Statistics and Probability Commons^™

Heaped Data In Count Models, Tammy Harris

Theses and Dissertations

Heaped data result when subjects who recall the frequency of events prefer for reporting from a limited set of rounded responses or preferred digits over reporting exact counts. These rounded responses and digit preferences (also referred to as data coarsening) could be characterized by reported frequencies (or counts) favoring multiples of 20, reporting counts ending with 0 or 5, or a preference for reporting an even number over an odd number or vice versa. This mixture of values is a type of measurement error (pattern of misreporting) that can lead to biased estimation and imprecision in discrete quantitative data. Sometimes …

Models And Software Development For Interval-Censored Data, Chun Pan

Theses and Dissertations

Interval-censored time-to-event data occur naturally in studies of diseases where the symptoms are not directly observable, and periodic clinical examinations are required for detection. Due to the lack of well-established procedures, interval-censored data have been conventionally treated as right-censored data, however, this introduces bias at the first place. This dissertation focuses on methodological research and software development for interval-censored data. Specifically, it consists of three projects. The first project is to create an R package for regression analysis and survival curve estimation of interval-censored data based on several published papers by our research team. In the second project, a Bayesian …

The Complete Plus-Minus: A Case Study Of The Columbus Blue Jackets, Nathan Spagnola

Theses and Dissertations

A new hockey statistic termed the Complete Plus-Minus (CPM) was created to calculate the abilities of hockey players in the National Hockey League (NHL). This new statistic was used to analyze the Columbus Blue Jackets for the 2011-2012 season. The CPM for the Blue Jackets was created using two logistic regressions that modeled a goal being scored for and against the Blue Jackets. Whether a goal was scored for or against the team were the responses, while events on the ice were the predictors in the model. It was found that the team's poor performance was due to a weak …

A New Method For The Comparison Of Survival Distributions, Jaymie Shanahan

Theses and Dissertations

The assessment of overall homogeneity of time-to-event curves is a key element in survival analysis in biomedical research. The currently commonly used testing methods, e.g. log-rank test, Wilcoxon test, and Kolmogorov-Smirnov test, may have a significant loss of statistical testing power under certain circumstances. In this thesis we replicate a testing method (Lin & Xu, 2009) that is robust for the comparison of the overall homogeneity of survival curves based on the absolute difference of the area under the survival curves using normal approximation by Greenwood's formula, and propose a new weight component to their test statistic. The weight component …

Protein Identification Using Bayesian Stochastic Search, Christina Nicole Lewis

Theses and Dissertations

Current methods for protein identification in tandem mass spectrometry (MS/MS) involve database searches or de novo peptide sequencing, with database searches being the standard method. With database searches, issues arise when the species is not in the database. Shortcomings of de novo peptide sequencing and database searches include chemical noise, overly complex fragments, and incomplete b and y ion sequences. Here we present a Bayesian approach to identifying peptides. Our model uses prior information about the average relative abundances of bond cleavages and the prior probability of any particular amino acid sequence. The proposed likelihood function is composed of two …

Modeling Mixed Unfolding/Monotone Dichotomous Item Exams, Na Yang

Theses and Dissertations

Item response theory (IRT) is widely applied to analyze educational and psychological assessments. Readily available IRT implementations allow for two common types of models: monotone models used for dominance scales (Guttman 1950; Rasch 1960/1980; Birnbaum 1968; Mokken 1971) and unfolding models used for proximity scales (Coombs, 1964; Andrich, 1996; Roberts, Donoghue and Laughlin, 2000).

When an exam contains items following both types of models, there is currently no method to distinguish the item types, estimate their characteristics, or estimate the examinee characteristics. Thus, there is no existing methodology to simultaneously analyze items like ``At a minimum, I am in favor …

Permutation Testing For Covariance Matrices, With Applications In Shape Analysis, Blake Cassidy Hill

Theses and Dissertations

In many applications, it is of interest to compare covariance structures. In this work, we propose hypothesis tests for comparing covariance matrices for data in different groups, especially in shape analysis. The main motivation for the work is comparing covariance matrices of the size and shapes of damaged versus undamaged DNA molecules. A practical motivation behind analyzing the differences between these DNA covariance matrices is to compare the variation between the two groups during situations where the molecules are repairing. The testing methods proposed in this dissertation consist of three types of permutation testing methods for differences in covariance structures. …

