Statistics and Probability Commons^™

Analysis Of Adverse Events In Drug Safety: A Multivariate Approach Using Stratified Quasi-Least Squares, Hanjoo Kim, Justine Shults, Scott Patterson, Robert Goldberg-Alberts

UPenn Biostatistics Working Papers

Safety assessment in drug development involves numerous statistical challenges, and yet statistical methodologies and their applications to safety data have not been fully developed, despite a recent increase of interest in this area. In practice, a conventional univariate approach for analysis of safety data involves application of the Fisher's exact test to compare the proportion of subjects who experience adverse events (AEs) between treatment groups; This approach ignores several common features of safety data, including the presence of multiple endpoints, longitudinal follow-up, and a possible relationship between the AEs within body systems. In this article, we propose various regression modeling …

Synthesis Analysis Of Regression Models With A Continuous Outcome, Andrew Zhou, Nan Hu, Guizhou Hu, Martin Root

UW Biostatistics Working Paper Series

Synthesis Analysis of Regression Models with a Continuous Outcome Xiao-Hua Zhou 1,2, Nan Hu 2, Guizhou Hu3, and Martin Root3 1 HSR&D Center of Excellence, VA Puget Sound Health Care System, Seattle, WA 98101. 2 Department of Biostatistics, University of Washington, Seattle, WA 98195. 3 BioSignia, Inc., 1822 East NC Highway 54, Suite 350, Durham, NC 27713 To estimate the multivariate regression model from multiple individual studies, it would be challenging to obtain results if the input from individual studies only provide univariate or incomplete multivariate regression information. Samsa et al [1] proposed a simple method to combine coefficients from …

A Trust-Based Secure Service Discovery (Tssd) Model For Pervasive Computing, Sheikh Iqbal Ahamed, Moushumi Sharmin

Mathematics, Statistics and Computer Science Faculty Research and Publications

To cope with the challenges posed by device capacity and capability, and also the nature of ad hoc networks, a Service discovery model is needed that can resolve security and privacy issues with simple solutions. The use of complex algorithms and powerful fixed infrastructure is infeasible due to the volatile nature of pervasive environment and tiny pervasive devices. In this paper, we present a trust-based secure Service discovery model, TSSD (trust-based secure service discovery) for a truly pervasive environment. Our model is a hybrid one that allows both secure and non-secure discovery of services. This model allows Service discovery and …

A Small Sample Correction For Estimating Attributable Risk In Case-Control Studies, Daniel B. Rubin

U.C. Berkeley Division of Biostatistics Working Paper Series

The attributable risk, often called the population attributable risk, is in many epidemiological contexts a more relevant measure of exposure-disease association than the excess risk, relative risk, or odds ratio. When estimating attributable risk with case-control data and a rare disease, we present a simple correction to the standard approach making it essentially unbiased, and also less noisy. As with analogous corrections given in Jewell (1986) for other measures of association, the adjustment often won't make a substantial difference unless the sample size is very small or point estimates are desired within fine strata, but we discuss the possible utility …

Bayesian Model Averaging For Clustered Data: Imputing Missing Daily Air Pollution Concentration, Howard H. Chang, Francesca Dominici, Roger D. Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

The presence of missing observations is a challenge in statistical analysis especially when data are clustered. In this paper, we develop a Bayesian model averaging (BMA) approach for imputing missing observations in clustered data. Our approach extends BMA by allowing the weights of competing regression models for missing data imputation to vary between clusters while borrowing information across clusters in estimating model parameters. Through simulation and cross-validation studies, we demonstrate that our approach outperforms the standard BMA imputation approach where model weights are assumed to be the same for all clusters. We then apply our proposed method to a national …

A Uniformly Dissipative Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang (Wendy) Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The purpose of this short communication is to announce that a class of numerical schemes, uniformly dissipative approximations, which uniformly preserve the dissipativity of the continuous infinite dimensional dissipative complex (chaotic) systems possess desirable properties in terms of approximating stationary statistics properties. in particular, the stationary statistical properties of these uniformly dissipative schemes converge to those of the continuous system at vanishing mesh size. the idea is illustrated on the infinite Prandtl number model for convection and semi-discretization in time, although the general strategy works for a broad class of dissipative complex systems and fully discretized approximations. as far as …

