Statistics and Probability Commons^™

A Novel And Simple Rule Of Thumb For Multiplicity Control In Equivalence Testing Using Two One-Sided Tests, Carolyn Lauzon, Brian S. Caffo

Johns Hopkins University, Dept. of Biostatistics Working Papers

Equivalence testing is growing in use in scientific research outside of its traditional role in the drug approval process. Largely due to its ease of use and recommendation from the United States Food and Drug Administration guidance, the most common statistical method for testing (bio)equivalence is the two one-sided tests procedure (TOST). Like classical point-null hypothesis testing, TOST is subject to multiplicity concerns as more comparisons are made. In this manuscript, a condition that bounds the family-wise error rate (FWER) using TOST is given. This condition then leads to a simple solution for controlling the FWER. Specifically, we demonstrate that …

Assessing Multivariate Heritability Through Nonparametric Methods, Benjamin Alan Carper

Theses and Dissertations

The similarities between generations of living subjects are often quantified by heritability. By distinguishing genotypic variation, or variation due to parental pairings, from phenotypic variation, or normal intraspecies variation, the heritability of traits can be estimated. Due to the multivariate nature of many traits, such as size and shape, computation of heritability can be difficult. Also, assessment of the variation of the heritability estimate is extremely difficult. This study uses nonparametric methods, namely the randomization test and the bootstrap, to obtain both a measure of the extremity of the observed heritability and an assessment of the uncertainty.

Fdr Controlling Procedure For Multi-Stage Analyses, Catherine Tuglus, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Multiple testing has become an integral component in genomic analyses involving microarray experiments where large number of hypotheses are tested simultaneously. However before applying more computationally intensive methods, it is often desirable to complete an initial truncation of the variable set using a simpler and faster supervised method such as univariate regression. Once such a truncation is completed, multiple testing methods applied to any subsequent analysis no longer control the appropriate Type I error rates. Here we propose a modified marginal Benjamini \& Hochberg step-up FDR controlling procedure for multi-stage analyses (FDR-MSA), which correctly controls Type I error in terms …

Estimating The Causal Effect Of Lower Tidal Volume Ventilation On Survival In Patients With Acute Lung Injury, Weiwei Wang, Daniel Scharfstein, Roy Brower, Dale Needham

Johns Hopkins University, Dept. of Biostatistics Working Papers

Acute lung injury (ALI) is a condition characterized by acute onset of severe hypoxemia and bliateral pulmonary infiltrates. ALI patients typically require mechanical ventilation in an intensive care unit. Low tidal volume ventilation (LTVV), a time-varying dynamic treatment regime, has been recommended as an effective ventilation strategy. This recommendation was based on the results of the ARMA study, a randomized clinical trial designed to compare low vs. high tidal volume strategies (ARDSNetwork, 2000) . After publication of the trial, some critics focused on the high non-adherence rates in the LTVV arm suggesting that non-adherence occurred because treating physicians felt that …

The Calculation Of The 97.5% Upper Confidence Bound: Application To Clustered Binary Data In A Binomial Non-Inferiority Two-Sample Trial., William F. Mccarthy

COBRA Preprint Series

This paper will discuss the analysis of a cluster randomized binomial non-inferiority two-sample trial. The determination of the intra-cluster correlation coefficient (ICC) and its use in the calculation of the 97.5% upper confidence bound for delta, the true difference in binomial proportions between the active control and the experimental treatment groups, will be outlined.

The Design And Sample Size Requirement For A Cluster Randomized Non-Inferiority Trial With Two Binary Co-Primary Outcomes., William F. Mccarthy

COBRA Preprint Series

This paper will discuss the design and sample size requirement for a cluster randomized non-inferiority trial with two binary co-primary outcomes. A hypothetical study (the EXAMPLE Trial) will be considered.

