Physical Sciences and Mathematics Commons^™

Statistical Inferences For The Youden Index, Haochuan Zhou

Mathematics Dissertations

In diagnostic test studies, one crucial task is to evaluate the diagnostic accuracy of a test. Currently, most studies focus on the Receiver Operating Characteristics Curve and the Area Under the Curve. On the other hand, the Youden index, widely applied in practice, is another comprehensive measurement for the performance of a diagnostic test. For a continuous-scale test classifying diseased and non-diseased groups, finding the Youden index of the test is equivalent to maximize the sum of sensitivity and specificity for all the possible values of the cut-point. This dissertation concentrates on statistical inferences for the Youden index. First, an …

Assessment Of The Sustained Financial Impact Of Risk Engineering Service On Insurance Claims Costs, Bobby I. Parker Mr.

Mathematics Theses

This research paper creates a comprehensive statistical model, relating financial impact of risk engineering activity, and insurance claims costs. Specifically, the model shows important statistical relationships among six variables including: types of risk engineering activity, risk engineering dollar cost, duration of risk engineering service, and type of customer by industry classification, dollar premium amounts, and dollar claims costs.

We accomplish this by using a large data sample of approximately 15,000 customer-years of insurance coverage, and risk engineering activity. Data sample is from an international casualty/property insurance company and covers four years of operations, 2006-2009. The choice of statistical model is …

On The 4 By 4 Irreducible Sign Pattern Matrices That Require Four Distinct Eigenvalues, Paul J. Kim

Mathematics Theses

A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive(respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrix A, the sign pattern class of A, denoted Q(A), is defined as {B: sgn(B) = A}.

An n by n sign pattern matrix A requires all distinct eigenvalues if every real matrix whose sign pattern is represented by A has n distinct eigenvalues. In this thesis, a number of sufficient and/or necessary conditions for a …

Analysis Of Faculty Evaluation By Students As A Reliable Measure Of Faculty Teaching Performance, Etienne Twagirumukiza

Mathematics Theses

Most American universities and colleges require students to provide faculty evaluation at end of each academic term, as a way of measuring faculty teaching performance. Although some analysts think that this kind of evaluation does not necessarily provide a good measurement of teaching effectiveness, there is a growing agreement in the academic world about its reliability. This study attempts to find any strong statistical evidence supporting faculty evaluation by students as a measure of faculty teaching effectiveness. Emphasis will be on analyzing relationships between instructor ratings by students and corresponding students’ grades. Various statistical methods are applied to analyze a …

Discrimination Of High Risk And Low Risk Populations For The Treatment Of Stds, Hui Zhao

Mathematics Theses

It is an important step in clinical practice to discriminate real diseased patients from healthy persons. It would be great to get such discrimination from some common information like personal information, life style, and the contact with diseased patient. In this study, a score is calculated for each patient based on a survey through generalized linear model, and then the diseased status is decided according to previous sexually transmitted diseases (STDs) records. This study will facilitate clinics in grouping patients into real diseased or healthy, which in turn will affect the method clinics take to screen patients: complete screening for …

The Path From Foster Care To Permanence: Does Proximity Outweigh Stability?, Michael Fost

Mathematics Theses

This thesis investigates the relationship between foster care placement settings and discharges. Placement settings are where foster children live: foster homes, group homes, etc. There may be one or several placements for any individual child. In the interest of stability, federal funding to states depends in part on low numbers of placement moves. Federal reviews, however, do not consider whether the placement settings resemble permanent family life (foster homes compared to congregate care) or the direction of placement moves. Competing risks regression was used to analyze time to discharge data of foster children in Georgia. Discharges (competing risks) were compared …

Revisiting The Dimensions Of Residential Segregation, Harry Sharp

Mathematics Theses

The first major work to analyze the dimensions of segregation, done in the late 1980s by Massey and Denton, found five dimensions which explained the phenomenon of segregation. Since the original work was done in 1988 it seems relevant to revisit the issue with new data. Massey and Denton used the technique of factor analysis to identify the latent structure underlying the phenomenon. In this research their methodology is applied to a more complete data set from the 1980 Census to confirm their results and extend the methodology. Due to problems identified during the analysis confirmation was not possible. However, …

Testing An Assumption Of Non-Differential Misclassification In Case-Control Studies, Qin Hui

Mathematics Theses

One of the issues regarding the misclassification in case-control studies is whether the misclassification error rates are the same for both cases and controls. Currently, a common practice is to assume that the rates are the same (“non-differential” assumption). However, it is suspicious that this assumption is valid in many case-control studies. Unfortunately, no test is available so far to test the validity of the assumption of non-differential misclassification when the validation data are not available. We propose the first such method to test the validity of non-differential assumption in a case-control study with 2 × 2 contingency table. First, …

