Physical Sciences and Mathematics Commons^™

Clustering Biological Data With Self-Adjusting High-Dimensional Sieve, Josselyn Gonzalez

Theses and Dissertations

Data classification as a preprocessing technique is a crucial step in the analysis and understanding of numerical data. Cluster analysis, in particular, provides insight into the inherent patterns found in data which makes the interpretation of any follow-up analyses more meaningful. A clustering algorithm groups together data points according to a predefined similarity criterion. This allows the data set to be broken up into segments which, in turn, gives way for a more targeted statistical analysis. Cluster analysis has applications in numerous fields of study and, as a result, countless algorithms have been developed. However, the quantity of options makes …

Adjusting For Mis-Reporting In Count Data, Gelareh Rahimighazikalayeh

Theses and Dissertations

Any counting system is prone to recording errors including underreporting and overreporting. Ignoring the misreporting pattern in count data can give rise to bias in the estimation of model parameters. Accordingly, Poisson, negative binomial and generalized Poisson regression have been expanded in some instances to capture reporting biases. However, to our knowledge, no program has been developed to allow users to apply all of these models when needed. In the first part of the dissertation, we review the available models for underreported counts and develop a Stata command to estimate Poisson, negative binomial and generalized Poisson regression models for underreported …

Examining The Confirmatory Tetrad Analysis (Cta) As A Solution Of The Inadequacy Of Traditional Structural Equation Modeling (Sem) Fit Indices, Hangcheng Liu

Theses and Dissertations

Structural Equation Modeling (SEM) is a framework of statistical methods that allows us to represent complex relationships between variables. SEM is widely used in economics, genetics and the behavioral sciences (e.g. psychology, psychobiology, sociology and medicine). Model complexity is defined as a model’s ability to fit different data patterns and it plays an important role in model selection when applying SEM. As in linear regression, the number of free model parameters is typically used in traditional SEM model fit indices as a measure of the model complexity. However, only using number of free model parameters to indicate SEM model complexity …

Estimation Procedures For Complex Survival Models And Their Applications In Epidemiology Studies, Jie Zhou

Theses and Dissertations

In this dissertation, we aim to address three important questions in practice, which can be solved through complex survival models. The first project focuses on studying the longitudinal fitness effect on cardiovascular disease (CVD) mortality. In the second project, we study the disease-death relation between CVD and all-cause mortality and evaluate important covariate effects on the disease or death transitions. In the third project, we compare antiretroviral treatment (ART) for HIV patients and consider both treatment effect and side effect of the drugs. The first two projects are motivated by the Aerobics Center Longitudinal Study (ACLS) datasets and the third …

Estimating The Respiratory Lung Motion Model Using Tensor Decomposition On Displacement Vector Field, Kingston Kang

Theses and Dissertations

Modern big data often emerge as tensors. Standard statistical methods are inadequate to deal with datasets of large volume, high dimensionality, and complex structure. Therefore, it is important to develop algorithms such as low-rank tensor decomposition for data compression, dimensionality reduction, and approximation.

With the advancement in technology, high-dimensional images are becoming ubiquitous in the medical field. In lung radiation therapy, the respiratory motion of the lung introduces variabilities during treatment as the tumor inside the lung is moving, which brings challenges to the precise delivery of radiation to the tumor. Several approaches to quantifying this uncertainty propose using a …

Penalized Mixed-Effects Ordinal Response Models For High-Dimensional Genomic Data In Twins And Families, Amanda E. Gentry

Theses and Dissertations

The Brisbane Longitudinal Twin Study (BLTS) was being conducted in Australia and was funded by the US National Institute on Drug Abuse (NIDA). Adolescent twins were sampled as a part of this study and surveyed about their substance use as part of the Pathways to Cannabis Use, Abuse and Dependence project. The methods developed in this dissertation were designed for the purpose of analyzing a subset of the Pathways data that includes demographics, cannabis use metrics, personality measures, and imputed genotypes (SNPs) for 493 complete twin pairs (986 subjects.) The primary goal was to determine what combination of SNPs and …

Comparison Of The Performance Of Simple Linear Regression And Quantile Regression With Non-Normal Data: A Simulation Study, Marjorie Howard

Theses and Dissertations

Linear regression is a widely used method for analysis that is well understood across a wide variety of disciplines. In order to use linear regression, a number of assumptions must be met. These assumptions, specifically normality and homoscedasticity of the error distribution can at best be met only approximately with real data. Quantile regression requires fewer assumptions, which offers a potential advantage over linear regression. In this simulation study, we compare the performance of linear (least squares) regression to quantile regression when these assumptions are violated, in order to investigate under what conditions quantile regression becomes the more advantageous method …