Lets assume the EXAMPLE Trial will consist of two separate binomial non-inferiority two-sample trials. Trial 1: the Coronary Artery Disease known population (co-primary 1) and Trial 2: the Coronary Artery Disease unknown population (co-primary 2). A physician-month cluster randomization scheme will be used. That is, for each trial (trial 1 and trial 2) every month for a 12-month period, each physician participating in the EXAMPLE Trial will be allocated a …

Bayesian Inference For Smoking Cessation With A Latent Cure State, Sheng Luo, Ciprian M. Crainiceanu, Thomas A. Louis, Nilanjan Chatterjee

Johns Hopkins University, Dept. of Biostatistics Working Papers

We present a Bayesian approach to modeling dynamic smoking addiction behavior processes when cure is not directly observed due to censoring. Subject-specic probabilities model the stochastic transitions among three behavioral states: smoking, transient quitting, and permanent quitting (absorbent state). A multivariate normal distribution for random e ects is used to account for the potential correlation among the subject-specic transition probabilities. Inference is conducted using a Bayesian framework via Markov Chain Monte Carlo simulation. This framework provides various measures of subject-specic predictions, which are useful for policy making, intervention development, and evaluation. Simulations are used to validate our Bayesian methodology, and …

Semiparametric And Nonparametric Methods For Evaluating Risk Prediction Markers In Case-Control Studies, Ying Huang, Margaret Pepe

UW Biostatistics Working Paper Series

The performance of a well calibrated risk model, Risk(Y)=P(D=1|Y), can be characterized by the population distribution of Risk(Y) and displayed with the predictiveness curve. Better performance is characterized by a wider distribution of Risk(Y), since this corresponds to better risk stratification in the sense that more subjects are identified at low and high risk for the outcome D=1. Although methods have been developed to estimate predictiveness curves from cohort studies, most studies to evaluate novel risk prediction markers employ case-control designs. Here we develop semiparametric and nonparametric methods that accommodate case-control data and assume apriori knowledge of P(D=1). Large and …

Ordinal Regression To Evaluate Student Ratings Data, Emily Brooke Bell

Theses and Dissertations

Student evaluations are the most common and often the only method used to evaluate teachers. In these evaluations, which typically occur at the end of every term, students rate their instructors on criteria accepted as constituting exceptional instruction in addition to an overall assessment. This presentation explores factors that influence student evaluations using the teacher ratings data of Brigham Young University from Fall 2001 to Fall 2006. This project uses ordinal regression to model the probability of an instructor receiving a good, average, or poor rating. Student grade, instructor status, class level, student gender, total enrollment, term, GE class status, …

Confluent Mappings And Arc Kelley Continua, W. J. Charatonik, Janusz R. Prajs, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A Kelley continuum X, also called a continuum with the property of Kelley, such that, for each p X, each subcontinuum K containing p is approximated by arc-wise connected continua containing p, is called an arc Kelley continuum. A continuum homeomorphic to the inverse limit of locally connected continua with confluent bonding maps is said to be confluently LC-representable. The main subject of the paper is a study of deep connections between the arc Kelley continua and confluent mappings. It is shown that if a continuum X admits, for each ε > 0, a confluent ε-mapping onto a(n) (arc) Kelley continuum, …

Existence Of Multiple-Stable Equilibria For A Multi-Drug-Resistant Model Of Mycobacterium Tuberculosis, Abba B. Gumel, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

The resurgence of multi-drug-resistant tuberculosis in some parts of Europe and North America calls for a mathematical study to assess the impact of the emergence and spread of such strain on the global effort to effectively control the burden of tuberculosis. This paper presents a deterministic compartmental model for the transmission dynamics of two strains of tuberculosis, a drug-sensitive (wild) one and a multi-drug-resistant strain. The model allows for the assessment of the treatment of people infected with the wild strain. The qualitative analysis of the model reveals the following. The model has a disease-free equilibrium, which is locally asymptotically …

Generically There Is But One Self Homeomorphism Of The Cantor Set, Ethan Akin, Eli Glasner, Benjamin Weiss

Mathematics and Statistics Faculty Research & Creative Works

We describe a self-homeomorphism R of the Cantor set X and then show that its conjugacy class in the Polish group H(X) of all homeomorphisms of X forms a dense Gδ subset of H(X). We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class. © 2008 American Mathematical Society.

