Statistics and Probability Commons^™

Extending The Latent Multinomial Model With Complex Error Processes And Dynamic Markov Bases, Simon J. Bonner, Matthew R. Schofield, Patrik Noren, Steven J. Price

Forestry and Natural Resources Faculty Publications

The latent multinomial model (LMM) of Link et al. [Biometrics 66 (2010) 178–185] provides a framework for modelling mark-recapture data with potential identification errors. Key is a Markov chain Monte Carlo (MCMC) scheme for sampling configurations of the latent counts of the true capture histories that could have generated the observed data. Assuming a linear map between the observed and latent counts, the MCMC algorithm uses vectors from a basis of the kernel to move between configurations of the latent data. Schofield and Bonner [Biometrics 71 (2015) 1070–1080] shows that this is sufficient for some models within the …

Salvage Brachytherapy For Biochemically Recurrent Prostate Cancer Following Primary Brachytherapy, John M. Lacy, William A. Wilson, Raevti Bole, Li Chen, Ali S. Meigooni, Randall G. Rowland, William H. St. Clair

Urology Faculty Publications

Purpose. In this study, we evaluated our experience with salvage brachytherapy after discovery of biochemical recurrence after a prior brachytherapy procedure. Methods and Materials. From 2001 through 2012 twenty-one patients treated by brachytherapy within University of Kentucky or from outside centers developed biochemical failure and had no evidence of metastases. Computed tomography (CT) scans were evaluated; patients who had an underseeded portion of their prostate were considered for reimplantation. Results. The majority of the patients in this study (61.9%) were low risk and median presalvage PSA was 3.49 (range 17.41–1.68). Mean follow-up was 61 months. At last follow-up after reseeding, …

Development In Normal Mixture And Mixture Of Experts Modeling, Meng Qi

Theses and Dissertations--Statistics

In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down’s syndrome. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical mixture model with varying weights, and develops a new data dependent information criterion (sFLIC).We apply our model and criteria to birth- weight and gestational …

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 …

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 …

Aggregated Quantitative Multifactor Dimensionality Reduction, Rebecca E. Crouch

Theses and Dissertations--Statistics

We consider the problem of making predictions for quantitative phenotypes based on gene-to-gene interactions among selected Single Nucleotide Polymorphisms (SNPs). Previously, Quantitative Multifactor Dimensionality Reduction (QMDR) has been applied to detect gene-to-gene interactions associated with elevated quantitative phenotypes, by creating a dichotomous predictor from one interaction which has been deemed optimal. We propose an Aggregated Quantitative Multifactor Dimensionality Reduction (AQMDR), which exhaustively considers all k-way interactions among a set of SNPs and replaces the dichotomous predictor from QMDR with a continuous aggregated score. We evaluate this new AQMDR method in a series of simulations for two-way and three-way interactions, …

Estimated Probability Of Becoming Alcohol Dependent: Extending A Multiparametric Approach, Olga A. Vsevolozhskaya, James C. Anthony

Biostatistics Presentations

Background: United States (US) epidemiological studies suggest that for every 5-8 who start drinking alcoholic beverages, at least one drinker will develop an alcohol dependence (AD) syndrome within the first 10 years after onset of drinking (Lopez-Quintero et al., 2011; Wagner & Anthony, 2002). Recently, we described a multiparametric functional analysis approach for new research to estimate these transition probabilities with a one-dimensional function (1D; Vsevolozhskaya & Anthony, 2015). Here, we demonstrate extension of this analysis to two-dimensional (2D) functions that combine information about number of recent drinking days and number of drinks on the typical drinking day.

Methods: Data …

Abcc9/Sur2 In The Brain: Implications For Hippocampal Sclerosis Of Aging And A Potential Therapeutic Target, Peter T. Nelson, Gregory A. Jicha, Wang-Xia Wang, Eseosa T. Ighodaro, Sergey C. Artiushin, Colin G. Nichols, David W. Fardo

Sanders-Brown Center on Aging Faculty Publications

The ABCC9 gene and its polypeptide product, SUR2, are increasingly implicated in human neurologic disease, including prevalent diseases of the aged brain. SUR2 proteins are a component of the ATP-sensitive potassium (“K _ATP ”) channel, a metabolic sensor for stress and/or hypoxia that has been shown to change in aging. The K _ATP channel also helps regulate the neurovascular unit. Most brain cell types express SUR2, including neurons, astrocytes, oligodendrocytes, microglia, vascular smooth muscle, pericytes, and endothelial cells. Thus it is not surprising that ABCC9 gene variants are associated with risk for human brain diseases. For example, Cantu syndrome is …

Functional Linear Models Extensions Uncover Pleiotropic Effects Of Chronic Pain Phenotypes, Dmitri V. Zaykin, L. Qing, G. D. Slade, R. Dubner, R. B. Fillingim, J. D. Greenspan, R. Ohrbach, W. Maixner, L. B. Diatchenko, Olga A. Vsevolozhskaya