A Semi-Implicit Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We propose a semisecret in time semi-implicit numerical scheme for the infinite Prandtl model for convection. Besides the usual finite time convergence, this scheme enjoys the additional highly desirable feature that the stationary statistical properties of the scheme converge to those of the infinite Prandtl number model at vanishing time stop. One of the key characteristics of the scheme is that it preserves the dissipativity of the infinite Prandtl number model uniformly in terms of the time stop. So far as wo know, this is the first rigorous result on convergence of stationary statistical properties of numerical schemes for infinite …

Spatial Misalignment In Time Series Studies Of Air Pollution And Health Data, Roger D. Peng, Michelle L. Bell

Johns Hopkins University, Dept. of Biostatistics Working Papers

Time series studies of environmental exposures often involve comparing daily changes in a toxicant measured at a point in space with daily changes in an aggregate measure of health. Spatial misalignment of the exposure and response variables can bias the estimation of health risk and the magnitude of this bias depends on the spatial variation of the exposure of interest. In air pollution epidemiology, there is an increasing focus on estimating the health effects of the chemical components of particulate matter. One issue that is raised by this new focus is the spatial misalignment error introduced by the lack of …

On The Mixed Sum Of Doubly Infinite And Finite Independent Random Variables, Mridula Garg

Applications and Applied Mathematics: An International Journal (AAM)

The aim of the present paper is to study the distribution of the mixed sum of two random variables. Here we establish a theorem which gives the probability density function (pdf) of sum of doubly infinite and finite independent random variables. The distribution of the infinite and finite independent random variables is given in the form of corollary. As an application of these results we have obtained a distribution of sum of bilateral exponential variate with triangular, Rayleigh with uniform and Weibull with triangular variate. Some graphs of these distributions have also been given.

Comparative Analysis Of Forecasting Techniques With Intermittent Demand, John Deforest

Industrial Engineering Undergraduate Honors Theses

The world and life are filled with uncertainty. Statistics, and more specifically, forecasting techniques allow us to quantify uncertainty and make decisions based on that information. Many find forecasting advantageous in areas such as predicting consumer demand, stock prices, terrorist attacks, epidemiology, etc. This thesis will focus on forecasting intermittent demand, which is the study of analyzing sporadic demand. One application includes an airplane manufacturer’s sporadic or intermittent demand for spare parts in their distribution center. Since spare parts are not needed on any regular schedule, it is thought of as intermittent. Knowing the projected quantity for a given time …

"G" And "H" Control Charts And Risk Analysis In The Banking Industry, James L. Bossert

All-Inclusive List of Electronic Theses and Dissertations

This research investigates the utilization of a new control chart in the Banking industry to minimize financial risk. There are processes in the banking industry that do not lend themselves to traditional control chart applications. These processes tend to be high volume. High volume meaning over a million transactions a day and a requirement for high levels of accuracy characterize these processes. The research has looked at these processes and applied the "g" control charts to determine if they provide timely feedback to the banking industry. The value of this research will give the banking industry an opportunity to react …

Space-Time Regression Modeling Of Tree Growth Using The Skew-T Distribution, Farouk S. Nathoo

COBRA Preprint Series

In this article we present new statistical methodology for the analysis of repeated measures of spatially correlated growth data. Our motivating application, a ten year study of height growth in a plantation of even-aged white spruce, presents several challenges for statistical analysis. Here, the growth measurements arise from an asymmetric distribution, with heavy tails, and thus standard longitudinal regression models based on a Gaussian error structure are not appropriate. We seek more flexibility for modeling both skewness and fat tails, and achieve this within the class of skew-elliptical distributions. Within this framework, robust space-time regression models are formulated using random …

Tolerance Intervals In Random-Effects Models, Kakotan Sanogo

Theses and Dissertations

In the pharmaceutical setting, it is often necessary to establish the shelf life of a drug product and sometimes suitable to assess the risk of product failure at the desired expiry period. The current statistical methodology use confidence intervals for the predicted mean to establish the expiry period and prediction intervals for a predicted new assay value or a tolerance interval for a proportion of the population for use in a risk assessment. A major concern is that most methodology treat a homogeneous subpopulation, say batch, either as a fixed effect and therefore uses a fixed-effects regression model (Graybill, 1976) …

