Statistics and Probability Commons^™

A Comparison Of Equivalence Testing In Combination With Hypothesis Testing And Effect Sizes, Christopher J. Mecklin

Journal of Modern Applied Statistical Methods

Equivalence testing, an alternative to testing for statistical significance, is little used in educational research. Equivalence testing is useful in situations where the researcher wishes to show that two means are not significantly different. A simulation study assessed the relationships between effect size, sample size, statistical significance, and statistical equivalence.

Semi-Parametric Box-Cox Power Transformation Models For Censored Survival Observations, Tianxi Cai, Lu Tian, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Unification Of Variance Components And Haseman-Elston Regression For Quantitative Trait Linkage Analysis, Wei-Min Chen, Karl W. Broman, Kung-Yee Liang

Johns Hopkins University, Dept. of Biostatistics Working Papers

Two of the major approaches for linkage analysis with quantitative traits in humans include variance components and Haseman-Elston regression. Previously, these have been viewed as quite separate methods. We describe a general model, fit by use of generalized estimating equations (GEE), for which the variance components and Haseman-Elston methods (including many of the extensions to the original Haseman-Elston method) are special cases, corresponding to different choices for a working covariance matrix. We also show that the regression-based test of Sham et al.(2002) is equivalent to a robust score statistic derived from our GEE approach. These results have several important implications. …

Smooth Quantile Ratio Estimation, Francesca Dominici, Leslie Cope, Daniel Q. Naiman, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

In a study of health care expenditures attributable to smoking, we seek to compare the distribution of medical costs for persons with lung cancer or chronic obstructive pulmonary disease (cases) to those without (controls) using a national survey which includes hundreds of cases and thousands of controls. The distribution of costs is highly skewed toward larger values, making estimates of the mean from the smaller sample dependent on a small fraction of the biggest values. One approach to deal with the smaller sample is to rely on a simple parametric model such as the log-normal, but this makes the undesirable …

Hierarchical Bivariate Time Series Models: A Combined Analysis Of The Effects Of Particulate Matter On Morbidity And Mortality, Francesca Dominici, Antonella Zanobetti, Scott L. Zeger, Joel Schwartz, Jonathan M. Samet

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper we develop a hierarchical bivariate time series model to characterize the relationship between particulate matter less than 10 microns in aerodynamic diameter (PM10) and both mortality and hospital admissions for cardiovascular diseases. The model is applied to time series data on mortality and morbidity for 10 metropolitan areas in the United States from 1986 to 1993. We postulate that these time series should be related through a shared relationship with PM10.

At the first stage of the hierarchy, we fit two seemingly unrelated Poisson regression models to produce city-specific estimates of the log relative rates of mortality …

Statistical Inferences Based On Non-Smooth Estimating Functions, Lu Tian, Jun S. Liu, Mary Zhao, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

On The Cox Model With Time-Varying Regression Coefficients, Lu Tian, David Zucker, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Maximum Likelihood Estimation Of Ordered Multinomial Parameters , Nicholas P. Jewell, Jack Kalbfleisch

The University of Michigan Department of Biostatistics Working Paper Series

The pool-adjacent violator-algorithm (Ayer et al., 1955) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see, Barlow et al., 1972). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of ‘ordered’ multinomial parameters pi = (p1i, p2i, . . . , pmi) for 1 < = I < = k, where ordered means that pj1 < = pj2 < = .. . < = pjk for each j with 1 < = j < = m-1. The data consist of k independent observations X1, . . . ,Xk where Xi has a multinomial distribution with probability parameter pi and known index ni > = 1. By making use of variants of the pool adjacent violator algorithm, …

Nonparametric Estimation Of The Bivariate Recurrence Time Distribution, Chiung-Yu Huang, Mei-Cheng Wang

Johns Hopkins University, Dept. of Biostatistics Working Papers

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution …

A Nested Unsupervised Approach To Identifying Novel Molecular Subtypes, Elizabeth Garrett, Giovanni Parmigiani

