Statistics and Probability Commons^™

A Modified Cluster-Weighted Approach To Nonlinear Time Series, Mark Ballatore Lyman

Theses and Dissertations

In many applications involving data collected over time, it is important to get timely estimates and adjustments of the parameters associated with a dynamic model. When the dynamics of the model must be updated, time and computational simplicity are important issues. When the dynamic system is not linear the problem of adaptation and response to feedback are exacerbated. A linear approximation of the process at various levels or “states” may approximate the non-linear system. In this case the approximation is linear within a state and transitions from state to state over time. The transition probabilities are parametrized as a Markov …

Assessment Of A Cgh-Based Genetic Instability, David A. Engler, Yiping Shen, J F. Gusella, Rebecca A. Betensky

Harvard University Biostatistics Working Paper Series

No abstract provided.

Survival Analysis With Large Dimensional Covariates: An Application In Microarray Studies, David A. Engler, Yi Li

Harvard University Biostatistics Working Paper Series

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time …

A Comparative Simulation Study Of Robust Estimators Of Standard Errors, Natalie Johnson

Theses and Dissertations

The estimation of standard errors is essential to statistical inference. Statistical variability is inherent within data, but is usually of secondary interest; still, some options exist to deal with this variability. One approach is to carefully model the covariance structure. Another approach is robust estimation. In this approach, the covariance structure is estimated from the data. White (1980) introduced a biased, but consistent, robust estimator. Long et al. (2000) added an adjustment factor to White's estimator to remove the bias of the original estimator. Through the use of simulations, this project compares restricted maximum likelihood (REML) with four robust estimation …

Super Learner, Mark J. Van Der Laan, Eric C. Polley, Alan E. Hubbard

U.C. Berkeley Division of Biostatistics Working Paper Series

Previous articles (van der Laan and Dudoit (2003); van der Laan et al. (2006); Sinisi et al. (2007)) advertised and theoretically validated the use of cross-validation to select among many candidate estimators to compute a so called super learner which outperforms any of the given candidate estimators. The theoretical basis was provided for this super learner based on oracle results for the cross-validation selector (e.g., van der Laan and Dudoit (2003); van der Laan et al. (2006)) and in Sinisi et al. (2007). In addition, these papers contained a practical demonstration of the adaptivity of this so called super learner …

Sensitivity To Distributional Assumptions In Estimation Of The Odp Thresholding Function, Wendy Jill Bunn

Theses and Dissertations

Recent technological advances in fields like medicine and genomics have produced high-dimensional data sets and a challenge to correctly interpret experimental results. The Optimal Discovery Procedure (ODP) (Storey 2005) builds on the framework of Neyman-Pearson hypothesis testing to optimally test thousands of hypotheses simultaneously. The method relies on the assumption of normally distributed data; however, many applications of this method will violate this assumption. This thesis investigates the sensitivity of this method to detection of significant but nonnormal data. Overall, estimation of the ODP with the method described in this thesis is satisfactory, except when the nonnormal alternative distribution has …

Double Integral Calculus Of Variations On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler-Lagrange equation.

On A Theorem Of Shchepin And Repovš Concerning The Smoothness Of Compacta, Ethan Akin, William Ott

Mathematics and Statistics Faculty Research & Creative Works

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations. © 2007 Elsevier B.V. All rights reserved.

A Dynamic-Trend Exponential Smoothing Model, Don Miller, Dan Williams

Publications and Research

Forecasters often encounter situations in which the local pattern of a time series is not expected to persist over the forecasting horizon. Since exponential smoothing models emphasize recent behavior, their forecasts may not be appropriate over longer horizons. In this paper, we develop a new model in which the local trend line projected by exponential smoothing converges asymptotically to an assumed future long-run trend line, which might be an extension of a historical long-run trend line. The rapidity of convergence is governed by a parameter. A familiar example is an economic series exhibiting persistent long-run trend with cyclic variation. This …

Using Box-Scores To Determine A Position's Contribution To Winning Basketball Games, Gilbert W. Fellingham, C. Shane Reese, Garritt L. Page

