Statistics and Probability Commons^™

Creation Of Synthetic Discrete Response Regression Models, Joseph Hilbe

Joseph M Hilbe

The development and use of synthetic regression models has proven to assist statisticians in better understanding bias in data, as well as how to best interpret various statistics associated with a modeling situation. In this article I present code that can be easily amended for the creation of synthetic binomial, count, and categorical response models. Parameters may be assigned to any number of predictors (which are shown as continuous, binary, or categorical), negative binomial heterogeneity parameters may be assigned, and the number of levels or cut points and values may be specified for ordered and unordered categorical response models. I …

Statistical Criteria For Selecting The Optimal Number Of Untreated Subjects Matched To Each Treated Subject When Using Many-To-One Matching On The Propensity Score, Peter C. Austin

Peter Austin

Propensity-score matching is increasingly being used to estimate the effects of treatments using observational data. In many-to-one (M:1) matching on the propensity score, M untreated subjects are matched to each treated subject using the propensity score. The authors used Monte Carlo simulations to examine the effect of the choice of M on the statistical performance of matched estimators. They considered matching 1–5 untreated subjects to each treated subject using both nearest-neighbor matching and caliper matching in 96 different scenarios. Increasing the number of untreated subjects matched to each treated subject tended to increase the bias in the estimated treatment effect; …

The Performance Of Different Propensity-Score Methods For Estimating Differences In Proportions (Risk Differences Or Absolute Risk Reductions) In Observational Studies, Peter C. Austin

Peter Austin

Propensity score methods are increasingly being used to estimate the effects of treatments on health outcomes using observational data. There are four methods for using the propensity score to estimate treatment effects: covariate adjustment using the propensity score, stratification on the propensity score, propensity-score matching, and inverse probability of treatment weighting (IPTW) using the propensity score. When outcomes are binary, the effect of treatment on the outcome can be described using odds ratios, relative risks, risk differences, or the number needed to treat. Several clinical commentators suggested that risk differences and numbers needed to treat are more meaningful for clinical …

Optimal Dynamic Policies For Influenza Management, Michael Ludkovski, Jarad Niemi

Jarad Niemi

Management policies for influenza outbreaks balance the expected morbidity and mortality costs versus the cost of intervention policies. We present a methodology for dynamic determination of optimal policies in a completely observed stochastic compartmental model with parameter uncertainty. Our approach is simulation-based and searches the full set of sequential control strategies. For each time point, it generates a policy map describing the optimal intervention to implement as a function of outbreak state and Bayesian parameter posteriors. As a running example, we study a stochastic SIR model with isolation and vaccination as two possible interventions. Numerical simulations based on a classic …

On K4 Of The Gaussian And Eisenstein Integers, Mathieu Dutour Sikiric, Herbert Gangl, Paul Gunnells, Jonathan Hanke, Achill Schürmann, Dan Yasaki

Paul Gunnells

Abstract. In this paper we investigate the structure of the algebraic K-groups K4(Z[i]) and K4(Z[ρ]), where i := √ −1 and ρ := (1 + √ −3)/2. We exploit the close connection between homology groups of GLn(R) for n 6 5 and those of related classifying spaces, then compute the former using Voronoi’s reduction theory of positive definite quadratic and Hermitian forms to produce a very large finite cell complex on which GLn(R) acts. Our main results are (i) K4(Z[i]) is a finite abelian 3-group, and (ii) K4(Z[ρ]) is trivial.

A Prospective Cohort Study Of Modifiable Risk Factors For Gestational Diabetes Among Hispanic Women: Design And Baseline Characteristics, Lisa Chasen-Taber, R. T. Fortner, A. Gollenberg, John Buonaccorsi, N. Dole, G. Markenson

John Buonaccorsi

OBJECTIVES: Women diagnosed with gestational diabetes mellitus (GDM) are at high risk for future diabetes, with rates of GDM consistently higher in Hispanic than non-Hispanic white women. Currently recognized risk factors for GDM are absent in up to half of affected women, and studies addressing modifiable risk factors for GDM in Hispanic women are sparse. METHODS: Proyecto Buena Salud is an ongoing prospective cohort study of Hispanic women in Massachusetts designed to assess physical activity, psychosocial stress, and GDM risk. Bilingual interviewers recruit prenatal care patients early in pregnancy and assess activity, trait anxiety, perceived stress, and depressive symptoms using …

Statistical Modeling Of Agatston Score In Multi-Ethnic Study Of Atherosclerosis (Mesa), Anna Liu, S. Ma, J. Carr, W. Post, R. Kronmal

Anna Liu

The MESA (Multi-Ethnic Study of Atherosclerosis) is an ongoing study of the prevalence, risk factors, and progression of subclinical cardiovascular disease in a multi-ethnic cohort. It provides a valuable opportunity to examine the development and progression of CAC (coronary artery calcium), which is an important risk factor for the development of coronary heart disease. In MESA, about half of the CAC scores are zero and the rest are continuously distributed. Such data has been referred to as “zero-inflated data” and may be described using two-part models. Existing two-part model studies have limitations in that they usually consider parametric models only, …

Gibbs Sampling For A Bayesian Hierarchical General Linear Model, Alicia A. Johnson, Galin L. Jones

Alicia A. Johnson

No abstract provided.

