Statistics and Probability Commons^™

Shrinkage Priors For Isotonic Probability Vectors And Binary Data Modeling, Philip S. Boonstra, Daniel R. Owen, Jian Kang

The University of Michigan Department of Biostatistics Working Paper Series

This paper outlines a new class of shrinkage priors for Bayesian isotonic regression modeling a binary outcome against a predictor, where the probability of the outcome is assumed to be monotonically non-decreasing with the predictor. The predictor is categorized into a large number of groups, and the set of differences between outcome probabilities in consecutive categories is equipped with a multivariate prior having support over the set of simplexes. The Dirichlet distribution, which can be derived from a normalized cumulative sum of gamma-distributed random variables, is a natural choice of prior, but using mathematical and simulation-based arguments, we show that …

A Modular Framework For Early-Phase Seamless Oncology Trials, Philip S. Boonstra, Thomas M. Braun, Elizabeth C. Chase

The University of Michigan Department of Biostatistics Working Paper Series

Background: As our understanding of the etiology and mechanisms of cancer becomes more sophisticated and the number of therapeutic options increases, phase I oncology trials today have multiple primary objectives. Many such designs are now 'seamless', meaning that the trial estimates both the maximum tolerated dose and the efficacy at this dose level. Sponsors often proceed with further study only with this additional efficacy evidence. However, with this increasing complexity in trial design, it becomes challenging to articulate fundamental operating characteristics of these trials, such as (i) what is the probability that the design will identify an acceptable, i.e. safe …

Rejoinder On ‘A Selective Overview Of Sparse Sufficient Dimension Reduction’, Lu Li, Xuewong Meggie Wen, Zhou Yu

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Tutorial Of Bland Altman Analysis In A Bayesian Framework, Krissina M. Alari, Steven B. Kim, Jeffrey O. Wand

Mathematics and Statistics Faculty Publications and Presentations

There are two schools of thought in statistical analysis, frequentist, and Bayesian. Though the two approaches produce similar estimations and predictions in large-sample studies, their interpretations are different. Bland Altman analysis is a statistical method that is widely used for comparing two methods of measurement. It was originally proposed under a frequentist framework, and it has not been used under a Bayesian framework despite the growing popularity of Bayesian analysis. It seems that the mathematical and computational complexity narrows access to Bayesian Bland Altman analysis. In this article, we provide a tutorial of Bayesian Bland Altman analysis. One approach we …

A Bivariate Life Distribution And Notions Of Negative Dependence, Prajamitra Bhuyan, Shyamal Ghosh, Priyanka Majumder, Murari Mitra

Journal Articles

Bivariate life distributions used to model negative dependence typically possess certain limitations; in particular, the correlation coefficient takes values in a restricted subrange of (Formula presented.). We construct a new bivariate life distribution to remedy this. Properties of the proposed distribution are studied. It is shown that the distribution satisfies most of the popular notions of negative dependence prevalent in the literature. Stress–strength reliability bounds are obtained, and parameter estimation methodology has been discussed. Performance of the estimators are compared through a simulation study.

Existence And Multiplicity Of Weak Solutions For A Neumann Elliptic Problem With -Laplacian, Martin Bohner, Giuseppe Caristi, Fariba Gharehgazlouei, Shapour Heidarkhani

Mathematics and Statistics Faculty Research & Creative Works

We are interested in the existence of multiple weak solutions for the Neumann elliptic problem involving the anisotropic -Laplacian operator, on a bounded domain with smooth boundary. We work on the anisotropic variable exponent Sobolev space, and by using a consequence of the local minimum theorem due to Bonanno, we establish existence of at least one weak solution under algebraic conditions on the nonlinear term. Also, we discuss existence of at least two weak solutions for the problem, under algebraic conditions including the classical Ambrosetti-Rabinowitz condition on the nonlinear term. Furthermore, by employing a three critical point theorem due to …

First Past The Poll: A Blog About Political Statistics, Bradley Wascher

Mahurin Honors College Capstone Experience/Thesis Projects

This Capstone Experience project details my efforts to become a political data journalist. I took the first major step in August 2018, starting First Past the Poll, my politics blog. For three semesters, this website was frequently updated with nonpartisan reports on the latest elections, deep dives on long-term polling trends, and commentary on political numbers more broadly. Hoping to buck the trend of the stodgy prose prevalent throughout politics, my stories combined academic rigor with accessible writing.