Faculty Publications

While it is generally recognized that the relative importance of different skills is not constant across different positions on a basketball team, quantification of the differences has not been well studied. 1163 box scores from games in the National Basketball Association during the 1996-97 season were used to study the relationship of skill performance by position and game outcome as measured by point differentials. A hierarchical Bayesian model was fit with individual players viewed as a draw from a population of players playing a particular position: point guard, shooting guard, small forward, power forward, center, and bench. Posterior distributions for …

Incidence, Patterns And Severity Of Reported Unintentional Injuries In Pakistan For Persons Five Years And Older: Results Of The National Health Survey Of Pakistan 1990–94, Zafar Fatmi, Wilbur C. Hadden, Junaid A. Razzak, Huma Qureshi, Adnan A. Hyder, Gregory Pappas

Community Health Sciences

Background

National level estimates of injuries are not readily available for developing countries. This study estimated the annual incidence, patterns and severity of unintentional injuries among persons over five years of age in Pakistan.

Methods

National Health Survey of Pakistan (NHSP 1990–94) is a nationally representative survey of the household. Through a two-stage stratified design, 18, 315 persons over 5 years of age were interviewed to estimate the overall annual incidence, patterns and severity of unintentional injuries for males and females in urban and rural areas over the preceding one year. Weighted estimates were computed adjusting for complex survey design …

Estimating Time-To-Event From Longitudinal Categorical Data Using Random Effects Markov Models: Application To Multiple Sclerosis Progression, Micha Mandel, Rebecca A. Betensky

Harvard University Biostatistics Working Paper Series

No abstract provided.

Simultaneous Confidence Intervals Based On The Percentile Bootstrap Approach, Micha Mandel, Rebecca A. Betensky

Harvard University Biostatistics Working Paper Series

No abstract provided.

Discrete Kato-Type Theorem On Inviscid Limit Of Navier-Stokes Flows, Wenfang Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The inviscid limit of wall bounded viscous flows is one of the unanswered central questions in theoretical fluid dynamics. Here we present a somewhat surprising result related to numerical approximation of the problem. More precisely, we show that numerical solutions of the incompressible Navier-Stokes equations converge to the exact solution of the Euler equations at vanishing viscosity and vanishing mesh size provided that small scales of the order of U in the directions tangential to the boundary are not resolved in the scheme. Here is the kinematic viscosity of the fluid and U is the typical velocity taken to be …

Note On The Emergence Of Large Scale Coherent Structure Under Small Scale Random Bombardments: The Discrete Case, Andrew Majda, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We continue our study on mathematical justification of the emergence of large-scale coherent structure in a two-dimensional fluid system under small scale random bombardments. We treat the case of small-scale random bombardments at discrete times which is different from our earlier work [Commun. Pure Appl. Math. 59, 467 (2006)], where we approximated the small-scale random kicks by a continuous in time random process. in the absence of geophysical effects, the large-scale structure emerging out of the small-scale random forcing is the same as the case of continuous in time forcing that we studied before. © 2007 American Institute of Physics.

Balanced Proper Orthogonal Decomposition For Model Reduction Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we extend a method for reduced order model derivation for finite dimensional systems developed by Rowley to infinite dimensional systems. The method is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method is also applicable to nonlinear systems. The method is applied to a convection diffusion equation.

Random Effects Models In A Meta-Analysis Of The Accuracy Of Diagnostic Tests Within A Gold Standard In The Presence Of Missing Data, Haitao Chu, Sining Chen, Thomas A. Louis

Johns Hopkins University, Dept. of Biostatistics Working Papers

In evaluating the accuracy of diagnosis tests, it is common to apply two imperfect tests jointly or sequentially to a study population. In a recent meta-analysis of the accuracy of microsatellite instability testing (MSI) and traditional mutation analysis (MUT) in predicting germline mutations of the mismatch repair (MMR) genes, a Bayesian approach (Chen, Watson, and Parmigiani 2005) was proposed to handle missing data resulting from partial testing and the lack of a gold standard. In this paper, we demonstrate an improved estimation of the sensitivities and specificities of MSI and MUT by using a nonlinear mixed model and a Bayesian …

Identifying Patients Who Need Additional Biomarkers For Better Prediction Of Health Outcome Or Diagnosis Of Clinical Phenotype, Lu Tian, Tianxi Cai, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Identifying Effect Modifiers In Air Pollution Time-Series Studies Using A Two-Stage Analysis, Sandrah P. Eckel, Thomas A. Louis