Biostatistics Presentations

Growing scientific evidence suggests that intricate interactions of genetic risk factors with environmental exposures play a major role in the development of chronic pain conditions. In studies of relative contribution of an individual’s genetic composition to the perception of pain, the general characteristics of pain sensitivity are typically measured by a wide range of different, yet possibly etiologically related pain phenotypes. Testing each of these pain-perception traits individually is subject to problems of multiple testing and low statistical power. Furthermore, pain-related traits may share common etiology and comprise binary, categorical, and quantitative measurements. In the current study, we propose a …

Patient-Specific Variations In Biomarkers Across Gingivitis And Periodontitis, Radhakrishnan Nagarajan, Craig S. Miller, Dolph Dawson, Mohanad Al-Sabbagh, J. L. Ebersole

Biostatistics Faculty Publications

This study investigates the use of saliva, as an emerging diagnostic fluid in conjunction with classification techniques to discern biological heterogeneity in clinically labelled gingivitis and periodontitis subjects (80 subjects; 40/group) A battery of classification techniques were investigated as traditional single classifier systems as well as within a novel selective voting ensemble classification approach (SVA) framework. Unlike traditional single classifiers, SVA is shown to reveal patient-specific variations within disease groups, which may be important for identifying proclivity to disease progression or disease stability. Salivary expression profiles of IL-1ß, IL-6, MMP-8, and MIP-1α from 80 patients were analyzed using four classification …

Novel Human Abcc9/Sur2 Brain-Expressed Transcripts And An Eqtl Relevant To Hippocampal Sclerosis Of Aging, Peter T. Nelson, Wang-Xia Wang, Bernard R. Wilfred, Angela Wei, James Dimayuga, Qingwei Huang, Eseosa T. Ighodaro, Sergey C. Artiushin, David W. Fardo

Sanders-Brown Center on Aging Faculty Publications

ABCC9 genetic polymorphisms are associated with increased risk for various human diseases including hippocampal sclerosis of aging. The main goals of this study were 1 > to detect the ABCC9 variants and define the specific 3′ untranslated region (3′UTR) for each variant in human brain, and 2 > to determine whether a polymorphism (rs704180) associated with risk for hippocampal sclerosis of aging pathology is also associated with variation in ABCC9 transcript expression and/or splicing. Rapid amplification of ABCC9 cDNA ends (3′RACE) provided evidence of novel 3′ UTR portions of ABCC9 in human brain. In silico and experimental studies were performed focusing on …

Test On Existence Of Histology Subtype-Specific Prognostic Signatures Among Early Stage Lung Adenocarcinoma And Squamous Cell Carcinoma Patients Using A Cox-Model Based Filter, Suyan Tian, Chi Wang, Ming-Wen An

Biostatistics Faculty Publications

BACKGROUND: Non-small cell lung cancer (NSCLC) is the predominant histological type of lung cancer, accounting for up to 85% of cases. Disease stage is commonly used to determine adjuvant treatment eligibility of NSCLC patients, however, it is an imprecise predictor of the prognosis of an individual patient. Currently, many researchers resort to microarray technology for identifying relevant genetic prognostic markers, with particular attention on trimming or extending a Cox regression model. Adenocarcinoma (AC) and squamous cell carcinoma (SCC) are two major histology subtypes of NSCLC. It has been demonstrated that fundamental differences exist in their underlying mechanisms, which motivated us …

Impact Of Population Stratification On Family-Based Association In An Admixed Population, T. B. Mersha, L. Ding, H. He, E. S. Alexander, X. Zhang, B. G. Kurowski, V. Pilipenko, L. Kottyan, L. J. Martin, David W. Fardo

Biostatistics Faculty Publications

Population substructure is a well-known confounder in population-based case-control genetic studies, but its impact in family-based studies is unclear. We performed population substructure analysis using extended families of admixed population to evaluate power and Type I error in an association study framework. Our analysis shows that power was improved by 1.5% after principal components adjustment. Type I error was also reduced by 2.2% after adjusting for family substratification. The presence of population substructure was underscored by discriminant analysis, in which over 92% of individuals were correctly assigned to their actual family using only 100 principal components. This study demonstrates the …

The Characteristic Imset Polytope Of Bayesian Networks With Ordered Nodes, Jing Xi, Ruriko Yoshida

Statistics Faculty Publications

In 2010, M. Studený, R. Hemmecke, and S. Lindner explored a new algebraic description of graphical models, called characteristic imsets. Compared with standard imsets, characteristic imsets have several advantages: they are still unique vector representatives of conditional independence structures, 0-1 vectors, and more intuitive in terms of graphs than standard imsets. After defining a characteristic imset polytope (cim-polytope) as the convex hull of all characteristic imsets with a given set of nodes, they also showed that a model selection in graphical models, which maximizes a quality criterion, can be converted into a linear programming problem over the cim-polytope. However, in …

Reassessment Of Risk Genotypes (Grn, Tmem106b, And Abcc9 Variants) Associated With Hippocampal Sclerosis Of Aging Pathology, Peter T. Nelson, Wang-Xia Wang, Amanda B. Partch, Sarah E. Monsell, Otto Valladares, Sally R. Ellingson, Bernard R. Wilfred, Adam C. Naj, Li-San Wang, Walter A. Kukull, David W. Fardo