As I began to find my footing in the field, First Past the Poll put me in the position to become …

How 6-12th Grade Staff Support Students With Depression: A Pilot Study To Develop Measures Of Implicit Associations, Explicit Attitudes And Helping Behavior, Paul M. Thompson

Electronic Theses and Dissertations

Students with emotional disabilities are disproportionately suspended and expelled in K-12 schools. Attribution theory suggests individuals are less likely to provide assistance to others if they believe the individuals are responsible for their own difficulties. To test attribution theory, this study created new measures of explicit attitudes and implicit associations of licensed 6-12th grade staff regarding students with depression as well as a helping behavior measure of staff toward students with depression. The survey was distributed within a single school district in the western United States. A majority of the sample (N = 52) held a mental health license (60%), …

After-Hours Incentives And Emergency Department Visits: Evidence From Ontario Forthcoming At Canadian Public Policy, Rose Anne Devlin, Koffi Ahoto Kpelitse, Lihua Li, Nirav Mehta, Sisira Sarma

Epidemiology and Biostatistics Publications

No abstract provided.

Evaluating The Effectiveness Of Aquatic Therapy On Mobility, Balance, And Level Of Functional Independence In Stroke Rehabilitation: A Systematic Review And Meta-Analysis., Alice Mary Iliescu, Amanda Mcintyre, Joshua C. Wiener, Jerome Iruthayarajah, Andrea Lee, Sarah Caughlin, Robert Teasell

Epidemiology and Biostatistics Publications

OBJECTIVE: To meta-analyze and systematically review the effectiveness of aquatic therapy in improving mobility, balance, and functional independence after stroke.

DATA SOURCES: Articles published in Medline, Embase, CINAHL, PsycINFO, and Scopus up to 20 August 2019.

STUDY SELECTION: Studies met the following inclusion criteria: (1) English, (2) adult stroke population, (3) randomized or non-randomized prospectively controlled trial (RCT or PCT, respectively) study design, (4) the experimental group received >1 session of aquatic therapy, and (5) included a clinical outcome measure of mobility, balance, or functional independence.

DATA EXTRACTION: Participant characteristics, treatment protocols, between-group outcomes, point measures, and measures of variability …

An Analysis Of The Success Of Farmers Markets In Kentucky Using Logistic Regression And Support Vector Machines, Jeron Russell

Mahurin Honors College Capstone Experience/Thesis Projects

The purpose of this research is to look at the relationship that market-specific, economic, and demographic variables have with the success of farmers markets in Kentucky. It additionally seeks to build a tool for predicting farmers market success that could be used by policy makers to aid in decision-making processes concerning farmers markets. Logistic regression and Support Vector Machines (SVMs) are used on data acquired from the Kentucky Department of Agriculture and the American Community Survey in order to analyze the data in a traditional statistical approach as well as a machine learning approach. The results included an SVM model …

Causal Effect Random Forest Of Interaction Trees For Learning Individualized Treatment Regimes In Observational Studies: With Applications To Education Study Data, Luo Li

CGU Theses & Dissertations

Learning individualized treatment regimes (ITR) using observational data holds great interest in various fields, as treatment recommendations based on individual characteristics may improve individual treatment benefits with a reduced cost. It has long been observed that different individuals may respond to a certain treatment with significant heterogeneity. ITR can be defined as a mapping between individual characteristics to a treatment assignment. The optimal ITR is the treatment assignment that maximizes expected individual treatment effects. Rooted from personalized medicine, many studies and applications of ITR are in medical fields and clinical practice. Heterogeneous responses are also well documented in educational interventions. …

A Multinational Study Of The Etiology And Clinical Teleology Of Moral Evaluations Of Patient Behaviors, Anna Yu Lee

