Statistics and Probability Commons^™

Bate Curve In Assessment Of Clinical Utility Of Predictive Biomarkers, Xiao-Hua Zhou, Yunbei Ma

UW Biostatistics Working Paper Series

In this paper, for time-to-event data, we propose a new statistical framework for casual inference in evaluating clinical utility of predictive biomarkers and in selecting an optimal treatment for a particular patient. This new casual framework is based on a new concept, called Biomarker Adjusted Treatment Effect (BATE) curve, which can be used to represent the clinical utility of a predictive biomarker and select an optimal treatment for one particular patient. We then propose semi-parametric methods for estimating the BATE curves of biomarkers and establish asymptotic results of the proposed estimators for the BATE curves. We also conduct extensive simulation …

Tmle: An R Package For Targeted Maximum Likelihood Estimation, Susan Gruber, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Targeted maximum likelihood estimation (TMLE) presents an approach for construction of an efficient double-robust semi-parametric substitution estimator of a target feature of the data generating distribution, such as a statistical association measure or a causal effect parameter. tmle is a recently developed R package that implements TMLE for estimation of the effect of a binary treatment at a single point in time on an outcome of interest, controlling for user supplied covariates: the additive treatment effect, the relative risk, the odds ratio. The package allows outcome data with missingness, and experimental units that contribute repeated records of the point-treatment data …

Causal Inference Under Multiple Versions Of Treatment, Tyler J. Vanderweele, Miguel A. Hernan

COBRA Preprint Series

In this article we discuss the no-multiple-versions-of-treatment assumption and extend the potential outcomes framework to accommodate causal inference under violations of this assumption. A variety of examples are discussed in which the assumption may be violated. Identification results are provided for the overall treatment effect and the effect of treatment on the treated when multiple versions of treatment are present and also for the causal effect comparing a version of one treatment to some other version of the same or a different treatment. Further identification and interpretative results are given for cases in which a treatment variable is dichotomized to …

Population Functional Data Analysis Of Group Ica-Based Connectivity Measures From Fmri, Shanshan Li, Brian S. Caffo, Suresh Joel, Stewart Mostofsky, James Pekar, Susan Spear Bassett

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this manuscript, we use a two-stage decomposition for the analysis of func- tional magnetic resonance imaging (fMRI). In the first stage, spatial independent component analysis is applied to the group fMRI data to obtain common brain networks (spatial maps) and subject-specific mixing matrices (time courses). In the second stage, functional principal component analysis is utilized to decompose the mixing matrices into population- level eigenvectors and subject-specific loadings. Inference is performed using permutation-based exact conditional logistic regression for matched pairs data. Simulation studies suggest the ability of the decomposition methods to recover population brain networks and the major direction of …

Differential Gene Expression In Liver And Small Intestine From Lactating Rats Compared To Age-Matched Virgin Controls Detects Increased Mrna Of Cholesterol Biosynthetic Genes, Antony Athippozhy, Liping Huang, Clavia Ruth Wooton-Kee, Tianyong Zhao, Paiboon Jungsuwadee, Arnold J. Stromberg, Mary Vore

Statistics Faculty Publications

BACKGROUND: Lactation increases energy demands four- to five-fold, leading to a two- to three-fold increase in food consumption, requiring a proportional adjustment in the ability of the lactating dam to absorb nutrients and to synthesize critical biomolecules, such as cholesterol, to meet the dietary needs of both the offspring and the dam. The size and hydrophobicity of the bile acid pool increases during lactation, implying an increased absorption and disposition of lipids, sterols, nutrients, and xenobiotics. In order to investigate changes at the transcriptomics level, we utilized an exon array and calculated expression levels to investigate changes in gene expression …

The (1,2)-Step Competition Graph Of A Tournament, Kim A. S. Factor, Sarah Merz

Mathematics, Statistics and Computer Science Faculty Research and Publications

The competition graph of a digraph, introduced by Cohen in 1968, has been extensively studied. More recently, in 2000, Cho, Kim, and Nam defined the m-step competition graph. In this paper, we offer another generalization of the competition graph. We define the (1,2)-step competition graph of a digraph D, denoted C_1,2(D), as the graph on V(D) where {x,y}∈E(C_1,2(D)) if and only if there exists a vertex z≠x,y, such that either d_D−y( …

