estimates. This article introduces a third approach, which has emerged in the psychometric literature, viz., unrestricted factor analysis (UFA). UFA …

Food Insecurity And Suicidal Behaviors Among Us High School Students*, Andrea D. Brown, Hilary Seligman, Sarah Silwa, Ellen Barnidge, Kathryn L. Krupsky, Zewiditu Demissie, Angela D. Liese

Faculty Publications

BACKGROUND: Food insecurity (FI) rates in the United States are particularly high among households with children. This research set aims to analyze if high school students experiencing FI had higher risk for mental health and suicidal behaviors.

METHODS: Using combined data from 11 states that conducted the 2017 Youth Risk Behavior Survey, a total of 26,962 and24,051 high school students were used to estimate race/ethnicity and sex-stratified prevalence ratios (PRs) from Poissonregression models. A single-question was used to measure the exposure of FI and outcomes of mental health and suicidalbehaviors.

RESULTS: Overall, 10.8% of students reported FI. Students experiencing FI …

A Comparison Of Inference Methods In High-Dimensional Linear Regression, Imtiaz Ebna Mannan

Theses and Dissertations

Building confidence/credible intervals for the high-dimensional (p >> n) linear models have been the subject of exploration for many years. In this paper, we explore three specific setups. First, we look at the Bayesian paradigm for the LASSO model. A double-exponential prior has been applied to the regression coefficient and from that, a posterior distribution is derived to get the necessary quantiles to calculate the credible intervals for the regression coefficients. Second, we explore the de-sparsified LASSO estimates, and using its asymptotic normality, we calculate the confidence intervals for the model coefficients. Finally, we incorporate an adaptive LASSO model. To …

Simplified Ranking Model For The College Football Playoff Through Weighted Ranking, Edward Buckhouse

Senior Theses

This research project looks to create a better system to rank college football teams in playoff contention. It uses surveys of coaches to create a weighted guideline to evaluate wins and losses for each team. This constructs a value for adjusted wins that is based on coaches’ data but strays away from the inherent bias that any single coach would have when ranking teams. The resulting Top 25 were then compared to the College Football Playoff final regular season rankings to gauge the success of the new system. The Adjusted Wins system that was established properly picked 13 out of …

Predicting Lower Body Soft Tissue Injuries In American Football With Gps Data, Nicholas Tice

Theses and Dissertations

It is of utmost importance to sports organizations that they keep their players as healthy as possible and contributing to the success of the team. Advancements in technology and investments by sports clubs have allowed researchers to better understand the role of load management in high-level athletes to mitigate injury risk. Through GPS tracking data provided by a collaborating Division I American college football team, we seek to predict lower body soft tissue injuries in future training sessions and reduce the number of potentially avoidable injuries within the organization. The difficulty of analyzing the injury data set is that the …

Bayesian Calibration Of The Icrp Zirconium Biokinetic Model And Use Of Canned Priors For The Evaluation Of Bioassay, Thomas Raymond Labone

Theses and Dissertations

The International Commission on Radiological Protection (ICRP) publishes biokinetic models that relate measurements of radioactive material in the body and excreta (bioassay) to the amount of the material taken into the body (intake). Given the intake and the biokinetic model, radiation dose to organs and tissues can be calculated. The ICRP approximates the biokinetics of radioactive materials in the body with compartmental models expressed mathematically as a system of ordinary differential equations, for which they provide point estimates of the rate constants. Inaccurate estimates of intake and radiation dose can result in cases where the biokinetics of an individual differ …

Association Between The Beta Band Neural Response And The Behavioral Performance In Aphasic And Neurologically Intact Individuals, Yilun Zhang

Theses and Dissertations

The complex motor act of speech requires integrating linguistic and sensorimotor processes. Sensorimotor interaction mainly supports speech production in the form of state feedback control architecture. While speaking, subjects react to perturbations in the pitch of voice auditory feedback by changing their tone in the opposite direction to pitch-shift stimuli to compensate for the perceived pitch shift. Aphasia is a communication impairment affecting patients’ speaking, understanding, reading, and writing. The present study aims to examine the association between brain neural activity and the ability for speech auditory feedback error correction in both post-stroke aphasia and neurologically intact individuals. There are …

The Classification Of Basket Neural Cells In The Mammalian Neocortex, Sreya Pudi

Senior Theses

Basket neuronal cells of the mammalian neocortex have been classically categorized into two or more groups. Originally, it was thought that the large and small types are the naturally occurring groups that emerge from reasons that relate to neurobiological function and anatomical position. Later, a study based on anatomical and physiological features of these neurons introduced a third type, the net basket cell which is intermediate in size as compared to the large and small types. In this study, multivariate analysis was used to test the hypothesis that the large and small types are morphologically distinct groups. The results of …

Using Concurrent Functional Regression To Reconstruct River Stage Data During Flood Events And Identify Influential Functional Measurements, Ryan Pittman

Theses and Dissertations

On October 4, 2015, the Cedar Creek gage at Congaree National Park stopped reporting stages, and the readings did not resume until approximately two weeks later because of record-breaking rainfall that led to some of the worst flooding in South Carolina history. Our goal is to reconstruct the Cedar Creek stage during this missing two-week window. The Congaree River gage in Congaree National Park remained functioning throughout the October 2015 flood, when the stage reached its maximum recorded crest. The stages from the two gages are directly related during floods as water travels through the local spillways and flood planes …