CGU Theses & Dissertations

This dissertation is a collection of four studies which collectively explore a hypothesized construct of ‘moral evaluation of patient behaviors’ (MEPB) as a driver of health professionals’ readiness to interact humanistically with their patients. In these studies, ‘humanistic interactions’ refer to the non-technical, intangible skills and factors of clinical competence; the factors specifically explored in these studies were compassion toward patients, self-efficacy for treating patients, and optimism toward patient treatment. For the purpose of specificity, all factors were examined as they pertained to patients with substance use disorders. Survey data from a convenience sample of 524 health professionals (i.e. physicians, …

Nutrition And Health Status Of Hemodialysis Patients In Dhaka, Bangladesh, Tanjina Rahman

Wayne State University Dissertations

Methods to identify patients at risk for End stage renal disease (ESRD) are a high priority in Bangladesh, where kidney transplants/dialysis options are limited and costly. Every year, 35,000 to 40,000 people reach ESRD in Bangladesh, but currently available facilities can hardly accommodate only 9000 to 10,000 new patients with twice weekly dialysis and the remaining 66% have no access to any kind of renal replacement therapy (RRT) in the form of dialysis or transplantation. Nutrition is an important factor in maintaining good health of hemodialysis patients. However, data on nutritional status of Bangladeshi dialysis patients is limited and is …

Theory Of Principal Components For Applications In Exploratory Crime Analysis And Clustering, Daniel Silva

All Graduate Theses, Dissertations, and Other Capstone Projects

The purpose of this paper is to develop the theory of principal components analysis succinctly from the fundamentals of matrix algebra and multivariate statistics. Principal components analysis is sometimes used as a descriptive technique to explain the variance-covariance or correlation structure of a dataset. However, most often, it is used as a dimensionality reduction technique to visualize a high dimensional dataset in a lower dimensional space. Principal components analysis accomplishes this by using the first few principal components, provided that they account for a substantial proportion of variation in the original dataset. In the same way, the first few principal …

Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown

Murray State Theses and Dissertations

Data and algorithmic modeling are two different approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classification and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to find the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in different cases depending on the data set. In our case, the data …

Predictors Of Colorectal Cancer Screening Among Maryland Adults, Aged 50–75 Years, Pamela Manwi Asangong

Walden Dissertations and Doctoral Studies

Screening plays an essential role in reducing colorectal cancer (CRC) incidence and mortality rates, yet CRC screening use remains low in Maryland and lower in some age and racial/ethnic groups with limited resources to participate in CRC screening programs. The purpose of this quantitative, cross-sectional study is to investigate whether age group, sex, race/ethnicity, education level, income level, health insurance coverage, and access to health care professional can predict an individual, 50–75 years of age, in Maryland to take action to fully meet the United States Preventive Services Task Force CRC screening test recommendation within the recommended time interval. The …

Integrated Multiple Adaptive Design Involving Sample Size Re-Estimation And (Covariate-Adjusted) Response-Adaptive Randomization For Continuous And Binary Outcomes, Christine M. Orndahl

Theses and Dissertations

Historically, clinical trials have been performed based on decisions made prior to the start of the trial. Adaptive designs have been developed to provide increased flexibility, allowing pre-specified changes to occur based on interim data. Each adaptive design addresses a unique pitfall of a non-adaptive design, such as minimizing the chance of an under- or over-powered study by utilizing interim data to update the sample size estimate (sample size re-estimation) or increasing the ethical benefit of a trial by allocating more participants to the better performing treatment group ([covariate-adjusted] response-adaptive randomization). Additional benefit is attainable by combining more than one …

Rickettsialpox – A Rare But Not Extinct Disease: A Review Of The Literature And New Directions, Marina Eremeeva, Kamalich Muniz-Rodriguez

Biostatistics, Epidemiology & Environmental Health Sciences: Faculty Publications

Smallpox rickettsia is an urban zoonosis caused by Rickettsia akari. To date, R. akari is the only characterized representative of the group of spotted fevers transmitted by the gamasid mite Liponyssoides sanguineus, which is common among peridomic rodents. This disease was first described in New York in 1946, and a few years later a similar outbreak occurred in the Ukrainian SSR. Numerous serological studies and diagnostics of sporadic cases of smallpox rickettsiosis suggest its widespread occurrence on the planet; however, the current geography and incidence of smallpox rickettsiosis is unknown. Smallpox rickettsiosis is characterized by the classic clinical triad of …

Wage-Productivity Analysis Of U.S. Domestic Airlines, Jesse Lucas, Khairul Azuar, Justin Tan, Syed Ilyas

Introduction to Research Methods RSCH 202

This study examines the impact of wages on productivity by examining US domestic airlines.