Non-Homogeneous Markov Process Models With Incomplete Observations: Application To A Dementia Disease Study, Xiao-Hua Zhou, Baojiang Chen

UW Biostatistics Working Paper Series

Identifying risk factors for transition rates among normal cognition, mildly cognitive impairment, dementia and death in an Alzheimer's disease study is very important. It is known that transition rates among these states are strongly time dependent. While Markov process models are often used to describe these disease progressions, the literature mainly focuses on time homogeneous processes, and limited tools are available for dealing with non-homogeneity. Further, patients may choose when they want to visit the clinics, which creates informative observations. In this paper, we develop methods to deal with non-homogeneous Markov processes through time scale transformation when observation times are …

Doubly Robust Estimates For Binary Longitudinal Data Analysis With Missing Response And Missing Covariates, Baojiang Chen, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Longitudinal studies often feature incomplete response and covariate data. Likelihood-based methods such as the EM algorithm give consistent estimators for model parameters when data are missing at random provided that the response model and the missing covariate model are correctly specified; but we do not need to specify the missing data mechanism. An alternative method is the weighted estimating equation which gives consistent estimators if the missing data and response models are correctly specified; but we do not need to specify the distribution of the covariates that have missing values. In this paper we develop a doubly robust estimation method …

Semiparametric Estimation Of The Covariate-Specific Roc Curve In Presence Of Ignorable Verification Bias, Danping Liu, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Covariate-specific ROC curves are often used to evaluate the classification accuracy of a medical diagnostic test or a biomarker, when the accuracy of the test is associated with certain covariates. In many large-scale screening tests, the gold standard is subject to missingness due to high cost or harmfulness to the patient. In this paper, we propose a semiparametric estimation method for the covariate-specific ROC curves with a partial missing gold standard. A location-scale model is constructed for the test result to model the covariates' effect, but the residual distributions are left unspecified. Thus the baseline and link functions of the …

Evaluating Markers For Treatment Selection Based On Survival Time, Xiao Song, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

For many medical conditions there are several treatment options available to patients. We consider evaluating markers based on a simple treatment selection policy that incorporates information on the patient's marker value exceeding a threshold. Although traditional regression methods may assess the effect of the marker and treatment on outcomes, it is appealing to quantify more directly the potential impact on the population of using the marker to select treatment. A useful tool is the selection impact (SI) curve proposed by Song and Pepe (2004, \textit{Biometrics} \textbf{60}, 874--883) for binary outcomes. However, this approach does not deal with continuous outcomes, nor …

A Flexible Spatio-Temporal Model For Air Pollution: Allowing For Spatio-Temporal Covariates, Johan Lindstrom, Adam A. Szpiro, Paul D. Sampson, Lianne Sheppard, Assaf Oron, Mark Richards, Tim Larson

UW Biostatistics Working Paper Series

Given the increasing interest in the association between exposure to air pollution and adverse health outcomes, the development of models that provide accurate spatio-temporal predictions of air pollution concentrations at small spatial scales is of great importance when assessing potential health effects of air pollution. The methodology presented here has been developed as part of the Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air), a prospective cohort study funded by the US EPA to investigate the relationship between chronic exposure to air pollution and cardiovascular disease. We present a spatio-temporal framework that models and predicts ambient air pollution by …

Functional Principal Components Model For High-Dimensional Brain Imaging, Vadim Zipunnikov, Brian S. Caffo, David M. Yousem, Christos Davatzikos, Brian S. Schwartz, Ciprian Crainiceanu

Johns Hopkins University, Dept. of Biostatistics Working Papers

We establish a fundamental equivalence between singular value decomposition (SVD) and functional principal components analysis (FPCA) models. The constructive relationship allows to deploy the numerical efficiency of SVD to fully estimate the components of FPCA, even for extremely high-dimensional functional objects, such as brain images. As an example, a functional mixed effect model is fitted to high-resolution morphometric (RAVENS) images. The main directions of morphometric variation in brain volumes are identified and discussed.

