Statistics and Probability Commons^™

Multi-State Models With Missing Covariates, Wenjie Lou

Theses and Dissertations--Statistics

Multi-state models have been widely used to analyze longitudinal event history data obtained in medical studies. The tools and methods developed recently in this area require the complete observed datasets. While, in many applications measurements on certain components of the covariate vector are missing on some study subjects. In this dissertation, several likelihood-based methodologies were proposed to deal with datasets with different types of missing covariates efficiently when applying multi-state models.

Firstly, a maximum observed data likelihood method was proposed when the data has a univariate missing pattern and the missing covariate is a categorical variable. The construction of the …

Statistical Methods For Handling Intentional Inaccurate Responders, Kristen J. Mcquerry

Theses and Dissertations--Statistics

In self-report data, participants who provide incorrect responses are known as intentional inaccurate responders. This dissertation provides statistical analyses for address intentional inaccurate responses in the data.

Previous work with adolescent self-report, labeled survey participants who intentionally provide inaccurate answers as mischievous responders. This phenomenon also occurs in clinical research. For example, pregnant women who smoke may report that they are nonsmokers. Our advantage is that we do not solely have self-report answers and can verify responses with lab values. Currently, there is no clear method for handling these intentional inaccurate respondents when it comes to making statistical inferences.

We …

Topics In Logistic Regression Analysis, Zhiheng Xie

Theses and Dissertations--Statistics

Discrete-time Markov chains have been used to analyze the transition of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient states, and death as competing risk. A multinomial logistic regression model is used to estimate the probability distribution in each row of the one-step transition matrix that correspond to the transient states. We investigate some goodness of fit tests for a multinomial distribution with covariates to assess the fit of this model to the data. We propose a modified chi-square test statistic and a score test statistic for the multinomial assumption in each …

Developing An Alternative Way To Analyze Nanostring Data, Shu Shen

Theses and Dissertations--Statistics

Nanostring technology provides a new method to measure gene expressions. It's more sensitive than microarrays and able to do more gene measurements than RT-PCR with similar sensitivity. This system produces counts for each target gene and tabulates them. Counts can be normalized by using an Excel macro or nSolver before analysis. Both methods rely on data normalization prior to statistical analysis to identify differentially expressed genes. Alternatively, we propose to model gene expressions as a function of positive controls and reference gene measurements. Simulations and examples are used to compare this model with Nanostring normalization methods. The results show that …

Statistical Inference On Dynamical Systems, Hongyuan Wang

Theses and Dissertations--Statistics

The ordinary differential equation (ODE) is one representative and popular tool in modeling dynamical systems, which are widely implemented in physics, biology, economics, chemistry and biomedical sciences, etc. Because of the importance of dynamical systems in scientific studies, they are the main focuses of my dissertation.

The first chapter of the dissertation is introduction and literature review, which mainly focuses on numerical integration algorithms of ODEs that are difficult to solve analytically, as well as derivative-free optimization algorithms for the so-called inverse problem.

The second chapter is on the estimation method based on numerical solvers of differential equations. We start …

Statistical Methods For Environmental Exposure Data Subject To Detection Limits, Yuchen Yang

Theses and Dissertations--Statistics

In this dissertation, we develop unified and efficient nonparametric statistical methods for estimating and comparing environmental exposure distributions in presence of detection limits. In the first part, we propose a kernel-smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and detection limit. We show that the proposed estimator is consistent and asymptotically normal. Simulation studies demonstrate that the proposed estimator performs well in practical situations. A colon cancer study is provided for illustration. In the second part, we develop a class of test statistics to compare exposure distributions between two groups by using …

Statistical Inference On Trimmed Means, Lorenz Curves, And Partial Area Under Roc Curves By Empirical Likelihood Method, Yumin Zhao

Theses and Dissertations--Statistics

Traditionally the inference on trimmed means, Lorenz Curves, and partial AUC (pAUC) under ROC curves have been done based on the asymptotic normality of the statistics. Based on the theory of empirical likelihood, in this dissertation we developed novel methods to do statistical inferences on trimmed means, Lorenz curves, and pAUC. A common characteristic among trimmed means, Lorenz curves, and pAUC is that their inferences are not based on the whole set of samples. Qin and Tsao (2002), Qin et al. (2013), and Qin et al. (2011) recently published their re- searches on the inferences of trimmed means, Lorenz curves, …

Improved Models For Differential Analysis For Genomic Data, Hong Wang

Theses and Dissertations--Statistics

This paper intend to develop novel statistical methods to improve genomic data analysis, especially for differential analysis. We considered two different data type: NanoString nCounter data and somatic mutation data. For NanoString nCounter data, we develop a novel differential expression detection method. The method considers a generalized linear model of the negative binomial family to characterize count data and allows for multi-factor design. Data normalization is incorporated in the model framework through data normalization parameters, which are estimated from control genes embedded in the nCounter system. For somatic mutation data, we develop beta-binomial model-based approaches to identify highly or lowly …

Evaluating A Bystander Intervention Program On Reproductive Coercion: Using Quasi-Experimental Design Strategies To Address Methodologic Issues In Randomized Community Prevention Trials, Catherine P. Starnes

Theses and Dissertations--Epidemiology and Biostatistics

Community (or cluster) randomized trials are trials in which communities or groups of individuals (clusters) are randomized to receive the intervention of interest. Community randomized trials frequently more closely resemble a natural experiment than a randomized controlled trial (RCT) following intervention allocation. In particular, the effects of non-compliance can pose methodologic challenges in estimating the intervention effect which may require a quasiexperimental approach in order to minimize bias.