Current literature places emphasis on jobs conducted in-flight, specifically pilots and cabin crew. This paper considers all job titles involved in the operations of the airline, including executives and management. Existing research focuses on factors such as governance, domestic economic level, and personal attributes such as intrinsic motivation, gender, and age. There is insufficient research regarding the relationship between wage and productivity. Thus, it is uncertain if high wage leads to high productivity. Preliminary findings suggest higher wage equates to higher productivity.

Joint Simulation Of Continuous And Categorical Variables For Mineral Resource Modeling And Recoverable Reserves Calculation, Sentle Augustinus Hlajoane

Dissertations, Master's Theses and Master's Reports

Spatial variability and uncertainty of continuous variables (grade) and categorical variables (rock-types) in mineral evaluation significantly impact the economics of mining projects. The conventional approach of simulating grades using deterministic rock- types is problematic since spatial variability, and uncertainty of grades at rock-type contacts are not well captured in deposits where the grade changes gradually between rock-types. Therefore, jointly simulating these variables can improve confidence (reduce uncertainty) in a resource model. Also, resource classification and recoverable reserve calculation can significantly improve the understanding of the deposit and its economic viability. This research utilized the Plural-Gaussian geostatistical simulation to jointly simulate …

Projecting Regions Of North Atlantic Right Whale, Eubalaena Glacialis, Habitat Suitability In The Gulf Of Maine In 2050, Camille Ross

Honors Theses

North Atlantic right whales (Eubalaena glacialis) are endangered. Understanding the role environmental conditions play in habitat suitability is key to determining the regions in need of protection for conservation of the species, particularly as climate change shifts suitable habitat. This thesis uses three species distribution modeling algorithms, together with historical data on whale abundance(1993 to 2009) and environmental covariates to build monthly ensemble models of past E. glacialis habitat suitability in the Gulf of Maine. Then, the models are projected onto the year 2050 for a range of climate scenarios. Specifically, the distribution of the species was modeled …

Webexpo : Vers Une Meilleure Interprétation Des Mesures D'Exposition Professionnelle Aux Substances Chimiques Sur Les Lieux De Travail, Jérôme Lavoué, Lawrence Joseph, Tracy L. Kirkham, France Labrèche, Gautier Mater, Frédéric Clerc

Rapports de recherche scientifique

Une grande partie de l'activité des hygiénistes du travail consiste à mesurer les niveaux d'exposition professionnelle des travailleurs. La plupart des rapports d'évaluation de l'exposition font état d'une importante variabilité spatiale et temporelle quant à l'intensité de l'exposition, laquelle fluctue souvent du simple au décuple en dépit de conditions apparemment similaires. Il en résulte depuis toujours un défi de taille en ce qui concerne l'interprétation des niveaux mesurés par rapport aux valeurs limites d’exposition professionnelle (VLEP). Il existe désormais un cadre consensuel – issu d'une élaboration progressive au cours des deux dernières décennies – concernant l'analyse des niveaux d’exposition par …

Webexpo: Towards A Better Interpretation Of Measurements Of Occupational Exposure To Chemicals In The Workplace, Jérôme Lavoué, Lawrence Joseph, Tracy L. Kirkham, France Labrèche, Gautier Mater, Frédéric Clerc