Advanced Methodology Developments In Mixture Cure Models, Chao Cai

Theses and Dissertations

Modern medical treatments have substantially improved cure rates for many chronic diseases and have generated increasing interest in appropriate statistical models to handle survival data with non-negligible cure fractions. The mixture cure models are designed to model such data set, which assume that studied population is a mixture of being cured and uncured. In this dissertation, I will develop two programs named smcure and NPHMC in R. The first program aims to facilitate estimating two popular mixture cure models: the proportional hazards (PH) mixture cure model and accelerated failure time (AFT) mixture cure model. The second program focuses on designing …

Copy Number Variants In Candidate Genes Are Genetic Modifiers Of Hirschsprung Disease, Qian Jiang, Yen Yi Ho, Li Hao, Courtney Nichols Berrios, Aravinda Chakravarti

Faculty Publications

Hirschsprung disease (HSCR) is a neurocristopathy characterized by absence of intramural ganglion cells along variable lengths of the gastrointestinal tract. The HSCR phenotype is highly variable with respect to gender, length of aganglionosis, familiality and the presence of additional anomalies. By molecular genetic analysis, a minimum of 11 neuro-developmental genes (RET, GDNF, NRTN, SOX10, EDNRB, EDN3, ECE1, ZFHX1B, PHOX2B, KIAA1279, TCF4) are known to harbor rare, high-penetrance mutations that confer a large risk to the bearer. In addition, two other genes (RET, NRG1) harbor common, low-penetrance polymorphisms that contribute only partially to risk and can act as genetic modifiers. To …

Dynamic Modeling And Statistical Analysis Of Event Times, Edsel A. Pena

Faculty Publications

This review article provides an overview of recent work in the modeling and analysis of recurrent events arising in engineering, reliability, public health, biomedicine and other areas. Recurrent event modeling possesses unique facets making it different and more difficult to handle than single event settings. For instance, the impact of an increasing number of event occurrences needs to be taken into account, the effects of covariates should be considered, potential association among the interevent times within a unit cannot be ignored, and the effects of performed interventions after each event occurrence need to be factored in. A recent general class …

Sibling Recurrence Risk Ratio Analysis Of The Metabolic Syndrome And Its Components Over Time., Wei J. Chen, Pi Hua Liu, Yen Yi Ho, Kuo Liong Chien, Min Tzu Lo, Wei Liang Shih, Yu Chun Yen, Wen Chung Lee

Faculty Publications

The purpose of this study was to estimate both cross-sectional sibling recurrence risk ratio (lambdas) and lifetime lambdas for the metabolic syndrome and its individual components over time among sibships in the prospectively followed-up cohorts provided by the Genetic Analysis Workshop 13. Five measures included in the operational criteria of the metabolic syndrome by the Adult Treatment Panel III were examined. A method for estimating sibling recurrence risk with correction for complete ascertainment was used to estimate the numerator, and the prevalence in the whole cohort was used as the denominator of lambdas. Considerable variability in the lambdas was found …

Large Deviations For Processes With Independent Increments, James Lynch, Jayaram Sethuraman

Faculty Publications

Let X be a topological space and F denote the Borel σ-field in X. A family of probability measures {Pλ} is said to obey the large deviation principle (LDP) with rate function I(⋅) if Pλ(A) can be suitably approximated by exp{−λinfx∈AI(x)} for appropriate sets A in F. Here the LDP is studied for probability measures induced by stochastic processes with stationary and independent increments which have no Gaussian component. It is assumed that the moment generating function of the increments exists and thus the sample paths of such stochastic processes lie in the space of functions of bounded variation. The …

Some Comments On The Erdos-Renyl Law And A Theorem Of Shepp, James Lynch

Faculty Publications

We show that the finiteness of the moment generating function is necessary for the finiteness of the lim sup of the moving averages considered by Shepp (1964). This also implies that the same must be true for the Erdos-Renyi law of large numbers.

Bayes Estimation Of Reliability For Mixtures Of Life Distributions, William J. Padgett, Chris P. Tsokos

Faculty Publications

No abstract provided.

A Random Differential-Equation Approach To Probability Distribution Of Bod And Do In Streams, William J. Padgett, G Schultz, Chris P. Tsokos

Faculty Publications

No abstract provided.

Stochastic Integro-Differential Equations Of Volterra Type, William J. Padgett, Chris P. Tsokos

Faculty Publications

No abstract provided.