Statistics and Probability Commons^™

Geographic Factors Of Residential Burglaries - A Case Study In Nashville, Tennessee, Jonathan A. Hall

Masters Theses & Specialist Projects

This study examines geographic patterns and geographic factors of residential burglary at the Nashville, TN area for a twenty year period at five year interval starting in 1988. The purpose of this study is to identify what geographic factors have impacted on residential burglary rates, and if there were changes in the geographic patterns of residential burglary over the study period. Several criminological theories guide this study, with the most prominent being Social Disorganization Theory and Routine Activities Theory. Both of these theories focus on the relationships of place and crime. A number of spatial analysis methods are hence adopted …

Multilevel Functional Principal Component Analysis For High-Dimensional Data, Vadim Zipunnikov, Brian Caffo, Ciprian Crainiceanu, David M. Yousem, Christos Davatzikos, Brian S. Schwartz

Johns Hopkins University, Dept. of Biostatistics Working Papers

We propose fast and scalable statistical methods for the analysis of hundreds or thousands of high dimensional vectors observed at multiple visits. The proposed inferential methods avoid the difficult task of loading the entire data set at once in the computer memory and use sequential access to data. This allows deployment of our methodology on low-resource computers where computations can be done in minutes on extremely large data sets. Our methods are motivated by and applied to a study where hundreds of subjects were scanned using Magnetic Resonance Imaging (MRI) at two visits roughly five years apart. The original data …

Landmark Prediction Of Survival, Layla Parast, Tianxi Cai

Harvard University Biostatistics Working Paper Series

No abstract provided.

Longitudinal Penalized Functional Regression, Jeff Goldsmith, Ciprian M. Crainiceanu, Brian Caffo, Daniel Reich

Johns Hopkins University, Dept. of Biostatistics Working Papers

We propose a new regression model and inferential tools for the case when both the outcome and the functional exposures are observed at multiple visits. This data structure is new but increasingly present in applications where functions or images are recorded at multiple times. This raises new inferential challenges that cannot be addressed with current methods and software. Our proposed model generalizes the Generalized Linear Mixed Effects Model (GLMM) by adding functional predictors. Smoothness of the functional coefficients is ensured using roughness penalties estimated by Restricted Maximum Likelihood (REML) in a corresponding mixed effects model. This method is computationally feasible …

On Two-Stage Hypothesis Testing Procedures Via Asymptotically Independent Statistics, James Dai, Charles Kooperberg, Michael L. Leblanc, Ross Prentice

UW Biostatistics Working Paper Series

Kooperberg and LeBlanc (2008) proposed a two-stage testing procedure to screen for significant interactions in genome-wide association (GWA) studies by a soft threshold on marginal associations (MA), though its theoretical properties and generalization have not been elaborated. In this article, we discuss conditions that are required to achieve strong control of the Family-Wise Error Rate (FWER) by such procedures for low or high-dimensional hypothesis testing. We provide proof of asymptotic independence of marginal association statistics and interaction statistics in linear regression, logistic regression, and Cox proportional hazard models in a randomized clinical trial (RCT) with a rare event. In case-control …

Stratifying Subjects For Treatment Selection With Censored Event Time Data From A Comparative Study, Lihui Zhao, Tianxi Cai, Lu Tian, Hajime Uno, Scott D. Solomon, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Comparison Of Non-Surgical And Surgical Endodontic Retreatment: A Systematic Review, Robert Corr

Loma Linda University Electronic Theses, Dissertations & Projects

Primary root canal therapy has been shown to be a predictable procedure with a high degree of success ^1-4, however failures can occur after treatment. Treatment options for the preservation of teeth that have had previous endodontic treatment but demonstrate persistent disease include non-surgical (orthograde) or surgical (retrograde) endodontic retreatment, assuming the tooth is restorable, periodontally sound, and the patient desires to retain the tooth. The purpose of this study was to conduct a systematic review of the current available evidence to compare the clinical and radiographic outcomes of nonsurgical with those of surgical endodontic retreatment. Methodology began with …

On Two-Stage Hypothesis Testing Procedures Via Asymptotically Independent Statistics, James Y. Dai, Charles Kooperberg, Michael Leblanc, Ross L. Prentice

UW Biostatistics Working Paper Series

Kooperberg08 proposed a two-stage testing procedure to screen for significant interactions in genome-wide association (GWA) studies by a soft threshold on marginal associations (MA), though its theoretical properties and generalization have not been elaborated. In this article, we discuss conditions that are required to achieve strong control of the Family-Wise Error Rate (FWER) by such procedures for low or high-dimensional hypothesis testing. We provide proof of asymptotic independence of marginal association statistics and interaction statistics in linear regression, logistic regression, and Cox proportional hazard models in a randomized clinical trial (RCT) with a rare event. In case-control studies nested within …

A Perturbation Method For Inference On Regularized Regression Estimates, Jessica Minnier, Lu Tian, Tianxi Cai

Harvard University Biostatistics Working Paper Series

No abstract provided.