Johns Hopkins University, Dept. of Biostatistics Working Papers

In classification problems arising in genomics research it is common to study populations for which a broad class assignment is known (say, normal versus diseased) and one seeks to find undiscovered subclasses within one or both of the known classes. Formally, this problem can be thought of as an unsupervised analysis nested within a supervised one. Here we take the view that the nested unsupervised analysis can successfully utilize information from the entire data set for constructing and/or selecting useful predictors. Specifically, we propose a mixture model approach to the nested unsupervised problem, where the supervised information is used to …

Generalized Residual Multiple Model Adaptive Estimation Of Parameters And States, Charles D. Ormsby

Theses and Dissertations

This dissertation develops a modification to the standard Multiple Model Adaptive Estimator (MMAE) which allows the use of a new "generalized residual" in the hypothesis conditional probability calculation. The generalized residual is a linear combination of traditional Kalman filter residuals and "post-fit" Kalman filter residuals which are calculated after measurement incorporation. This modified MMAE is termed a Generalized Residual Multiple Model Adaptive Estimator (GRMMAE). The dissertation provides a derivation of the hypothesis conditional probability formula which the GRMMAE uses to calculate probabilities that each elemental filter in the GRMMAE contains the correct parameter value. Through appropriate choice of a single …

A Population Pharmacokinetic Model With Time-Dependent Covariates Measured With Errors, Lang Lil, Xihong Lin, Mort B. Brown, Suneel Gupta, Kyung-Hoon Lee

The University of Michigan Department of Biostatistics Working Paper Series

We propose a population pharmacokinetic (PK) model with time-dependent covariates measured with errors. This model is used to model S-oxybutynin's kinetics following an oral administration of Ditropan, and allows the distribution rate to depend on time-dependent covariates blood pressure and heart rate, which are measured with errors. We propose two two-step estimation methods: the second order two-step method with numerical solutions of differential equations (2orderND), and the second order two-step method with closed form approximate solutions of differential equations (2orderAD). The proposed methods are computationally easy and require fitting a linear mixed model at the first step and a nonlinear …

Student Fact Book, Fall 2003, Twenty-Seventh Annual Edition, Wright State University, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 2003.

Almost Periodic Sets And Subactions In Topological Dynamics, Ethan Akin, Joseph Auslander

Mathematics and Statistics Faculty Research & Creative Works

Let Γ be a group with subgroup λ. We show, under certain conditions, that an almost periodic point for the action of λ is also almost periodic for Γ. This is applied to obtain a theorem of Glasner.

Exact Multiplicity For Periodic Solutions Of Duffing Type, Hongbin Chen, Yi Li, Xiaojie Hou

Mathematics and Statistics Faculty Publications

In this paper, we study the following Duffing-type equation:

x″+cx′+g(t,x)=h(t),

where g(t,x) is a 2π-periodic continuous function in t and concave–convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

Stochastic Models Based On Molecular Hybridization Theory For Short Oligonucleotide Microarrays, Zhijin Wu, Richard Leblanc, Rafael A. Irizarry

Johns Hopkins University, Dept. of Biostatistics Working Papers

High density oligonucleotide expression arrays are a widely used tool for the measurement of gene expression on a large scale. Affymetrix GeneChip arrays appear to dominate this market. These arrays use short oligonucleotides to probe for genes in an RNA sample. Due to optical noise, non-specific hybridization, probe-specific effects, and measurement error, ad-hoc measures of expression, that summarize probe intensities, can lead to imprecise and inaccurate results. Various researchers have demonstrated that expression measures based on simple statistical models can provide great improvements over the ad-hoc procedure offered by Affymetrix. Recently, physical models based on molecular hybridization theory, have been …

Efficient Semiparametric Marginal Estimation For Longitudinal/Clustered Data, Naisyin Wang, Raymond J. Carroll, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

We consider marginal generalized semiparametric partially linear models for clustered data. Lin and Carroll (2001a) derived the semiparametric efficinet score funtion for this problem in the mulitvariate Gaussian case, but they were unable to contruct a semiparametric efficient estimator that actually achieved the semiparametric information bound. We propose such an estimator here and generalize the work to marginal generalized partially liner models. Asymptotic relative efficincies of the estimation or throughout are investigated. The finite sample performance of these estimators is evaluated through simulations and illustrated using a longtiudinal CD4 count data set. Both theoretical and numerical results indicate that properly …

