Statistics and Probability Commons^™

Some New And Generalized Distributions Via Exponentiation, Gamma And Marshall-Olkin Generators With Applications, Hameed Abiodun Jimoh

College of Graduate Studies: Theses & Dissertations

Three new generalized distributions developed via completing risk, gamma generator, Marshall-Olkin generator and exponentiation techniques are proposed and studied. Structural properties including quantile functions, hazard rate functions, moment, conditional moments, mean deviations, R\'enyi entropy, distribution of order statistics and maximum likelihood estimates are presented. Monte Carlo simulation is employed to examine the performance of the proposed distributions. Applications of the generalized distributions to real lifetime data are presented to illustrate the usefulness of the models.

Using The Roc Curve To Measure Association And Evaluate Prediction Accuracy For A Binary Outcome, Jingjing Yin, Robert L. Vogel

Biostatistics: Faculty Publications

This review article addresses the ROC curve and its advantage over the odds ratio to measure the association between a continuous variable and a binary outcome. A simple parametric model under the normality assumption and the method of Box-Cox transformation for non-normal data are discussed. Applications of the binormal model and the Box-Cox transformation under both univariate and multivariate inference are illustrated by a comprehensive data analysis tutorial. Finally, a summary and recommendations are given as to the usage of the binormal ROC curve.

Using Ranked Auxiliary Covariate As A More Efficient Sampling Design For Ancova Model: Analysis Of A Psychological Intervention To Buttress Resilience, Rajai Jabrah, Hani Samawi, Robert Vogel, Haresh Rochani, Daniel Linder

Biostatistics: Faculty Publications

Drawing a sample can be costly or time consuming in some studies. However, it may be possible to rank the sampling units according to some baseline auxiliary covariates, which are easily obtainable, and/or cost efficient. Ranked set sampling (RSS) is a method to achieve this goal. In this paper, we propose a modified approach of the RSS method to allocate units into an experimental study that compares L groups. Computer simulation estimates the empirical nominal values and the empirical power values for the test procedure of comparing L different groups using modified RSS based on the regression approach in analysis …

A Markov Decision Process Approach To Adaptive Contact Strategies, Artur Grygorian

College of Graduate Studies: Theses & Dissertations

In the field of survey methodology, optimizing contact strategies helps organizations increase response rates using their allocated budget. Markov Decision Processes (MDP) are widely used to model decision-making strategies in situations where the outcomes have a random component. In this research, we use MDPs and adaptive sampling techniques to construct a strategy that, based on target audience characteristics, suggests the best contact policy. The data we use comes from the First Destination Survey conducted by the Office of Career Services at Georgia Southern University. The constructed model is quite flexible and can be used by other organizations to optimize their …

Quasi-Random Action Selection In Markov Decision Processes, Samuel D. Walker

College of Graduate Studies: Theses & Dissertations

In Markov decision processes an operator exploits known data regarding the environment it inhabits. The information exploited is learned from random exploration of the state-action space. This paper proposes to optimize exploration through the implementation of quasi-random sequences in both discrete and continuous state-action spaces. For the discrete case a permutation is applied to the indices of the action space to avoid repetitive behavior. In the continuous case sequences of low discrepancy, such as Halton sequences, are utilized to disperse the actions more uniformly.

Modeling Volatility Of Financial Time Series Using Arc Length, Benjamin H. Hoerlein

College of Graduate Studies: Theses & Dissertations

This thesis explores how arc length can be modeled and used to measure the risk involved with a financial time series. Having arc length as a measure of volatility can help an investor in sorting which stocks are safer/riskier to invest in. A Gamma autoregressive model of order one(GAR(1)) is proposed to model arc length series. Kernel regression based bias correction is studied when model parameters are estimated using method of moment procedure. As an application, a model-based clustering involving thirty different stocks is presented using k-means++ and hierarchical clustering techniques.

Audio-Based Productivity Forecasting Of Construction Cyclic Activities, Chris A. Sabillon

College of Graduate Studies: Theses & Dissertations

Due to its high cost, project managers must be able to monitor the performance of construction heavy equipment promptly. This cannot be achieved through traditional management techniques, which are based on direct observation or on estimations from historical data. Some manufacturers have started to integrate their proprietary technologies, but construction contractors are unlikely to have a fleet of entirely new and single manufacturer equipment for this to represent a solution. Third party automated approaches include the use of active sensors such as accelerometers and gyroscopes, passive technologies such as computer vision and image processing, and audio signal processing. Hitherto, most …

Evaluating The Efficiency Of Treatment Comparison In Crossover Design By Allocating Subjects Based On Ranked Auxiliary Variable, Yisong Huang, Hani Samawi, Robert Vogel, Jingjing Yin, Worlanyo E. Gato, Daniel Linder