Rapports de recherche scientifique

Une grande partie de l'activité des hygiénistes du travail consiste à mesurer les niveaux d'exposition professionnelle des travailleurs. La plupart des rapports d'évaluation de l'exposition font état d'une importante variabilité spatiale et temporelle quant à l'intensité de l'exposition, laquelle fluctue souvent du simple au décuple en dépit de conditions apparemment similaires. Il en résulte depuis toujours un défi de taille en ce qui concerne l'interprétation des niveaux mesurés par rapport aux valeurs limites d’exposition professionnelle (VLEP). Il existe désormais un cadre consensuel – issu d'une élaboration progressive au cours des deux dernières décennies – concernant l'analyse des niveaux d’exposition par …

Adjusting For Dropout In Randomized Controlled Clinical Trials, Katharine Stromberg

Theses and Dissertations

Dropout is a common issue in randomized controlled clinical trials and can negatively impact the internal validity of a study and potentially bias the treatment effect. When subjects discontinue study participation, they are not being given the opportunity to gain from the investigational therapy as if they had remained in the study, defeating one of the main purposes of clinical trials, providing treatment. Specifically in unblinded studies, such as the wait-list control (WLC) design, dropout is often due to group membership. Subjects allocated to the control group often dropout at higher rates than in the treatment group. Adaptive designs have …

Zero-Inflated Longitudinal Mixture Model For Stochastic Radiographic Lung Compositional Change Following Radiotherapy Of Lung Cancer, Viviana A. Rodríguez Romero

Theses and Dissertations

Compositional data (CD) is mostly analyzed as relative data, using ratios of components, and log-ratio transformations to be able to use known multivariable statistical methods. Therefore, CD where some components equal zero represent a problem. Furthermore, when the data is measured longitudinally, observations are spatially related and appear to come from a mixture population, the analysis becomes highly complex. For this matter, a two-part model was proposed to deal with structural zeros in longitudinal CD using a mixed-effects model. Furthermore, the model has been extended to the case where the non-zero components of the vector might a two component mixture …

Applications Of Dynamic Linear Models To Random Allocation Models, Albert H. Lee Iii

Theses and Dissertations

Although advances in modern computational algorithms have provided researchers the ability to work problems which were once too computationally complex to solve, problems with high computation or large parameter spaces still remain. Problems such as those involving Time Series can be such problems. Chapter 1 looks at the the use of Exponentially Weighted Moving Averages developed by \citep{holt2004forecasting, winters1960forecasting} which were thought to provide sufficient solutions to these Time Series. A discussion is provided which illustrates the shortcomings of the EWMA and how its infinite number of possible starting values provides the modeler with an endless number of possible solutions …

Utilizing Design Structure For Improving Design Selection And Analysis, Ahlam Ali Alzharani

Theses and Dissertations

Recent work has shown that the structure for design plays a role in the simplicity or complexity of data analysis. To increase the knowledge of research in these areas, this dissertation aims to utilize design structure for improving design selection and analysis. In this regard, minimal dependent sets and block diagonal structure are both important concepts that are relevant to the orthogonality of the columns of a design. We are interested in finding ways to improve the data analysis especially for active effect detection by utilizing minimal dependent sets and block diagonal structure for design.

We introduce a new classification …

Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman

Mathematics Faculty Publications

In this study, a stochastic numerical technique is used to investigate the numerical solution of heat transfer temperature distribution system using feed forward artificial neural networks. Mathematical model of fin equation is formulated with the help of artificial neural networks. The effect of the heat on a rectangular fin with thermal conductivity and temperature de-pendent internal heat generation is calculated through neural networks optimization with optimizers like active set technique, interior point technique, pattern search, genetic algorithm and a hybrid approach of pattern search - interior point technique, genetic algorithm - active set technique, genetic algorithm - interior point technique, …

Simulation Based Inference In Epidemic Models, Tejitha Dharmagadda

Theses, Dissertations and Culminating Projects

From ancient times to the modern day, public health has been an area of great interest. Studies on the nature of disease epidemics began around 400 BC and has been a continuous area of study for the well-being of individuals around the world. For over 100 years, epidemiologists and mathematicians have developed numerous mathematical models to improve our understanding of infectious disease dynamics with an eye on controlling and preventing disease outbreak and spread. In this thesis, we discuss several types of mathematical compartmental models such as the SIR, and SIS models. To capture the noise inherent in the real-world, …