Johns Hopkins University, Dept. of Biostatistics Working Papers

Studies of the health effects of air pollution such as the National Morbidity and Mortality Air Pollution Study (NMMAPS) relate changes in daily pollution to daily deaths in a sample of cities and calendar years. Generally, city-specific estimates are combined into regional and national estimates using two-stage models. Our two-stage analysis identifies effect modifiers of the relation between single-day lagged PM10 and daily mortality in people age 65 and older from the 50 largest NMMAPS cities. We build on the standard approach by "fractionating" city-specific analyses to produce month-year-city specific estimated air pollution effects (slopes) in Stage I. In Stage …

Responses To Weight Loss Treatment Among Obese Individuals With And Without Bed: A Matched-Study Meta-Analysis, Bruce E. Blaine, J. Rodman

Statistics Faculty/Staff Publications

The moderating influence of binge eating status on obese individuals’ responses to weight loss treatment was evaluated with a meta-analysis of 36 tests of weight loss treatment (n=792) that were matched to control key background variables. After controlling for pre-treatment weight, treatment produced more weight loss in samples of obese non- BED compared with obese BED participants. Weight loss treatment produced large posttreatment reductions in depression in both obese BED and non-BED samples. The results indicate that BED status moderated post-treatment weight loss among people in weight treatment programs. Obese BED (average weight loss= 1.3 kg) samples lost negligible weight …

Salivary Characteristics In 3 And 4 Year-Old Children With And Without Visible Caries, Gloria Yañez

Loma Linda University Electronic Theses, Dissertations & Projects

PURPOSE: To compare salivary characteristics in 3 and 4 year-old Head Start children with and without visible caries.

METHODS: This case-control study was performed on 84 healthy 3 and 4 year-old Head Start children. After consent and inclusion criteria were met, each child was screened and assigned to one of two test groups based on their caries status. Group 1 consisted of children with no visible evidence of caries, although non-visible caries may have been present. Group II consisted of children with visible evidence demonstrating three or more carious lesions. Each child's unstimulated and stimulated whole saliva samples were collected …

Comparison Of Laser And Phosphoric Acid Etching On Sealant Shear Bond Strength, Seth David Latimer

Loma Linda University Electronic Theses, Dissertations & Projects

PURPOSE: To compare the effect of traditional phosphoric acid etching with Er,Cr:YSGG laser enamel etching on the shear bond strength of sealant material.

METHODS: Extracted healthy third molars were mounted in acrylic exposing the flattest surface available. Three groups of twenty teeth were used to evaluate traditional acid etching with 37% phosphoric acid as a control group as well as two different laser settings. The sealant material was attached using specialized jigs and then subjected to shear bond strength testing utilizing the ultradent method (MTS machine). Statistical methods employed were the Kruskal-Wallis rank test and the Mann-Whitney U test.

RESULTS: …

Temporally Correlated Dirichlet Processes In Pollution Receptor Modeling, Matthew J. Heaton

Theses and Dissertations

Understanding the effect of human-induced pollution on the environment is an important precursor to promoting public health and environmental stability. One aspect of understanding pollution is understanding pollution sources. Various methods have been used and developed to understand pollution sources and the amount of pollution those sources emit. Multivariate receptor modeling seeks to estimate pollution source profiles and pollution emissions from concentrations of pollutants such as particulate matter (PM) in the air. Previous approaches to multivariate receptor modeling make the following two key assumptions: (1) PM measurements are independent and (2) source profiles are constant through time. Notwithstanding these assumptions, …

The Analysis Of Pixel Intensity (Myocardial Signal Density) Data: The Quantification Of Myocardial Perfusion By Imaging Methods., William F. Mccarthy, Douglas R. Thompson

COBRA Preprint Series

This paper described a number of important issues in the analysis of pixel intensity data, as well as approaches for dealing with these. We particularly emphasized the issue of clustering, which may be ubiquitous in studies of pixel intensity data. Clustering can take many forms, e.g., measurements of different sections of a heart or repeated measurements of the same research participant. Clustering typically has the effect of increasing variance estimates. When one fails to account for clustering, variance estimates may be unrealistically small, resulting in spurious significance. We illustrated several possible approaches to account for clustering, including adjusting standard errors …