Biostatistics: Faculty Publications

The validity of statistical inference depends on proper randomization methods. However, even with proper randomization, we can have imbalanced with respect to important characteristics. In this paper, we introduce a method based on ranked auxiliary variables for treatment allocation in crossover designs using Latin squares models. We evaluate the improvement of the efficiency in treatment comparisons using the proposed method. Our simulation study reveals that our proposed method provides a more powerful test compared to simple randomization with the same sample size. The proposed method is illustrated by conducting an experiment to compare two different concentrations of titanium dioxide nanofiber …

Estimation Of P(X > Y) When X And Y Are Dependent Random Variables Using Different Bivariate Sampling Schemes, Hani M. Samawi, Amal Helu, Haresh Rochani, Jingjing Yin, Daniel Linder

Biostatistics: Faculty Publications

The stress-strength models have been intensively investigated in the literature in regards of estimating the reliability θ = P (X > Y) using parametric and nonparametric approaches under different sampling schemes when X and Y are independent random variables. In this paper, we consider the problem of estimating θ when (X, Y) are dependent random variables with a bivariate underlying distribution. The empirical and kernel estimates of θ = P (X > Y), based on bivariate ranked set sampling (BVRSS) are considered, when (X, Y) are paired dependent continuous random variables. The estimators obtained are compared to their counterpart, bivariate simple random …

Improved Estimation Of Optimal Cut-Off Point Associated With Youden Index Using Ranked Set Sampling, Jingjing Yin, Hani M. Samawi, Daniel Linder

Biostatistics: Faculty Publications

A diagnostic cut-off point of a biomarker measurement is needed for classifying a random subject to be either diseased or healthy. However, the cut-off point is usually unknown and needs to be estimated by some optimization criteria. One important criterion is the Youden index, which has been widely adopted in practice. The Youden index, which is defined as the maximum of (sensitivity + specificity −1), directly measures the largest total diagnostic accuracy a biomarker can achieve. Therefore, it is desirable to estimate the optimal cut-off point associated with the Youden index. Sometimes, taking the actual measurements of a biomarker is …

A Test Of Symmetry Based On The Kernel Kullback-Leibler Information With Application To Base Deficit Data, Hani M. Samawi, Robert L. Vogel

Biostatistics: Faculty Publications

The assumption of the symmetry of the underlying distribution is important to many statistical inference and modeling procedures. This paper provides a test of symmetry using kernel density estimation and the Kullback-Leibler information. Based on simulation studies, the new test procedure outperforms other tests of symmetry found in the literature, including the Runs Test of Symmetry. We illustrate our new procedure using real data.

Garch(1,1) With Sifted Gamma-Distributed Errors, Alan C. Budd

College of Graduate Studies: Theses & Dissertations

Typical General Autoregressive Conditional Heteroskedastic (GARCH) processes involve normally-distributed errors, and they model strictly-positive error processes poorly. This thesis will present a method for estimating the parameters of a GARCH(1,1) process with shifted Gamma-distributed errors, conduct a simulation study to test the method, and apply the method to real time series data.

Missing Data In Clinical Trial: A Critical Look At The Proportionality Of Mnar And Mar Assumptions For Multiple Imputation, Theophile B. Dipita

College of Graduate Studies: Theses & Dissertations

Randomized control trial is a gold standard of research studies. Randomization helps reduce bias and infer causality. One constraint of these studies is that it depends on participants to obtain the desired data. Whatever the researcher can do, there is a possibility to end up with incomplete data. The problem is more relevant in clinical trials when missing data can be related to the condition under study. The benefits of randomization is compromised by missing data. Multiple imputation is a valid method of treating missing data under the assumption of MAR. Unfortunately this is an unverified assumptions. Current practice advise …

Correction Of Verication Bias Using Log-Linear Models For A Single Binaryscale Diagnostic Tests, Haresh Rochani, Hani M. Samawi, Robert L. Vogel, Jingjing Yin

Biostatistics: Faculty Publications

In diagnostic medicine, the test that determines the true disease status without an error is referred to as the gold standard. Even when a gold standard exists, it is extremely difficult to verify each patient due to the issues of costeffectiveness and invasive nature of the procedures. In practice some of the patients with test results are not selected for verification of the disease status which results in verification bias for diagnostic tests. The ability of the diagnostic test to correctly identify the patients with and without the disease can be evaluated by measures such as sensitivity, specificity and predictive …

Monitoring For Adverse Events Post Marketing Approval Of Drugs, Karl E. Peace, Macaulay Okwuokenye

Biostatistics: Faculty Publications

This brief communication provides information to those developing monitoring plans for serious adverse events (SAE’s) following regulatory approval of a new drug. In addition, we (1) illustrate how many patients would need to be treated in order to have high confidence of seeing at least 1 pre-specified SAE, (2) show that absence of proof of a SAE is not proof of absence of that SAE, and (3) identify statistical methodology that could be used for formal statistical monitoring of SAE’s.