Principled Sure Independence Screening For Cox Models With Ultra-High-Dimensional Covariates, Sihai Dave Zhao, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Data Mining As Applied To The Socialsciences, Walter Morris

Cornerstone 3 Reports : Interdisciplinary Informatics

No abstract provided.

Optimizing Randomized Trial Designs To Distinguish Which Subpopulations Benefit From Treatment, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

It is a challenge to evaluate experimental treatments where it is suspected that the treatment effect may only be strong for certain subpopulations, such as those having a high initial severity of disease, or those having a particular gene variant. Standard randomized controlled trials can have low power in such situations. They also are not optimized to distinguish which subpopulations benefit from a treatment. With the goal of overcoming these limitations, we consider randomized trial designs in which the criteria for patient enrollment may be changed, in a preplanned manner, based on interim analyses. Since such designs allow data-dependent changes …

The Strength Of Statistical Evidence For Composite Hypotheses: Inference To The Best Explanation, David R. Bickel

COBRA Preprint Series

A general function to quantify the weight of evidence in a sample of data for one hypothesis over another is derived from the law of likelihood and from a statistical formalization of inference to the best explanation. For a fixed parameter of interest, the resulting weight of evidence that favors one composite hypothesis over another is the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function over the parameter of interest. Since the weight of evidence is generally only known up to a nuisance parameter, it is approximated by replacing the likelihood function with …

Model-Robust Regression And A Bayesian `Sandwich' Estimator, Adam A. Szpiro, Kenneth M. Rice, Thomas Lumley

UW Biostatistics Working Paper Series

The published version of this paper in Annals of Applied Statistics (Vol. 4, No. 4 (2010), 2099–2113) is available from the journal web site at http://dx.doi.org/10.1214/10-AOAS362.

We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber-White sandwich estimator. The sandwich estimator is known to provide asymptotically correct frequentist inference, even when standard modeling assumptions such as linearity and homoscedasticity in the data-generating mechanism are violated. Our derivation provides a compelling Bayesian justification for using this simple and popular tool, and it also clarifies what is being estimated …

Asymptotic Properties Of The Sequential Empirical Roc And Ppv Curves, Joseph S. Koopmeiners, Ziding Feng

UW Biostatistics Working Paper Series

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three common measures of performance for a diagnostic biomarker. The independent increments covariance structure assumption is common in the group sequential study design literature. Showing that summary measures of the ROC, PPV and NPV curves have an independent increments covariance structure will provide the theoretical foundation for designing group sequential diagnostic biomarker studies. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. In this paper we derive asymptotic theory …

Estimating Causal Effects In Trials Involving Multi-Treatment Arms Subject To Non-Compliance: A Bayesian Frame-Work, Qi Long, Roderick J. Little, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Super Learner In Prediction, Eric C. Polley, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Super learning is a general loss based learning method that has been proposed and analyzed theoretically in van der Laan et al. (2007). In this article we consider super learning for prediction. The super learner is a prediction method designed to find the optimal combination of a collection of prediction algorithms. The super learner algorithm finds the combination of algorithms minimizing the cross-validated risk. The super learner framework is built on the theory of cross-validation and allows for a general class of prediction algorithms to be considered for the ensemble. Due to the previously established oracle results for the cross-validation …

Assessing Noninferiority In A Three-Arm Trial Using The Bayesian Approach, Pulak Ghosh, Farouk S. Nathoo, Mithat Gonen, Ram C. Tiwari

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm clinical trial is usually recommended for non-inferiority trials by the Food and Drug Administration (FDA). The three-arm trial consists of a placebo, a reference, and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with …

Survival Prediction For Brain Tumor Patients Using Gene Expression Data, Vinicius Bonato

Dissertations and Theses (Open Access)

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. …

Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations, Lu Wang, Andrea Rotnitzky, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Simple Examples Of Estimating Causal Effects Using Targeted Maximum Likelihood Estimation, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We present a brief overview of targeted maximum likelihood for estimating the causal effect of a single time point treatment and of a two time point treatment. We focus on simple examples demonstrating how to apply the methodology developed in (van der Laan and Rubin, 2006; Moore and van der Laan, 2007; van der Laan, 2010a,b). We include R code for the single time point case.