A Generalized Approach For Testing The Association Of A Set Of Predictors With An Outcome: A Gene Based Test, Benjamin A. Goldstein, Alan E. Hubbard, Lisa F. Barcellos

U.C. Berkeley Division of Biostatistics Working Paper Series

In many analyses, one has data on one level but desires to draw inference on another level. For example, in genetic association studies, one observes units of DNA referred to as SNPs, but wants to determine whether genes that are comprised of SNPs are associated with disease. While there are some available approaches for addressing this issue, they usually involve making parametric assumptions and are not easily generalizable. A statistical test is proposed for testing the association of a set of variables with an outcome of interest. No assumptions are made about the functional form relating the variables to the …

How Long Does A Santa Barbara Divorce Take?, Samuel J. Frame, Brian H. Burke

Statistics

There has been considerable research about the amount of time the psychological grief process requires when couples divorce. However, there has been little research on the time the actual process of divorce requires. To address this, we obtained free and publicly available information on divorce cases from Santa Barbara County. We are able to offer some insight about the relationship among the length of divorce, marriage length, and having minor children. Our results are consistent with those found in other literature that focuses on the length of the grief process, and our results are consistent with our experiences in family …

Book Review Of Graphics For Statistics And Data Analysis With R By Kevin J. Keen, Samuel J. Frame

Statistics

No abstract provided.

Using Local Correlation To Explain Success In Baseball, Jeff Hamrick, John Rasp

Master of Science in Analytics (MSAN) Faculty Research

Statisticians have long employed linear regression models in a variety of circumstances, including the analysis of sports data, because of their flexibility, ease of interpretation, and computational tractability. However, advances in computing technology have made it possible to develop and employ more complicated, nonlinear, and nonparametric procedures. We propose a fully nonparametric nonlinear regression model that is associated to a local correlation function instead of the usual Pearson correlation coefficient. The proposed nonlinear regression model serves the same role as a traditional linear model, but generates deeper and more detailed information about the relationships between the variables being analyzed. We …

Balanced Pod For Model Reduction Of Linear Pde Systems: Convergence Theory, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We consider convergence analysis for a model reduction algorithm for a class of linear infinite dimensional systems. The algorithm computes an approximate balanced truncation of the system using solution snapshots of specific linear infinite dimensional differential equations. The algorithm is related to the proper orthogonal decomposition, and it was first proposed for systems of ordinary differential equations by Rowley (Int. J. Bifurc. Chaos Appl. Sci. Eng. 15(3), 997-1013, 2005). For the convergence analysis, we consider the algorithm in terms of the Hankel operator of the system, rather than the product of the system Gramians as originally proposed by Rowley. For …

Balanced Pod For Linear Pde Robust Control Computations, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also "nearby" systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale nite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Convergence theory is given, and numerical results are presented …

A Model Based Feedback Controller For Wing-Twist Via Piezoceramic Actuation, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

In this paper we present a model for a rubber plate with piezoceramic actuators to represent a bioinspired flexible wing. Using a Galerkin based finite element approximation to the system, we compute a linear quadratic based tracking control for piezoelectric actuators placed along both leading and trailing edges. Using these piezoceramic devices, we demonstrate the effectiveness of model based feedback control in achieving a desired wing tip position; this modified shape is analogous to aircraft roll moment generation via wing twist.

Convergent Snapshot Algorithms For Infinite-Dimensional Lyapunov Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We consider two algorithms to approximate the solution Z of a class of stable operator Lyapunov equations of the form AZ + ZA* + BB* = 0. The algorithms utilize time snapshots of solutions of certain linear infinite-dimensional differential equations to construct the approximations. Matrix approximations of the operators a and B are not required and the algorithms are applicable as long as the rank of B is relatively small. The first algorithm produces an optimal low-rank approximate solution using proper orthogonal decomposition. The second algorithm approximates the product of the solution with a few vectors and can be implemented …

Sub-Supersolution Method In Variational Inequalities With Multivalued Operators Given By Integrals, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee

Mathematics Faculty Publications

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …

Global Stability Of Complex-Valued Neural Networks On Time Scales, Martin Bohner, V. Sree Hari Rao, Suman Sanyal

Mathematics and Statistics Faculty Research & Creative Works

In this paper, activation dynamics of complex-valued neural networks are studied on general time scales. Besides presenting conditions guaranteeing the existence of a unique equilibrium pattern, its global exponential stability is discussed. Some numerical examples for different time scales are given in order to highlight the results. © 2011 Foundation for Scientific Research and Technological Innovation.