Analysis Of Dependently Truncated Sample Using Inverse Probability Weighted Estimator, Yang Liu

Mathematics Theses

Many statistical methods for truncated data rely on the assumption that the failure and truncation time are independent, which can be unrealistic in applications. The study cohorts obtained from bone marrow transplant (BMT) registry data are commonly recognized as truncated samples, the time-to-failure is truncated by the transplant time. There are clinical evidences that a longer transplant waiting time is a worse prognosis of survivorship. Therefore, it is reasonable to assume the dependence between transplant and failure time. To better analyze BMT registry data, we utilize a Cox analysis in which the transplant time is both a truncation variable and …

Minimum Degree Conditions For Tilings In Graphs And Hypergraphs, Andrew Lightcap

Mathematics Theses

We consider tiling problems for graphs and hypergraphs. For two graphs and , an -tiling of is a subgraph of consisting of only vertex disjoint copies of . By using the absorbing method, we give a short proof that in a balanced tripartite graph , if every vertex is adjacent to of the vertices in each of the other vertex partitions, then has a -tiling. Previously, Magyar and Martin [11] proved the same result (without ) by using the Regularity Lemma.

In a 3-uniform hypergraph , let denote the minimum number of edges that contain for all pairs of vertices. …

Jackknife Empirical Likelihood For The Accelerated Failure Time Model With Censored Data, Maxime K. Bouadoumou

Mathematics Theses

Kendall and Gehan estimating functions are used to estimate the regression parameter in accelerated failure time (AFT) model with censored observations. The accelerated failure time model is the preferred survival analysis method because it maintains a consistent association between the covariate and the survival time. The jackknife empirical likelihood method is used because it overcomes computation difficulty by circumventing the construction of the nonlinear constraint. Jackknife empirical likelihood turns the statistic of interest into a sample mean based on jackknife pseudo-values. U-statistic approach is used to construct the confidence intervals for the regression parameter. We conduct a simulation study …

Prevalence Of Chronic Diseases And Risk Factors For Death Among Elderly Americans, Guangming Han

Mathematics Theses

The main aim of this study is to explore the effects of risk factors contributing to death in the elderly American population. To achieve this purpose, we constructed Cox proportional hazard regression models and logistic regression models with the complex survey dataset from the national Second Longitudinal Study of Aging (LSOA II) to calculate the hazard ratios (HR)/odds ratios (OR) and confidence interval (CI) of risk factors. Our results show that in addition to chronic disease conditions, many risk factors, such as demographic factors (gender and age), social factors (interaction with friends or relatives), personal health behaviors (smoking and exercise), …

Estimation Algorithm For Mixture Of Experts Recurrent Event Model, Timesha U. Brooks

Mathematics Theses

This paper proposes a mixture of experts recurrent events model. This general model accommodates an unobservable frailty variable, intervention effect, influence of accumulating event occurrences, and covariate effects. A latent class variable is utilized to deal with a heterogeneous population and associated covariates. A homogeneous nonparametric baseline hazard and heterogeneous parametric covariate effects are assumed. Maximum likelihood principle is employed to obtain parameter estimates. Since the frailty variable and latent classes are unobserved, an estimation procedure is derived through the EM algorithm. A simulated data set is generated to illustrate the data structure of recurrent events for a heterogeneous population.

Three Topics In Analysis: (I) The Fundamental Theorem Of Calculus Implies That Of Algebra, (Ii) Mini Sums For The Riesz Representing Measure, And (Iii) Holomorphic Domination And Complex Banach Manifolds Similar To Stein Manifolds, Panakkal J. Mathew

Mathematics Dissertations

We look at three distinct topics in analysis. In the first we give a direct and easy proof that the usual Newton-Leibniz rule implies the fundamental theorem of algebra that any nonconstant complex polynomial of one complex variable has a complex root. Next, we look at the Riesz representation theorem and show that the Riesz representing measure often can be given in the form of mini sums just like in the case of the usual Lebesgue measure on a cube. Lastly, we look at the idea of holomorphic domination and use it to define a class of complex Banach manifolds …

Some Topics In Roc Curves Analysis, Xin Huang

Mathematics Dissertations

The receiver operating characteristic (ROC) curves is a popular tool for evaluating continuous diagnostic tests. The traditional definition of ROC curves incorporates implicitly the idea of "hard" thresholding, which also results in the empirical curves being step functions. The first topic is to introduce a novel definition of soft ROC curves, which incorporates the idea of "soft" thresholding. The softness of a soft ROC curve is controlled by a regularization parameter that can be selected suitably by a cross-validation procedure. A byproduct of the soft ROC curves is that the corresponding empirical curves are smooth.