Existence Of Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li

Yi Li

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.

Digraphs With Isomorphic Underlying And Domination Graphs: 4-Cycles And Pairs Of Paths, Kim A. S. Factor, Larry J. Langley

Mathematics, Statistics and Computer Science Faculty Research and Publications

A domination graph of a digraph D, dom(D), is created using the vertex set of D, V(D). There is an edge uv in dom(D) whenever (u, z) or (v, z) is in the arc set of D, A(D), for every other vertex z ε V(D). For only some digraphs D has the structure of dom(D) been characterized. Examples of this are tournaments and regular digraphs. The authors have characterizations for the structure of digraphs D for …

Gliomapredict: A Clinically Useful Tool For Assigning Glioma Patients To Specific Molecular Subtypes, Aiguo Li, Serdar Bozdag, Yuri Kotliarov, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Advances in generating genome-wide gene expression data have accelerated the development of molecular-based tumor classification systems. Tools that allow the translation of such molecular classification schemas from research into clinical applications are still missing in the emerging era of personalized medicine.

Results: We developed GliomaPredict as a computational tool that allows the fast and reliable classification of glioma patients into one of six previously published stratified subtypes based on sets of extensively validated classifiers derived from hundreds of glioma transcriptomic profiles. Our tool utilizes a principle component analysis (PCA)-based approach to generate a visual representation of the analyses, quantifies …

Not Every Co-Existential Map Is Confluent, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A continuous surjection between compacta is co-existential if it is the second of two maps whose composition is a standard ultracopower projection. Co-existential maps are always weakly confluent, and are even monotone when the range space is locally connected; so it is a natural question to ask whether they are always confluent. Here we give a negative answer. This is an interesting question, mainly because of the fact that most theorems about confluent maps have parallel versions for co-existential maps---notably, both kinds of maps preserve hereditary indecomposability. Where the known parallels break down is in the question of chainability. It …

Racial/Ethnic Health Disparities In Northeast Ohio, Mark Salling, Joseph Ahern

All Maxine Goodman Levin School of Urban Affairs Publications

Racial/Ethnic Health Disparities in Northeast Ohio, Planning & Action, The Center for Community Solutions, Vol. 63, No. 4 (July), 2010, pp. 12-15.

Putting Artists On The Map: A Five Part Study Of Greater Cleveland Artists' Location Decisions - Part 1: Summary Report, Mark Salling, Gregory Soltis, Charles Post, Sharon Bliss, Ellen Cyran

All Maxine Goodman Levin School of Urban Affairs Publications

A series of reports detailing the residential and work space location preferences of Cuyahoga county's artists.

The Beta Maxwell Distribution, Grace Ebunoluwa Amusan

Theses, Dissertations and Capstones

In this work we considered a general class of distributions gener- ated from the logit of the beta random variable. We looked at various works that have been done and discussed some of the results that were obtained. Special cases of this class include the beta-normal distribution, the beta-exponential distribution, the beta-Gumbell distribution, the beta-Weibull distribution, the beta-Pareto distribution and the beta-Rayleigh distribution. We looked at the probability distribution functions of each of these distributions and also look at some of their properties. Another special case of this family, a three-parameter beta-Maxwell distribution was dened and studied. Various properties of …

Sustainable Agriculture Bibliography, Matt Bogard

Agriculture Department Seminar Series

An annotated bibliography related to the sustainability of biotechnology and pharmaceutical technologies used in modern agriculture.

Using R, Matt Bogard

Economics Faculty Publications

R is a statistical programming language with a command line interface that is becoming more and more popular every day. I have used R for data visualization, data mining/machine learning, as well as social network analysis. Initially embraced largely in academia, R is becoming the software of choice in various corporate settings.

Mathematical Themes In Economics, Machine Learning, And Bioinformatics, Matt Bogard

Economics Faculty Publications

Graduate students in economics are often introduced to some very useful mathematical tools that many outside the discipline may not associate with training in economics. This essay looks at some of these tools and concepts, including constrained optimization, separating hyperplanes, supporting hyperplanes, and ‘duality.’ Applications of these tools are explored including topics from machine learning and bioinformatics.

Using Twitter To Demonstrate Basic Concepts From Network Analysis, Matt Bogard

Economics Faculty Publications

Social network analysis focuses on finding patterns in interactions between people or entities. These patterns may be described in the form of a network. Network analysis in general has many applications including models of student integration and persistence, business to business supply chains, terrorist cells, or analysis of social media such as Facebook and Twitter. This presentation provides a reference for basic concepts from social network analysis with examples using tweets from Twitter.

Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn

Mathematics Faculty Publications

It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.