Likelihood Ratio Testing For Admixture Models With Application To Genetic Linkage Analysis, Chong-Zhi Di, Kung-Yee Liang

Johns Hopkins University, Dept. of Biostatistics Working Papers

We consider likelihood ratio tests (LRT) and their modifications for homogeneity in admixture models. The admixture model is a special case of two component mixture model, where one component is indexed by an unknown parameter while the parameter value for the other component is known. It has been widely used in genetic linkage analysis under heterogeneity, in which the kernel distribution is binomial. For such models, it is long recognized that testing for homogeneity is nonstandard and the LRT statistic does not converge to a conventional 2 distribution. In this paper, we investigate the asymptotic behavior of the LRT for …

Graphical Procedures For Evaluating Overall And Subject-Specific Incremental Values From New Predictors With Censored Event Time Data, Hajime Uno, Tianxi Cai, Lu Tian, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

A New Class Of Dantzig Selectors For Censored Linear Regression Models, Yi Li, Lee Dicker, Sihai Dave Zhao

Harvard University Biostatistics Working Paper Series

No abstract provided.

Statistical Power Analysis Using Sas And R, Peter Osmena

Statistics

Statistical power is something that has to be considered when designing an experiment. The power is used to determine the usefulness of the test. In this paper the concept of power and what it is will be discussed. A general ANOVA test and a Chi Squared test will be discussed in greater depth. Computers make these power calculations relatively easy to compute, considering they are used right. SAS and R both have the capabilities to make these calculations for a different variety of tests. Calculating power for a general ANOVA test and a Chi Squared test using these programs are …

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

Gamma-Ray Spectroscopy: Meteorite Samples And The Search For 98tc, Kristopher L. Merolla

Physics

The focus of this project is low-count-level gamma-ray spectroscopy on meteorite samples in search of a particular isotope of Technetium (98Tc), which according to stellar theory, should be present in the universe. The spectral lines for 99Tc have, however, been observed in S-, M-, and N- type stars, which makes finding 98Tc created naturally a possibility, and thus a search can be justified.

Penalized Functional Regression, Jeff Goldsmith, Jennifer Feder, Ciprian M. Crainiceanu, Brian Caffo, Daniel Reich

Johns Hopkins University, Dept. of Biostatistics Working Papers

We develop fast fitting methods for generalized functional linear models. An undersmooth of the functional predictor is obtained by projecting on a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. Our method can be applied to many functional data designs including functions measured with and without error, sparsely or densely sampled. The methods also extend to the case of multiple functional predictors or functional predictors with a natural multilevel structure. Our approach can be implemented using standard mixed effects software and is computationally fast. Our methodology is motivated by a diffusion tensor imaging …

Regression Adjustment And Stratification By Propensty Score In Treatment Effect Estimation, Jessica A. Myers, Thomas A. Louis

Johns Hopkins University, Dept. of Biostatistics Working Papers

Propensity score adjustment of effect estimates in observational studies of treatment is a common technique used to control for bias in treatment assignment. In situations where matching on propensity score is not possible or desirable, regression adjustment and stratification are two options. Regression adjustment is used most often and can be highly efficient, but it can lead to biased results when model assumptions are violated. Validity of the stratification approach depends on fewer model assumptions, but is less efficient than regression adjustment when the regression assumptions hold. To investigate these issues, by simulation we compare stratification and regression adjustments. We …

Comparison And Application Of Three Decorrelation Methods Pca, Maf And Acdc, Jacqueline Ferreira

Theses : Honours

Geostatistics is a branch of applied mathematics that deals with spatially correlated data. Analysing and modelling spatially correlated data can be difficult and time consuming, especially for a multivariate data set. One of the techniques used to make analysis and modelling easier involves decorrelation, whereby a linear transformation on the sample variables is used to associate the spatially correlated variables with a set of decorrelated factors which are statistically and spatially independent. PCA was one of the first multivariate techniques and is mostly used as a data reduction technique. A popular alternative decorrelation technique often used in the mining industry …