Equivalent Kernels Of Smoothing Splines In Nonparametric Regression For Clustered/Longitudinal Data, Xihong Lin, Naisyin Wang, Alan H. Welsh, Raymond J. Carroll

The University of Michigan Department of Biostatistics Working Paper Series

We compare spline and kernel methods for clustered/longitudinal data. For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, the recent work of Welsh, et al. (2002) shows that the same is not true for clustered/longitudinal data. First, conventional kernel methods fail to account for the within- cluster correlation, while spline methods are able to account for this correlation. Second, kernel methods and spline methods were found to have different local behavior, with conventional kernels being local and splines being non-local. To resolve these differences, we show that a smoothing …

Histospline Method In Nonparametric Regression Models With Application To Clustered/Longitudinal Data, Raymond J. Carroll, Peter Hall, Tatiyana V. Apanasovich, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

Kernel and smoothing methods for nonparametric function and curve estimation have been particularly successful in "standard" settings, where function values are observed subject to independent errors. However, when aspects of the function are known parametrically, or where the sampling scheme has significant structure, it can be quite difficult to adapt standard methods in such a way that they retain good statistical performance and continue to enjoy easy computability and good numerical properties. In particular, when using local linear modeling it is often awkward to both respect the sampling scheme and produce an estimator with good variance properties, without resorting to …

Measuring Treatment Effects Using Semiparametric Models, Zhuo Yu, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In order to estimate the causal effect of treatments on an outcome of interest, one has to account for the effect of confounding factors which covary with the treatments and also contribute to the outcome of interest. In this paper, we use the semiparametric regression model to estimate the causal parameters. We assume the causal effect of the treatments can be described by the parametric component of the semiparametric regression model. Following the general methodology which was developed in van der Laan and Robins (2002) we give the orthogonal complement of the nuisance tangent space which identifies all the estimating …

A Varying-Coefficient Cox Model For The Effect Of Age At A Marker Event On Age At Menopause, Bin Nan, Xihong Lin, Lynda D. Lisabeth, Sioban D. Harlow

The University of Michigan Department of Biostatistics Working Paper Series

. It is of recent interest in reproductive health research to investigate the validity of a marker event for the onset of menopausal transition and to estimate age at menopause using age at the marker event. We propose a varying coefficient Cox model to investigate the association between age at a marker event, denned as a specific bleeding pattern change, and age at menopause, where both events are subject to censoring and their association varies with age at the marker event. Estimation proceeds using the regression spline method. The proposed method is applied to the Tremin Trust Data to evaluate …

Asymptotically Optimal Model Selection Method With Right Censored Outcomes, Sunduz Keles, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

Over the last two decades, non-parametric and semi-parametric approaches that adapt well known techniques such as regression methods to the analysis of right censored data, e.g. right censored survival data, became popular in the statistics literature. However, the problem of choosing the best model (predictor) among a set of proposed models (predictors) in the right censored data setting have not gained much attention. In this paper, we develop a new cross-validation based model selection method to select among predictors of right censored outcomes such as survival times. The proposed method considers the risk of a given predictor based on the …

Tree-Based Multivariate Regression And Density Estimation With Right-Censored Data , Annette M. Molinaro, Sandrine Dudoit, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a unified strategy for estimator construction, selection, and performance assessment in the presence of censoring. This approach is entirely driven by the choice of a loss function for the full (uncensored) data structure and can be stated in terms of the following three main steps. (1) Define the parameter of interest as the minimizer of the expected loss, or risk, for a full data loss function chosen to represent the desired measure of performance. Map the full data loss function into an observed (censored) data loss function having the same expected value and leading to an efficient estimator …

Ranked Set Sampling Based On Binary Water Quality Data With Covariates, Paul Kvam

Department of Math & Statistics Faculty Publications

A ranked set sample (RSS) is composed of independent order statistics, formed by collecting and ordering independent subsamples, then measuring only one item from each subsample. If the cost of sampling is dominated by data measurement rather than collection or ranking, the RSS technique is known to be superior to ordinary sampling. Experiments based on binary data are not designed to exploit the advantages of ranked set sampling because categorical data typically are as easily measured as ranked, making RSS methods impractical. However, in some environmental and biological studies, the success probability of a bivariate outcome is related to one …