A Semiparametric Stochastic Volatility Model, Jun Yu

Research Collection School Of Economics

This paper examines how volatility responds to return news in the context of stochastic volatility (SV) using a nonparametric method. The correlation structure in the classical leverage SV model is generalized based on a linear spline. In the new model the correlation between the return innovation and volatility innovation is dependent on the type of news arrived to the market. Theoretical properties of the proposed model are examined. A simulation-based maximum likelihood method is developed to estimate the new model. Simulations show that the estimation method provides reliable parameter estimates. The new model is fitted to daily and weekly data …

On The Designation Of The Patterned Associations For Longitudinal Bernoulli Data: Weight Matrix Versus True Correlation Structure?, Hanjoo Kim, Joseph M. Hilbe, Justine Shults

UPenn Biostatistics Working Papers

Due to potential violation of standard constraints for the correlation for binary data, it has been argued recently that the working correlation matrix should be viewed as a weight matrix that should not be confused with the true correlation structure. We propose two arguments to support our view to the contrary for the first-order autoregressive AR(1) correlation matrix. First, we prove that the standard constraints are not unduly restrictive for the AR(1) structure that is plausible for longitudinal data; furthermore, for the logit link function the upper boundary value only depends on the regression parameter and the change in covariate …

Bringing Game Theory To Hypothesis Testing: Establishing Finite Sample Bounds On Inference, Karl H. Schlag

COBRA Preprint Series

Small sample properties are of fundamental interest when only limited data is available. Exact inference is limited by constraints imposed by specific nonrandomized tests and of course also by lack of more data. These effects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a fictitious game against nature. We use this method to investigate sequential …

Perbandingan Analisis Regresi Logistik Dengan Analisis Propensity Score Matching Pada Studi Kasus Imunisasi Bayi, Waras Budi Utomo

Kesmas

Analisis multivariat konvensioanal tidak selalu merupakan metode ideal untuk memprediksi efek pajanan pada studi-studi observasional. Ketika distribusi kovariat antara kelompok pajanan berbeda besar, penyesuaan dengan teknik multivariat konvensioanl tidak cukup menyeimbangkan kelompok tersebut. Bias yang tersisa dapat menghambat penarikan kesimpulan yang valid. Tujuan penelitian ini adalah membandingkan hasil analisis multivariat konvensional dengan analisis metoda propensity score matching pada studi kasus data sekunder imunisasi bayi ASUH KAP2 2003. Penelitian ini menemukan nilai OR metoda regresi logistik (0,99) berbeda dengan metoda propensity score matching (0,96). Metoda propensity score matching berhasil menjodohkan 574 subjek (68,27%). Untuk evaluasi pengaruh faktor risiko disarankan menggunakan model …

Transient Optical Sky Survey Automated Telescope System, Elena Hadjiyska, Philip Lubin, Scott Taylor, Gary B. Hughes

Statistics

We describe the optical design of a sky survey system comprised of small aperture telescope tube assemblies mounted on a common semi-equatorial frame with a single polar axis. It is the first ground-based instrument to create a map of transients down to optical m=17 by imaging a fixed-declination strip of the sky on a nightly basis. The system is fully remotely automated and physically robust. The mount tracks the sky using a motion controller, drive motor, and a laser rotary encoder. The prototype configuration is suited to house up to 6 telescopes on the current mount and is easily expandable …

Estimation And Testing For The Effect Of A Genetic Pathway On A Disease Outcome Using Logistic Kernel Machine Regression Via Logistic Mixed Models, Dawei Liu, Debashis Ghosh, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Powerful And Flexible Multilocus Association Test For Quantitative Traits, Lydia Coulter Kwee, Dawei Liu, Xihong Lin, Debashis Ghosh, Michael P. Epstein

Harvard University Biostatistics Working Paper Series

No abstract provided.

Nonparametric Regression Using Local Kernel Estimating Equations For Correlated Failure Time Data, Zhangsheng Yu, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Comparison Of Methods For Estimating The Causal Effect Of A Treatment In Randomized Clinical Trials Subject To Noncompliance, Rod Little, Qi Long, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Semiparametric Maximum Likelihood Estimation In Normal Transformation Models For Bivariate Survival Data, Yi Li, Ross L. Prentice, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Accounting For Errors From Predicting Exposures In Environmental Epidemiology And Environmental Statistics, Adam A. Szpiro, Lianne Sheppard, Thomas Lumley

UW Biostatistics Working Paper Series

PLEASE NOTE THAT AN UPDATED VERSION OF THIS RESEARCH IS AVAILABLE AS WORKING PAPER 350 IN THE UNIVERSITY OF WASHINGTON BIOSTATISTICS WORKING PAPER SERIES (http://www.bepress.com/uwbiostat/paper350).