Size And Power Of Tests Of Hypotheses On Survival Parameters From The Lindley Distribution With Covariates, Macaulay Okwuokenye, Karl E. Peace

Biostatistics: Faculty Publications

The Lindley model is considered as an alternative model facilitating analyses of time-to-event data with covariates. Covariate information is incorporated using the Cox’s proportional hazard model with the Lindley model at the timedependent component. Simulation studies are performed to assess the size and power of tests of hypotheses on parameters arising from maximum likelihood estimators of parameters in the Lindley model. Results are contrasted with that arising from Cox’s partial maximum likelihood estimator. The Linley model is used to analyze a publicly available data set and contrasted with other models.

Joint Modeling Of Treatment Effect On Time-To-Event Endpoint And Safety Covariates In Control Clinical Trial Data Analysis, Kao-Tai Tsai, Karl E. Peace

Biostatistics: Faculty Publications

It is a common practice to perform a separate analysis of efficacy and safety data from clinical trials to estimate the benefit and risk aspects of a particular treatment regimen. However, by doing so, one is likely to miss the complete picture of the treatment effect given that these data are generated from the same study subjects and therefore most likely will be correlated. Therefore, it is desirable to analyze these data jointly to obtain a more complete profile of the treatment regimen. A substantial number of statistical methodologies have been proposed in the last decade to model the time-to-event …

Inequalities And Approximations Of Weighted Distributions By Lindley Reliability Measures, And The Lindley-Cox Model With Applications, Broderick O. Oluyede, Macaulay Okwuokenye, Karl E. Peace

Biostatistics: Faculty Publications

In this note, stochastic comparisons and results for weighted and Lindley models are presented. Approximation of weighted distributions via Lindley distribution in the class of increasing failure rate (IFR) and decreasing failure rate (DFR) weighted distributions with monotone weight functions are obtained including approximations via the length-biased Lindley distribution. Some useful bounds and moment-type inequality for weighted life distributions and applications are presented. Incorporation of covariates into Lindley model is considered and an application to illustrate the usefulness and applicability of the proposed Lindley-Cox model is given.

How Long Does That 10-Year Smoke Alarm Really Last? A Survival Analysis Of Smoke Alarms Installed Through The Saife Program In Rural Georgia, Haresh Rochani, Valamar Malika Reagon, Steve Davidson

Biostatistics: Faculty Publications

Background: When functioning properly, a smoke alarm alerts individuals in the residence that smoke is near the alarm. Smoke alarms serve as a primary prevention mechanism to abate morbidity and mortality related to residential fires.

Methods: Using survival analysis, we examined the length of operability of 10-year lithium battery powered smoke alarms installed through the Georgia Public Health/CDC SAIFE program in Moultrie, Georgia. Attempts were made to reach all homes in the city limits. The premise of the study is that geographic clusters (in the case of Moultrie city quadrants) are associated with decreases in the length of time that …

The Sensitivity Of A Test Based On Spearman's Rho In Cross-Correlation Change Point Problems, Congjian Liu

College of Graduate Studies: Theses & Dissertations

In change point problems, there are three main questions that researchers are interested in. First of all, is there a change point or not? Second, when does the change point occur in a time series? Third, how quickly can we detect the change point? In this thesis, we first explain what a change point is, and what a cross-correlation is. We then discuss prior research in this area. Then we discuss and examine a test based on Spearman's rho, introduced by Wied and Dehling (2011), which tests the null hypothesis of no change point, and compare the change point we …

Bayesian Inference Of The Weibull-Pareto Distribution, James Dow

College of Graduate Studies: Theses & Dissertations

The Weibull distribution has many applications in various topics. Some of these topics include survival analysis, reliability engineering, general insurance, electrical engineering, and industrial engineering. The Weibull distribution was further extended by the Weibull-Pareto distribution. A desirable property this distribution has is its shape can skew being able to better model left or right skewed data. Examples of skewed data include human longevity and actuarial data. In this work a hierarchical Bayesian model was developed using the Weibull-Pareto distribution.

A More Efficient Nonparametric Test Of Symmetry Based On Overlapping Coefficient, Hani M. Samawi, Robert L. Vogel

Biostatistics: Faculty Publications

In this paper we provide a more efficient nonparametric test of symmetry based on the empirical overlap coefficient using kernel density estimation applied to an extreme order statistics, namely extreme ranked set sampling. Our simulation investigation reveals that our proposed test of symmetry is at least as powerful as currently available tests of symmetry. Intensive simulation is conducted to examine the power of the proposed test. An illustration is provided using cardiac output and body weight of neonates in a neonatal intensive care unit.