The second topic is on …

Estimation Of Hazard Function For Right Truncated Data, Yong Jiang

Mathematics Theses

This thesis centers on nonparametric inferences of the cumulative hazard function of a right truncated variable. We present three variance estimators for the Nelson-Aalen estimator of the cumulative hazard function and conduct a simulation study to investigate their performances. A close match between the sampling standard deviation and the estimated standard error is observed when an estimated survival probability is not close to 1. However, the problem of poor tail performance exists due to the limitation of the proposed variance estimators. We further analyze an AIDS blood transfusion sample for which the disease latent time is right truncated. We compute …

A Review Of Cross Validation And Adaptive Model Selection, Ali R. Syed

Mathematics Theses

We perform a review of model selection procedures, in particular various cross validation procedures and adaptive model selection. We cover important results for these procedures and explore the connections between different procedures and information criteria.

A New Jackknife Empirical Likelihood Method For U-Statistics, Zhengbo Ma

Mathematics Theses

U-statistics generalizes the concept of mean of independent identically distributed (i.i.d.) random variables and is widely utilized in many estimating and testing problems. The standard empirical likelihood (EL) for U-statistics is computationally expensive because of its onlinear constraint. The jackknife empirical likelihood method largely relieves computation burden by circumventing the construction of the nonlinear constraint. In this thesis, we adopt a new jackknife empirical likelihood method to make inference for the general volume under the ROC surface (VUS), which is one typical kind of U-statistics. Monte Carlo simulations are conducted to show that the EL confidence intervals perform well in …

Stability Selection Of The Number Of Clusters, Gabriella V. Reizer

Mathematics Theses

Selecting the number of clusters is one of the greatest challenges in clustering analysis. In this thesis, we propose a variety of stability selection criteria based on cross validation for determining the number of clusters. Clustering stability measures the agreement of clusterings obtained by applying the same clustering algorithm on multiple independent and identically distributed samples. We propose to measure the clustering stability by the correlation between two clustering functions. These criteria are motivated by the concept of clustering instability proposed by Wang (2010), which is based on a form of clustering distance. In addition, the effectiveness and robustness of …

On The Lebesgue Integral, Jeremiah D. Kastine

Mathematics Theses

We look from a new point of view at the definition and basic properties of the Lebesgue measure and integral on Euclidean spaces, on abstract spaces, and on locally compact Hausdorff spaces. We use mini sums to give all of them a unified treatment that is more efficient than the standard ones. We also give Fubini's theorem a proof that is nicer and uses much lighter technical baggage than the usual treatments.

Racial Disparities Study In Diabetes-Related Complication Using National Health Survey Data, Fengxia Yan

Mathematics Theses

The main aim of this study is to compare the prevalence of diabetes-related complications in white to the prevalence in other racial and ethnic groups in United States using 2009 Behavioral Risk Factor Surveillance System (BRFSS). By constructing the logistic regression model, odds ratios (OR) were calculated to compare the prevalence of diabetes complications in white and other groups. Compared to white, the prevalence of hypertension and stroke in African Americans were higher, while the prevalence of heart attack and coronary heart disease were lower. The Asian Americans or Pacific Islanders, African Americans and Hispanics were more likely to develop …

Empirical Likelihood Confidence Intervals For Roc Curves Under Right Censorship, Hanfang Yang

Mathematics Theses

In this thesis, we apply smoothed empirical likelihood method to investigate confidence intervals for the receiver operating characteristic (ROC) curve with right censoring. As a particular application of comparison of distributions from two populations, the ROC curve is constructed by the combination of cumulative distribution function and quantile function. Under mild conditions, the smoothed empirical likelihood ratio converges to chi-square distribution, which is the well-known Wilks's theorem. Furthermore, the performances of the empirical likelihood method are also illustrated by simulation studies in terms of coverage probability and average length of confidence intervals. Finally, a primary biliary cirrhosis data is used …

Looking In The Crystal Ball: Determinants Of Excess Return, Kokou S. Akolly

Mathematics Theses

This paper investigates the determinants of excess returns using dividend yields as a proxy in a cross-sectional setting. First, we find that types of industry and the current business cycle are determining factors of returns. Second, our results suggest that dividend yield serves a signaling mechanism indicating “healthiness” of a firm among prospective investors. Third we see that there is a positive relationship between dividend yield and risk, especially in the utility and financial sectors. And finally, using actual excess returns, instead of dividend yield in our model shows that all predictors of dividend yield were also significant predictors of …