Variation In Sclerotinia Sclerotiorum Bean Isolates From Multisite Resistance Screening Locations, Lindsey Otto-Hanson, James R, Steadman, Rebecca Higgins, Kent M. Eskridge

Department of Statistics: Faculty Publications

There is no complete resistance to Sclerotinia sclerotiorum, cause of white mold in dry bean (Phaseolus vulgaris). Variable resistance expression is one problem in screening for improved white mold resistance. With no previous information in the literature, pathogen variation in multisite screening nurseries was evaluated as one cause of diverse resistance expression. In all, 10 isolates of S. sclerotiorum used in greenhouse screening and 146 isolates collected from nine white mold field screening nurseries in major bean production areas in the United States were compared using mycelial compatibility groupings (MCGs) and an aggressiveness test. These 10 greenhouse …

Development Of An Internet Based System For Modeling Biotin Metabolism Using Bayesian Networks, Jinglei Zhou, Dong Wang, Vicki L. Schlegel, Janos Zempleni

Department of Statistics: Faculty Publications

Biotin is an essential water-soluble vitamin crucial for maintaining normal body functions. The importance of biotin for human health has been under-appreciated but there is plenty of opportunity for future research with great importance for human health. Currently, carrying out predictions of biotin metabolism involves tedious manual manipulations. In this paper, we report the development of BiotinNet, an internet based program that uses Bayesian networks to integrate published data on various aspects of biotin metabolism. Users can provide a combination of values on the levels of biotin related metabolites to obtain the predictions on other metabolites that are not specified. …

If The Shoe Fits They Might Acquit: The Value Of Forensic Science Testimony, Jonathan Koehler

Faculty Working Papers

The probative value of forensic science evidence (such as a shoeprint) varies widely depending on how the evidence and hypothesis of interest is characterized. This paper uses a likelihood ratio (LR) approach to identify the probative value of forensic science evidence. It argues that the "evidence" component should be characterized as a "reported match," and that the hypothesis component should be characterized as "the matching person or object is the source of the crime scene sample." This characterization of the LR forces examiners to incorporate risks from sample mix-ups and examiner error into their match statistics. But how will legal …

Monitoring Radiation Use In Cardiac Fluoroscopy Imaging Procedures, Nathaniel Stevens, S H. Steiner, I R. Smith, R J. Mackay

Mathematics

Objective: Timely identification of systematic changes in radiation delivery of an imaging system can lead to a reduction in risk for the patients involved. However, existing quality assurance programs involving the routine testing of equipment performance using phantoms are limited in their ability to effectively carry out this task. To address this issue we propose the implementation of an ongoing monitoring process that utilizes procedural data to identify unexpected large or small radiation exposures for individual patients, as well as to detect persistent changes in the radiation output of imaging platforms.

Methods: Data used in this study were obtained from …

Approximating Confidence Intervals About Discrete Time Survival/Cumulative Incidence Estimates Using The Delta Method, Alexis Dinno, Jong-Sung Kim

Community Health Faculty Publications and Presentations

Poster focuses on answering the questions whether and when and event will happen in a population at risk.

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

Flipping The Winner Of A Poset Game, Adam O. Kalinich '12

Student Publications & Research

Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element and all elements greater than it, and whoever takes the last element wins. Examples of poset games include Nim and Chomp. We investigate the complexity of computing which player of a poset game has a winning strategy. We give an inductive procedure that modifies poset games to change the nim-value which informally captures the winning strategies in the game. For a generic …