Multiple Frailty Model For Spatially Correlated Interval-Censored, Wanfang Zhang

Theses and Dissertations

In this paper, we consider the problem of multiple frailty selection for general interval-censored spatial survival data, which often occurs in clinical trials and epidemiological studies. The general interval-censored data is a mixture of left-, right- and interval-censored data. We propose a Bayesian semiparametric approach based on the Cox proportional hazard model, where monotone splines were used for non-parametrical modeling of the cumulative baseline hazards where the variable selection priors were used for frailty selection. A two-stage data augmentation with Poisson latent variables is developed for efficient computation. The approach is evaluated based a simulation study and illustrated using a …

Marginally Interpretable Models And Multilevel Models For Quantile Regression With Random-Effects, Nahid Sultana Sumi

Theses and Dissertations

The quantile regression model is an active area of statistical research that has received a lot of attention. This complements the most widely used statistical tool, that is, mean regression analysis. Quantile regression analysis It has become more flexible because of its properties that include no assumption on the distribution of the response variable, equivalent to monotone transformations, and robustness to outliers. However, regression analysis offers methodological challenges if the observations are not independent. Cluster, multilevel, and repeated measures (longitudinal data) designs introduce such dependence. The correlation between observations on the same units or clusters should be accounted for to …

Correcting For Measurement Error In The Outcome When Estimating The Distribution Of Time To Pregnancy With The Current Duration Approach, Nicole Nasrallah

Theses and Dissertations

The current duration approach to modeling time-to-pregnancy (TTP) models the length of pregnancy attempt for women that are currently attempting pregnancy. There is a scarcity of studies, let alone TTP studies, that account for measurement error in the outcome. Previously, the benefits of a piecewise constant model with regards to bias in estimates of the survival function with measurement error and the parametric modelling of TTP was shown. In this thesis, correcting for measurement error in the outcome with the current duration approach is explored through piecewise constant models with log-normal measurement error. Five different methods are compared to determine …

Associations Between Fasting Duration, Timing Of First And Last Meal, And Cardiometabolic Endpoints In The National Health And Nutrition Examination Survey, Michael David Wirth, Longgang Zhao, Gabrielle Turner-Mcgrievy, Andrew Ortaglia

Faculty Publications

Background: Research indicates potential cardiometabolic benefits of energy consumption earlier in the day. This study examined the association between fasting duration, timing of first and last meals, and cardiometabolic endpoints using data from the National Health and Nutrition Examination Survey (NHANES). Methods: Cross-sectional data from NHANES (2005–2016) were utilized. Diet was obtained from one to two 24-h dietary recalls to characterize nighttime fasting duration and timing of first and last meal. Blood samples were obtained for characterization of C-reactive protein (CRP); glycosylated hemoglobin (HbA1c %); insulin; glucose; and high-density lipoprotein (HDL), low-density lipoprotein (LDL), and total cholesterol. Survey design procedures …

A Comparison Of Spatial Clustering Assessment Methods, Nadeesha Dilhani Vidanapathirana

Theses and Dissertations

Spatial clustering detection methods are widely used in many fields of research including sociology, epidemiology, ecology, and criminology. The objective of this study is to assess the performance of four spatial clustering detection methods: the average nearest neighbor ratio, Ripley’s K function, local Moran’s I and Getis-Ord Gi* statistics. We conduct a simulation study to evaluate the performance of each method for areal data under different types of spatial dependence and three different areal structures; a 20x20 regular grid, United States counties in six states and Canadian forward sortation areas (FSAs) in three provinces. The results shows that the empirical …

Accurate And Integrative Detection Of Copy Number Variants With High-Throughput Data, Xizhi Luo

Theses and Dissertations

Copy number variation, as a major source of genetic variation in the human genome, are gains or losses of the DNA segments. Copy number variation has gained considerable interest as it plays important roles in human complex diseases. Therefore, accurate detection of CNVs with data generated by modern genotyping technologies, such as SNP array and whole-exome sequencing (WES), comprises a critical step toward a better understanding of disease etiology. However, current statistical methodologies for CNV detection still face analytical challenges due to numerous genetic and technological factors that may lead to spurious findings. First, existing methods assume the independent observations …

Regression Methods For Group Testing Data, Michael Stutz

Theses and Dissertations

Group testing is an efficient method of disease screening, whereby individual specimens (e.g., blood, urine, etc.) are pooled together and tested as a whole for the presence of disease. A common goal is to use data arising from these testing protocols to better understand the relationship between disease status and potential risk factors (e.g., age, symptom status, etc.). Numerous statistical methodologies have been developed for this purpose, most of which are built within the framework of a generalized linear model. Recent authors have suggested the inadequacy of such regression methods to capture the true functional relationships when nonlinear effects are …

Diet Quality And Risk Of Lung Cancer In The Multiethnic Cohort Study, Song-Yi Park, Carol J. Boushey, Yurii B. Shvetsov, Michael David Wirth Msph,Ph.D., Nitin Shivappa Ph.D., James R. Hébert Sc.D., Christopher A. Haiman, Lynee R. Wilkens, Loic Le Marchand

Faculty Publications

Diet quality, assessed by the Healthy Eating Index-2015 (HEI-2015), the Alternative Healthy Eating Index-2010 (AHEI-2010), the alternate Mediterranean Diet (aMED) score, the Dietary Approaches to Stop Hypertension (DASH) score, and the Dietary Inflammatory Index (DII®), was examined in relation to risk of lung cancer in the Multiethnic Cohort Study. The analysis included 179,318 African Americans, Native Hawaiians, Japanese Americans, Latinos, and Whites aged 45–75 years, with 5350 incident lung cancer cases during an average follow-up of 17.5 ± 5.4 years. In multivariable Cox models comprehensively adjusted for cigarette smoking, the hazard ratios (95% confidence intervals) for the highest vs. lowest …