In environmental epidemiology and related problems in environmental statistics, it is typically not practical to directly measure the exposure for each subject. Environmental monitoring is employed with a statistical model to assign exposures to individuals. The result is a form of exposure misspecification that can result in complicated errors in the health effect estimates if the exposure is naively treated as known. The exposure error is neither “classical” nor “Berkson”, so standard regression calibration methods …

A Naive, Robust And Stable State Estimate, Todd Gordon Remund

Theses and Dissertations

A naive approach to filtering for feedback control of dynamic systems that is robust and stable is proposed. Simulations are run on the filters presented to investigate the robustness properties of each filter. Each simulation with the comparison of the filters is carried out using the usual mean squared error. The filters to be included are the classic Kalman filter, Krein space Kalman, two adjustments to the Krein filter with input modeling and a second uncertainty parameter, a newly developed filter called the Naive filter, bias corrected Naive, exponentially weighted moving average (EWMA) Naive, and bias corrected EWMA Naive filter.

Supervised Distance Matrices: Theory And Applications To Genomics, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a new approach to studying the relationship between a very high dimensional random variable and an outcome. Our method is based on a novel concept, the supervised distance matrix, which quantifies pairwise similarity between variables based on their association with the outcome. A supervised distance matrix is derived in two stages. The first stage involves a transformation based on a particular model for association. In particular, one might regress the outcome on each variable and then use the residuals or the influence curve from each regression as a data transformation. In the second stage, a choice of distance …

Analysis Of Subgroup Effects In Randomized Trials When Subgroup Membership Is Informatively Missing: Application To The Madit Ii Study, Daniel O. Scharfstein, Georgiana Onicescu, Steven Goodman

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper, we develop and implement a general sensitivity analysis methodology for drawing inference about subgroup effects in a two-arm randomized trial when subgroup status is only known for a non-random sample in one of the trial arms. The methodology is developed in the context of the MADIT II study, a randomized trial designed to evaluate the effectiveness of implantable defibrillators on survival.

Causal Inference In Observational Studies With Outcome-Dependent Sampling, Weiwei Wang, Daniel Scharfstein, Zhiqiang Tan, Ellen J. Mackenzie

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper, we consider estimation of the causal effect of a treatment on an outcome from observational data collected in two phases. In the first phase, a simple random sample of individuals are drawn from a population. On these individuals, information is obtained on treatment, outcome, and a few low-dimensional confounders. These individuals are then stratified according to these factors. In the second phase, a random sub-sample of individuals are drawn from each stratum, with known, stratum-specific selection probabilities. On these individuals, a rich set of confounding factors are collected. In this setting, we introduce four estimators: (1) simple …

Statistical Methods For Image Registration And Denoising, Matthew D. Sambora

Theses and Dissertations

This dissertation describes research into image processing techniques that enhance military operational and support activities. The research extends existing work on image registration by introducing a novel method that exploits local correlations to improve the performance of projection-based image registration algorithms. The dissertation also extends the bounds on image registration performance for both projection-based and full-frame image registration algorithms and extends the Barankin bound from the one-dimensional case to the problem of two-dimensional image registration. It is demonstrated that in some instances, the Cramer-Rao lower bound is an overly-optimistic predictor of image registration performance and that under some conditions, the …

Model-Based Clustering Of Methylation Array Data: A Recursive-Partitioning Algorithm For High-Dimensional Data Arising As A Mixture Of Beta Distributions, E. Andres Houseman, Brock C. Christensen, Ru-Fang Yeh, Carmen J. Marsit, Margaret R. Karagas, Margaret Wrensch, Heather H. Nelson, Joseph Wiemels, Shichun Zheng, John K. Wiencke, Karl T. Kelsey

Harvard University Biostatistics Working Paper Series

No abstract provided.

Confidence Intervals For The Population Mean Tailored To Small Sample Sizes, With Applications To Survey Sampling, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

The validity of standard confidence intervals constructed in survey sampling is based on the central limit theorem. For small sample sizes, the central limit theorem may give a poor approximation, resulting in confidence intervals that are misleading. We discuss this issue and propose methods for constructing confidence intervals for the population mean tailored to small sample sizes.

We present a simple approach for constructing confidence intervals for the population mean based on tail bounds for the sample mean that are correct for all sample sizes. Bernstein's inequality provides one such tail bound. The resulting confidence intervals have guaranteed coverage probability …