The motivating example to illustrate these issues is the Green Dot High School (GDHS) study. The GDHS study was a longitudinal, cluster-randomized controlled trial designed to assess the effectiveness of a bystander …

Existence Of Periodic Solutions For A Quantum Volterra Equation, Muhammad Islam, Jeffrey T. Neugebauer

Mathematics Faculty Publications

The objective of this paper is to study the periodicity properties of functions that arise in quantum calculus, which has been emerging as an important branch of mathematics due to its various applications in physics and other related fields. The paper has two components. First, a relation between two existing periodicity notions is established. Second, the existence of periodic solutions of a q-Volterra integral equation, which is a general integral form of a first order q-difference equation, is obtained. At the end, some examples are provided. These examples show the effectiveness of the relation between the two periodicity notions that …

Positive Solutions For A Singular Fourth Order Nonlocal Boundary Value Problem, John M. Davis, Paul W. Eloe, John R. Graef, Johnny Henderson

Mathematics Faculty Publications

Positive solutions are obtained for the fourth order nonlocal boundary value problem, u⁽⁴⁾=f(x,u), 0 < x < 1, u(0) = u''(0) = u'(1) = u''(1) - u''(2/3)=0, where f(x,u) is singular at x = 0, x=1, y=0, and may be singular at y=∞. The solutions are shown to exist at fixed points for an operator that is decreasing with respect to a cone.

Almost Automorphic Solutions Of Delayed Neutral Dynamic Systems On Hybrid Domains, Murat Adıvar, Halis Can Koyuncuoğlu, Youssef Raffoul

Mathematics Faculty Publications

We study the existence of almost automorphic solutions of the delayed neutral dynamic system on hybrid domains that are additively periodic. We use exponential dichotomy and prove uniqueness of projector of exponential dichotomy to obtain some limit results leading to sufficient conditions for existence of almost automorphic solutions to neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of the coefficient matrices in the system. Hence, we significantly improve the results in the existing literature. Finally, we also provide an existence result for an almost periodic solutions of the system.

Stochastic Models Of Evidence Accumulation In Changing Environments, Alan Veliz-Cuba, Zachary P. Kilpatrick, Krešimir Josić

Mathematics Faculty Publications

Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing world. What effect does such impermanence have on classical results about decision making? To address this question we use sequential analysis to derive a tractable model of evidence accumulation when the correct option changes in time. Our analysis shows that ideal observers discount prior evidence at a rate determined by the volatility of the environment, and the dynamics of evidence accumulation is governed by the information …

Necessary And Sufficient Conditions For Stability Of Volterra Integro-Dynamic Equation Systems On Time Scales, Youssef Raffoul

Mathematics Faculty Publications

In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.

Grief And Gratitude, Lynne Steuerle Schofield

Mathematics & Statistics Faculty Works

No abstract provided.

Semiparametric Regression Analysis Of Panel Count Data And Interval-Censored Failure Time Data, Bin Yao

Theses and Dissertations

This dissertation discusses three important research topics on semiparametric regression analysis of panel count data and interval-censored data. Both types of data arise commonly in real-life studies in many fields such as epidemiology, social science, and medical research. In these studies, subjects are usually examined multiple times at periodical or irregular follow-up examinations. For panel count data, the response variable is the counts of some recurrent events, whose exact occurrence times are usually unknown. For interval-censored data, the response variable is the time to some events of interest, often called survival time or failure time, and the exact response time …

Student Performance In Curricula Centered On Simulation-Based Inference: A Preliminary Report, Beth Chance, Jimmy Wong, Nathan L. Tintle

Faculty Work Comprehensive List

"Simulation-based inference"(e.g., bootstrapping and randomization tests) has been advocated recently with the goal of improving student understanding of statistical inference, as well as the statistical investigative process as a whole. Preliminary assessment data have been largely positive. This article describes the analysis of the first year of data from a multi-institution assessment effort by instructors using such an approach in a college-level introductory statistics course, some for the first time. We examine several pre-/post-measures of student attitudes and conceptual understanding of several topics in the introductory course. We highlight some patterns in the data, focusing on student level and instructor …

Data, Data, Data, Mary Whisner

Librarians' Articles

The legal profession often requires extensive data for everything from simple statistical questions to large-scale empirical research projects. Ms. Whisner discusses some of her favorite sources for finding and evaluating statistics.

Empirical Likelihood And Differentiable Functionals, Zhiyuan Shen

Theses and Dissertations--Statistics

Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. It has been shown by Owen (1988,1990) and many others that empirical likelihood ratio (ELR) method can be used to produce nice confidence intervals or regions. Owen (1988) shows that -2logELR converges to a chi-square distribution with one degree of freedom subject to a linear statistical functional in terms of distribution functions. However, a generalization of Owen's result to the right censored data setting is difficult since no explicit maximization can be obtained under constraint in terms of distribution functions. Pan and Zhou (2002), instead, study the …

Continuous Time Multi-State Models For Interval Censored Data, Lijie Wan

Theses and Dissertations--Statistics

Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models.

Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was …