Digital Commons Network^™

Variable Selection For Poisson Regression Model, Felix Famoye, Daniel E. Rothe

Journal of Modern Applied Statistical Methods

Poisson regression is useful in modeling count data. In a study with many independent variables, it is desirable to reduce the number of variables while maintaining a model that is useful for prediction. This article presents a variable selection technique for Poisson regression models. The data used is log-linear, but the methods could be adapted to other relationships. The model parameters are estimated by the method of maximum likelihood. The use of measures of goodness-of-fit to select appropriate variables is discussed. A forward selection algorithm is presented and illustrated on a numerical data set. This algorithm performs as well if …

Bootstrapping Confidence Intervals For Robust Measures Of Association, Jason E. King

Journal of Modern Applied Statistical Methods

A Monte Carlo simulation study compared four bootstrapping procedures in generating confidence intervals for the robust Winsorized and percentage bend correlations. Results revealed the superior resiliency of the robust correlations over r, with neither outperforming the other. Unexpectedly, the bootstrapping procedures achieved roughly equivalent outcomes for each correlation.

Letters To The Editor, Jmasm Editors

Journal of Modern Applied Statistical Methods

No abstract provided.

On Treating A Survey Of Convenience Sample As A Simple Random Sample, W. Gregory Thatcher, J. Wanzer Drane

Journal of Modern Applied Statistical Methods

Threat of bias has kept many from using data gathered in less than optimal conditions. We maintain that when convenience sampling represents race and gender at nearly correct proportions and can be beneficial, as these two variables are quite often used as stratification variables. We compared a convenience sample with a proven sample. Race and Sex were nearly proportional as was found in the proven sample. We conclude that the convenience sample can be used as though it is simple random.

Fortune Cookies, Measurement Error, And Experimental Design, Greogry R. Hancock

Journal of Modern Applied Statistical Methods

This article pertains to the theoretical and practical detriments of measurement error in traditional univariate and multivariate experimental design, and points toward modern methods that facilitate greater accuracy in effect size estimates and power in hypothesis testing.

Correcting Publication Bias In Meta-Analysis: A Truncation Approach, Guillermo Montes, Bohdan S. Lotyczewski

Journal of Modern Applied Statistical Methods

Meta-analyses are increasingly used to support national policy decision making. The practical implications of publications bias in meta-analysis are discussed. Standard approaches to correct for publication bias require knowledge of the selection mechanism that leads to publication. In this study, an alternative approach is proposed based on Cohen’s corrections for a truncated normal. The approach makes less assumptions, is easy to implement, and performs well in simulations with small samples. The approach is illustrated with two published meta-analyses.

Comparison Of Viral Trajectories In Aids Studies By Using Nonparametric Mixed-Effects Models, Chin-Shang Li, Hua Liang, Ying-Hen Hsieh, Shiing-Jer Twu

Journal of Modern Applied Statistical Methods

The efficacy of antiretroviral therapies for human immunodeficiency virus (HIV) infection can be assessed by studying the trajectory of the changing viral load with treatment time, but estimation of viral trajectory parameters by using the implicit function form of linear and nonlinear parametric models can be problematic. Using longitudinal viral load data from a clinical study of HIV-infected patients in Taiwan, we described the viral trajectories by applying a nonparametric mixed-effects model. We were then able to compare the efficacies of highly active antiretroviral therapy (HAART) and conventional therapy by using Young and Bowman’s (1995) test.

Deconstructing Arguments From The Case Against Hypothesis Testing, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

The main purpose of this article is to contest the propositions that (1) hypothesis tests should be abandoned in favor of confidence intervals, and (2) science has not benefited from hypothesis testing. The minor purpose is to propose (1) descriptive statistics, graphics, and effect sizes do not obviate the need for hypothesis testing, (2) significance testing (reporting p values and leaving it to the reader to determine significance) is subjective and outside the realm of the scientific method, and (3) Bayesian and qualitative methods should be used for Bayesian and qualitative research studies, respectively.

A Critical Examination Of The Use Of Preliminary Tests In Two-Sample Tests Of Location, Kimberly T. Perry

Journal of Modern Applied Statistical Methods

This paper explores the appropriateness of testing the equality of two means using either a t test, the Welch test, or the Wilcoxon-Mann-Whitney test for two independent samples based on the results of using two classes of preliminary tests (i.e., tests for population variance equality and symmetry in underlying distributions).

Confidence Intervals For P(X Less Than Y) In The Exponential Case With Common Location Parameter, Ayman Baklizi

Journal of Modern Applied Statistical Methods

The problem considered is interval estimation of the stress - strength reliability R = P(Xθ and λ respectively and a common location parameter μ . Several types of asymptotic, approximate and bootstrap intervals are investigated. Performances are investigated using simulation techniques and compared in terms of attainment of the nominal confidence level, symmetry of lower and upper error rates, and expected length. Recommendations concerning their usage are given.

Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara

Journal of Modern Applied Statistical Methods

The aim of the present study is to obtain and compare confidence intervals for the variance of a Gaussian distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the variance of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with the well known classical method. The Bayesian approach relies only on the observations. It is shown that the proposed approximate Bayesian approach relies only on the observations. The classical method, that uses the Chi-square statistic, does …

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 …