The Psychological Characteristics Of Obese Children, Thomas Taylor Mitchell

Loma Linda University Electronic Theses, Dissertations & Projects

Several studies along with the surgeon general of the United States have identified obesity as a national health issue. Research indicates that adult obesity treatment has relatively poor long-term effects. Consequently increased attention has been given to addressing obesity in children. This focus is particularly vital due to the fact that children are one of the populations showing the most rapid increase in overweight and obesity. The purpose of this study was to identify the some of the unique psychological characteristics of obese children by analyzing the intake data of children and adolescents attending the Loma Linda University Growing Fit …

The Radiopacity Of 29 Resin Restorative Materials Compared To Enamel, Peter Lubisich Iv

Loma Linda University Electronic Theses, Dissertations & Projects

The radiodensity of a composite resin can greatly influence a clinician's ability to analyze a restoration for failure. The purpose of this study was to determine the relative radiopacities of 29 resin restorative materials compared to enamel, and to verify the comparable radiopacity between shades of 23 of the restorative composite resin materials. Composite resin discs measuring >5mm in diameter and 2 mm in thickness were made and polymerized. Radiographs were taken of the composite resin discs, which included an aluminum step wedge for calibration and a densitometer was used to measure the radiodensity of the composite resin samples. The …

Quantification Of Bone Deposition In Onlay Bone Grafting, Gregory Alan Kammeyer

Loma Linda University Electronic Theses, Dissertations & Projects

The purpose of this study was to quantitatively evaluate; 1) mandibular posterior mono-cortical block onlay bone graft success rates 2) the amount of grafted bone retained after initial resorption in radiographic projections. Seven consecutive patients with 14 mandibular posterior implant sites requiring bone augmentation for implants of a standard 3.8mm x 10mm dimension were sought. Mono-cortical block bone grafts from the ipsilateral ascending ramus were placed then observed with two standardized CT scans, dividing them into two groups: Group A had the first CT at 4 weeks after graft placement and a second taken before Prosthodontic reconstruction, 36.7 weeks later. …

Cross-Calibration Of Stroke Disability Measures: Bayesian Analysis Of Longitudinal Ordinal Categorical Data Using Negative Dependence, Giovanni Parmigiani, Heidi W. Ashih, Gregory P. Samsa, Pamela W. Duncan, Sue Min Lai, David B. Matchar

Johns Hopkins University, Dept. of Biostatistics Working Papers

It is common to assess disability of stroke patients using standardized scales, such as the Rankin Stroke Outcome Scale (RS) and the Barthel Index (BI). The Rankin Scale, which was designed for applications to stroke, is based on assessing directly the global conditions of a patient. The Barthel Index, which was designed for general applications, is based on a series of questions about the patient’s ability to carry out 10 basis activities of daily living. As both scales are commonly used, but few studies use both, translating between scales is important in gaining an overall understanding of the efficacy of …

Randomization Tests For Small Samples: An Application For Genetic Expression Data, Gary L. Gadbury, Grier P. Page, Moonseong Heo, John D. Mountz, David B. Allison

Mathematics and Statistics Faculty Research & Creative Works

An advantage of randomization tests for small samples is that an exact P-value can be computed under an additive model. a disadvantage with very small sample sizes is that the resulting discrete distribution for P-values can make it mathematically impossible for a P-value to attain a particular degree of significance. We investigate a distribution of P-values that arises when several thousand randomization tests are conducted simultaneously using small samples, a situation that arises with microarray gene expression data. We show that the distribution yields valuable information regarding groups of genes that are differentially expressed between two groups: A treatment group …

Modern Statistical Methods For Handling Missing Repeated Measurements In Obesity Trial Data: Beyond Locf, Gary L. Gadbury, C. S. Coffey, D. B. Allison

Mathematics and Statistics Faculty Research & Creative Works

This paper brings together some modern statistical methods to address the problem of missing data in obesity trials with repeated measurements. Such missing data occur when subjects miss one or more follow-up visits or drop out early from an obesity trial. a common approach to dealing with missing data because of dropout is 'last observation carried forward' (LOCF). This method, although intuitively appealing, requires restrictive assumptions to produce valid statistical conclusions. We review the need for obesity trials, the assumptions that must be made regarding missing data in such trials, and some modern statistical methods for analyzing data containing missing …