Cox Model Analysis With The Dependently Left Truncated Data, Ji Li

Mathematics Theses

A truncated sample consists of realizations of a pair of random variables (L, T) subject to the constraint that L ≤T. The major study interest with a truncated sample is to find the marginal distributions of L and T. Many studies have been done with the assumption that L and T are independent. We introduce a new way to specify a Cox model for a truncated sample, assuming that the truncation time is a predictor of T, and this causes the dependence between L and T. We develop an algorithm to obtain the adjusted risk sets and use the Kaplan-Meier …

Weak Primary Decomposition Of Modules Over A Commutative Ring, Harrison Stalvey

Mathematics Theses

This paper presents the theory of weak primary decomposition of modules over a commutative ring. A generalization of the classic well-known theory of primary decomposition, weak primary decomposition is a consequence of the notions of weakly associated prime ideals and nearly nilpotent elements, which were introduced by N. Bourbaki. We begin by discussing basic facts about classic primary decomposition. Then we prove the results on weak primary decomposition, which are parallel to the classic case. Lastly, we define and generalize the Compatibility property of primary decomposition.

Some Contributions In Statistical Discrimination Of Different Pathogens Using Observations Through Ftir, Dongmei Wang

Mathematics Theses

Fourier Transform Infrared (FTIR) has been use to discriminate different pathogens by signals from cells infected with these versus normal cells as references. To do the statistical analysis, Partial Least Square Regression (PLSR) was utilized to distinguish any two kinds of virus‐infected cells and normal cells. Validation using Bootstrap method and Cross‐validations were employed to calculate the shrinkages of Area Under the ROC Curve (AUC) and specificities corresponding to 80%, 90%, and 95% sensitivities. The result shows that our procedure can significantly discriminate these pathogens when we compare infected cells with the normal cells. On the height of this success, …

Theoretical And Numerical Study Of Tikhonov's Regularization And Morozov's Discrepancy Principle, Marygeorge L. Whitney

Mathematics Theses

A concept of a well-posed problem was initially introduced by J. Hadamard in 1923, who expressed the idea that every mathematical model should have a unique solution, stable with respect to noise in the input data. If at least one of those properties is violated, the problem is ill-posed (and unstable). There are numerous examples of ill- posed problems in computational mathematics and applications. Classical numerical algorithms, when used for an ill-posed model, turn out to be divergent. Hence one has to develop special regularization techniques, which take advantage of an a priori information (normally available), in order to solve …

Analyzing Gene Expression Data In Terms Of Gene Sets: Gene Set Enrichment Analysis, Wei Li

Mathematics Theses

The DNA microarray biotechnology simultaneously monitors the expression of thousands of genes and aims to identify genes that are differently expressed under different conditions. From the statistical point of view, it can be restated as identify genes strongly associated with the response or covariant of interest. The Gene Set Enrichment Analysis (GSEA) method is one method which focuses the analysis at the functional related gene sets level instead of single genes. It helps biologists to interpret the DNA microarray data by their previous biological knowledge of the genes in a gene set. GSEA has been shown to efficiently identify gene …

Analysis Of The Total Food Folate Intake Data From The National Health And Nutrition Exa-Amination Survey (Nhanes) Using Generalized Linear Model, Kyung Ah Lee

Mathematics Theses

The National health and nutrition examination survey (NHANES) is a respected nation-wide program in charge of assessing the health and nutritional status of adults and children in United States. Recent cal research found that folic acid play an important role in preventing baby birth defects. In this paper, we use the generalized estimating equation (GEE) method to study the generalized linear model (GLM) with compound symmetric correlation matrix for the NHANES data and investigate significant factors to ence the intake of food folic acid.

Comparative Studies Between Robotic Laparoscopic Myomectomy And Abdominal Myomectomy With Factors Affecting Short-Term Surgical Outcomes, Amy N. Fomo

Mathematics Theses

The purpose of this study is to compare short-term surgical outcomes of robotic and abdominal myomectomy and to analyze the factors affecting the total operative time, estimated blood loss and length of hospital stay from a retrospective study of a consecutive case series of 122 pa-tients with symptomatic leiomyomata. Wilcoxon, t tests, multiple linear and logistic regressions analyses were performed. Patients in abdominal group had larger number of leiomyomata, larger tumor size and BMI. The operative time was longer in robotic group and was affected by the size and number of tumors, parity and interaction between parity and BMI. Estimated …