Pathology and Laboratory Medicine Faculty Publications

Hippocampal sclerosis of aging (HS-Aging) is a common high-morbidity neurodegenerative condition in elderly persons. To understand the risk factors for HS-Aging, we analyzed data from the Alzheimer’s Disease Genetics Consortium and correlated the data with clinical and pathologic information from the National Alzheimer’s Coordinating Center database. Overall, 268 research volunteers with HS-Aging and 2,957 controls were included; detailed neuropathologic data were available for all. The study focused on single-nucleotide polymorphisms previously associated with HS-Aging risk: rs5848 ( GRN ), rs1990622 ( TMEM106B ), and rs704180 ( ABCC9 ). Analyses of a subsample that was not previously evaluated (51 HS-Aging cases …

Diffuse Optical Measurements Of Head And Neck Tumor Hemodynamics For Early Prediction Of Chemo-Radiation Therapy Outcomes, Lixin Dong

Theses and Dissertations--Biomedical Engineering

Chemo-radiation therapy is a principal modality for the treatment of head and neck cancers, and its efficacy depends on the interaction of tumor oxygen with free radicals. In this study, we adopted a novel hybrid diffuse optical instrument combining a commercial frequency-domain tissue oximeter (Imagent) and a custom-made diffuse correlation spectroscopy (DCS) flowmeter, which allowed for simultaneous measurements of tumor blood flow and blood oxygenation. Using this hybrid instrument we continually measured tumor hemodynamic responses to chemo-radiation therapy over the treatment period of 7 weeks. We also explored monitoring dynamic tumor hemodynamic changes during radiation delivery. Blood flow data analysis …

Multi-State Models For Interval Censored Data With Competing Risk, Shaoceng Wei

Theses and Dissertations--Statistics

Multi-state models are often used to evaluate the effect of death as a competing event to the development of dementia in a longitudinal study of the cognitive status of elderly subjects. In this dissertation, both multi-state Markov model and semi-Markov model are used to characterize the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient, cognitive states and death as a competing risk.

Firstly, a multi-state Markov model with three transient states: intact cognition, mild cognitive impairment (M.C.I.) and global impairment (G.I.) and one absorbing state: dementia is used to model …

Empirical Likelihood Confidence Band, Shihong Zhu

Theses and Dissertations--Statistics

The confidence band represents an important measure of uncertainty associated with a functional estimator and empirical likelihood method has been proved to be a viable approach to constructing confidence bands in many cases. Using the empirical likelihood ratio principle, this dissertation developed simultaneous confidence bands for many functions of fundamental importance in survival analysis, including the survival function, the difference and ratio of survival functions, the hazards ratio function, and other parameters involving residual lifetimes. Covariate adjustment was incorporated under the proportional hazards assumption. The proposed method can be very useful when, for example, an individualized survival function is desired …

New Results In Ell_1 Penalized Regression, Edward A. Roualdes

Theses and Dissertations--Statistics

Here we consider penalized regression methods, and extend on the results surrounding the l1 norm penalty. We address a more recent development that generalizes previous methods by penalizing a linear transformation of the coefficients of interest instead of penalizing just the coefficients themselves. We introduce an approximate algorithm to fit this generalization and a fully Bayesian hierarchical model that is a direct analogue of the frequentist version. A number of benefits are derived from the Bayesian persepective; most notably choice of the tuning parameter and natural means to estimate the variation of estimates – a notoriously difficult task for the …

Developments In Nonparametric Regression Methods With Application To Raman Spectroscopy Analysis, Jing Guo

Theses and Dissertations--Epidemiology and Biostatistics

Raman spectroscopy has been successfully employed in the classification of breast pathologies involving basis spectra for chemical constituents of breast tissue and resulted in high sensitivity (94%) and specificity (96%) (Haka et al, 2005). Motivated by recent developments in nonparametric regression, in this work, we adapt stacking, boosting, and dynamic ensemble learning into a nonparametric regression framework with application to Raman spectroscopy analysis for breast cancer diagnosis. In Chapter 2, we apply compound estimation (Charnigo and Srinivasan, 2011) in Raman spectra analysis to classify normal, benign, and malignant breast tissue. We explore both the spectra profiles and their derivatives to …

Nonlinear Hierarchical Models For Longitudinal Experimental Infection Studies, Michael David Singleton

Theses and Dissertations--Epidemiology and Biostatistics

Experimental infection (EI) studies, involving the intentional inoculation of animal or human subjects with an infectious agent under controlled conditions, have a long history in infectious disease research. Longitudinal infection response data often arise in EI studies designed to demonstrate vaccine efficacy, explore disease etiology, pathogenesis and transmission, or understand the host immune response to infection. Viral loads, antibody titers, symptom scores and body temperature are a few of the outcome variables commonly studied. Longitudinal EI data are inherently nonlinear, often with single-peaked response trajectories with a common pre- and post-infection baseline. Such data are frequently analyzed with statistical methods …