Overview Of Inference About Roc Curve In Medical Diagnosis, Jingjing Yin

Biostatistics: Faculty Publications

Medical diagnosis aims to identify diseased individuals through the evaluation of the measurements of some biomarkers by performing a diagnostic test based on some biomarker measurements. Biomarkers are measured on either discrete or continuous scale and continuous biomarkers are utilized more often in medical practice. This article introduces the most popular tool for evaluating continuous biomarkers: the Receiver Operating Characteristic (ROC) curve.

Lung Flute Improves Symptoms And Health Status In Copd With Chronic Bronchitis: A 26 Week Randomized Controlled Trial, Sanjay Sethi, Jingjing Yin, Pamela K. Anderson

Biostatistics: Faculty Publications

Background: Chronic obstructive pulmonary disease (COPD) is characterized by mucus hypersecretion that contributes to disease related morbidity and is associated with increased mortality. The Lung Flute® is a new respiratory device that produces a low frequency acoustic wave with moderately vigorous exhalation to increase mucus clearance. We hypothesized that the Lung Flute, used on a twice daily basis will provide clinical benefit to patients with COPD with chronic bronchitis.

Methods: We performed a 26 week randomized, non-intervention controlled, single center, open label trial in 69 patients with COPD and Chronic Bronchitis. The primary endpoint was change in respiratory symptoms measured …

A Novel Three Serum Phospholipid Panel Differentiates Normal Individuals From Those With Prostate Cancer, Nima Patel, Robert L. Vogel, Kumar Chandra-Kuntal, Wayne Glasgow, Uddhav Kelavkar

Biostatistics: Faculty Publications

Background: The results of prostate specific antigen (PSA) and digital rectal examination (DRE) screenings lead to both under and over treatment of prostate cancer (PCa). As such, there is an urgent need for the identification and evaluation of new markers for early diagnosis and disease prognosis. Studies have shown a link between PCa, lipids and lipid metabolism. Therefore, the aim of this study was to examine the concentrations and distribution of serum lipids in patients with PCa as compared with serum from controls.

Method: Using Electrospray ionization mass spectrometry (ESI-MS/MS) lipid profiling, we analyzed serum phospholipids from age-matched subjects who …

A Phylogenetic Model For Understanding The Effect Of Gene Duplication On Cancer Progression, Qin Ma, Jaxk H. Reeves, David A. Liberles, Lili Yu, Zheng Chang, Jing Zhao, Juan Cui, Ying Xu, Liang Liu

Biostatistics: Faculty Publications

As biotechnology advances rapidly, a tremendous amount of cancer genetic data has become available, providing an unprecedented opportunity for understanding the genetic mechanisms of cancer. To understand the effects of duplications and deletions on cancer progression, two genomes (normal and tumor) were sequenced from each of five stomach cancer patients in different stages (I, II, III and IV). We developed a phylogenetic model for analyzing stomach cancer data. The model assumes that duplication and deletion occur in accordance with a continuous time Markov Chain along the branches of a phylogenetic tree attached with five extended branches leading to the tumor …

Comparing K Population Means With No Assumption About The Variances, Tony Yaacoub

College of Graduate Studies: Theses & Dissertations

In the analysis of most statistically designed experiments, it is common to assume equal variances along with the assumptions that the sample measurements are independent and normally distributed. Under these three assumptions, a likelihood ratio test is used to test for the difference in population means. Typically, the assumption of independence can be justified based on the sampling method used by the researcher. The likelihood ratio test is robust to the assumption of normality. However, the equality of variances is often difficult to justify. It has been found that the assumption of equal variances cannot be made even after transforming …

Statistical Analysis Of Unreplicated Factorial Designs Using Contrasts, Meixi Yang

College of Graduate Studies: Theses & Dissertations

Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, …

Generalized Weibull And Inverse Weibull Distributions With Applications, Valeriia Sherina

College of Graduate Studies: Theses & Dissertations

In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included …

Generalized Classes Of Distributions With Applications To Income And Lifetime Data, Shujiao Huang

College of Graduate Studies: Theses & Dissertations

In this thesis, new classes of distributions namely: exponentiated Kumaraswamy-Dagum (EKD), Log-exponentiated Kumaraswamy-Dagum (Log-EKD), McDonald Log-logistic (McLLog) and Gamma-Dagum (GD) distributions are presented. A thorough and comprehensive investigation of these classes of distributions is conducted. Mathematical properties of these classes of distributions including series expansion, hazard and reverse hazard functions, moments, generating functions, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics, moments of order statistics and entropies are presented. Estimation of parameters of these distributions via maximum likelihood technique, Fisher information and asymptotic confidence intervals are given. Maximum likelihood estimation of the parameters of the exponentiated …