Coronary Evaluation Using Multi-Detector Spiral Computed Tomography Angiography: Statistical Design And Analysis, William F. Mccarthy, Douglas R. Thompson, Bruce A. Barton

COBRA Preprint Series

Contrast-enhanced multi-detector row spiral computed tomography (MDCT) has been introduced as a method for non-invasive visualization of coronary artery stenosis. To determine the diagnostic accuracy of MDCT coronary angiography, as compared to the “gold standard” invasive coronary angiography, sensitivity and specificity are estimated (95% Confidence Intervals). Three separate levels of estimation are computed: at the patient level, at the coronary artery level, and at the coronary artery segment level. We review the methodology for the estimation of sensitivity and specificity of non-clustered binary data (patient level analysis) and present a methodology for the estimation of sensitivity and specificity that considers …

Bayesian Bivariate Image Analysis With Application To Dual Autoradiography, Timothy D. Johnson, Morand Piert

The University of Michigan Department of Biostatistics Working Paper Series

We present a Bayesian bivariate image model and apply it to a study that was designed to investigate the relationship between hypoxia and angiogenesis in an animal tumor model. Two radiolabeled tracers (one measuring angio- genesis, the other measuring hypoxia) were simultaneously injected into the animals, the tumors removed and autoradiographic images of the tracer concentrations were obtained. We model correlation between tracers with a mixture of bivariate normal distributions and the spatial correlation inherent in the images by means of the celebrated Potts model. Although the Potts model is typically used for image segmentation, we use it solely as …

Estimating The Effect Of Vigorous Physical Activity On Mortality In The Elderly Based On Realistic Individualized Treatment And Intention-To-Treat Rules, Oliver Bembom, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

The effect of vigorous physical activity on mortality in the elderly is difficult to estimate using conventional approaches to causal inference that define this effect by comparing the mortality risks corresponding to hypothetical scenarios in which all subjects in the target population engage in a given level of vigorous physical activity. A causal effect defined on the basis of such a static treatment intervention can only be identified from observed data if all subjects in the target population have a positive probability of selecting each of the candidate treatment options, an assumption that is highly unrealistic in this case since …

Evaluating The Roc Performance Of Markers For Future Events, Margaret Pepe, Yingye Zheng, Yuying Jin

UW Biostatistics Working Paper Series

Receiver operating characteristic (ROC) curves play a central role in the evaluation of biomarkers and tests for disease diagnosis. Predictors for event time outcomes can also be evaluated with ROC curves, but the time lag between marker measurement and event time must be acknowledged. We discuss different definitions of time-dependent ROC curves in the context of real applications. Several approaches have been proposed for estimation. We contrast retrospective versus prospective methods in regards to assumptions and flexibility, including their capacities to incorporate censored data, competing risks and different sampling schemes. Applications to two datasets are presented.

Analyzing Sequentially Randomized Trials Based On Causal Effect Models For Realistic Individualized Treatment Rules, Oliver Bembom, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In this paper, we argue that causal effect models for realistic individualized treatment rules represent an attractive tool for analyzing sequentially randomized trials. Unlike a number of methods proposed previously, this approach does not rely on the assumption that intermediate outcomes are discrete or that models for the distributions of these intermediate outcomes given the observed past are correctly specified. In addition, it generalizes the methodology for performing pairwise comparisons between individualized treatment rules by allowing the user to posit a marginal structural model for all candidate treatment rules simultaneously. If only a small number of candidate treatment rules are …

Quantitative Magnetic Resonance Image Analysis Via The Em Algorithm With Stochastic Variation, Xiaoxi Zhang, Timothy D. Johnson, Roderick J.A. Little

The University of Michigan Department of Biostatistics Working Paper Series

Quantitative Magnetic Resonance Imaging (qMRI) provides researchers insight into pathological and physiological alterations of living tissue, with the help of which, researchers hope to predict (local) therapeutic efficacy early and determine optimal treatment schedule. However, the analysis of qMRI has been limited to ad-hoc heuristic methods. Our research provides a powerful statistical framework for image analysis and sheds light on future localized adaptive treatment regimes tailored to the individual’s response. We assume in an imperfect world we only observe a blurred and noisy version of the underlying “true” scene via qMRI, due to measurement errors or unpredictable influences. We use …