Maximizing Warfighter Capability Using Surveyed Necessity Measurement: Application To The Usaf F-15c Fleet, John M. Colombi, David R. Jacques, Dennis D. Strouble

Faculty Publications

Within the Department of Defense, with changing missions to counter dynamic and asymmetrical threats, the acquisition workforce strives to maximize capability for joint warfighting. How acquisition professionals measure and select capability improvements for the nation’s weapon systems is a perpetual challenge, made even more complex with constrained defense budgets. This study identifies a method for determining which upgrades should be purchased (production) for which aircraft in the F- 15C fleet by optimizing a capability proxy measure. Each upgrade’s “necessity” for a given mission area was obtained by conducting a survey of over 250 experienced F-15C pilots. The solution presented in …

Approximations To Continuous Processes In Hierarchical Models, Amanda Cangelosi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Models for natural nonlinear processes, such as population dynamics, have been given much attention in applied mathematics. For example, species competition has been extensively modeled by differential equations. Often, the scientist has preferred to model the underlying dynamical processes (i.e., theoretical mechanisms) in continuous-time. It is of both scientific and mathematical interest to implement such models in a statistical framework to quantify uncertainty associated with the models in the presence of observations. That is, given discrete observations arising from the underlying continuous process, the unobserved process can be formally described while accounting for multiple sources of uncertainty ( …

Predicting Intra-Urban Variation In Air Pollution Concentrations With Complex Spatio-Temporal Interactions, Adam A. Szpiro, Paul D. Sampson, Lianne Sheppard, Thomas Lumley, Sara D. Adar, Joel Kaufman

UW Biostatistics Working Paper Series

We describe a methodology for assigning individual estimates of long-term average air pollution concentrations that accounts for a complex spatio-temporal correlation structure and can accommodate unbalanced observations. This methodology has been developed as part of the Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air), a prospective cohort study funded by the U.S. EPA to investigate the relationship between chronic exposure to air pollution and cardiovascular disease. Our hierarchical model decomposes the space-time field into a “mean” that includes dependence on covariates and spatially varying seasonal and long-term trends and a “residual” that accounts for spatially correlated deviations from the …

Parameter Estimation For The Beta Distribution, Claire Elayne Bangerter Owen

Theses and Dissertations

The beta distribution is useful in modeling continuous random variables that lie between 0 and 1, such as proportions and percentages. The beta distribution takes on many different shapes and may be described by two shape parameters, alpha and beta, that can be difficult to estimate. Maximum likelihood and method of moments estimation are possible, though method of moments is much more straightforward. We examine both of these methods here, and compare them to three more proposed methods of parameter estimation: 1) a method used in the Program Evaluation and Review Technique (PERT), 2) a modification of the two-sided power …

Reversal In Declining Trend Of Adult Mortality In Many States Of India, 1970-2001: Is It Due To Aids?, Abhaya Indrayan, Ajay Kumar Bansal

COBRA Preprint Series

Objectives: To investigate the reversal in adult mortality trend from declining to rising in some segments of population in India, and to use an indirect demographic method to examine if this increase could be due to AIDS mortality. Also, to estimate the total excess deaths.

Design: Cross-sectional data on age-specific death rate in 5-year age-intervals from 25 to 44 years for the years 1970 to 1998 for rural/urban and male/female segments for each of 16 major states of India obtained from the government reports, and their projections till the year 2001.

Methods: In view of reversal of trend in some …

Optimal Cutpoint Estimation With Censored Data, Mithat Gonen, Camelia Sima

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

We consider the problem of selecting an optimal cutpoint for a continuous marker when the outcome of interest is subject to right censoring. Maximal chi square methods and receiver operating characteristic (ROC) curves-based methods are commonly-used when the outcome is binary. In this article we show that selecting the cutpoint that maximizes the concordance, a metric similar to the area under an ROC curve, is equivalent to maximizing the Youden index, a popular criterion when the ROC curve is used to choose a threshold. We use this as a basis for proposing maximal concordance as a metric to use with …

A New Class Of Rank Tests For Interval-Censored Data, Guadalupe Gomez, Ramon Oller Pique

Harvard University Biostatistics Working Paper Series

No abstract provided.

The Highest Confidence Density Region And Its Usage For Inferences About The Survival Function With Censored Data, Lu Tian, Rui Wang, Tianxi Cai, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Change-Point Problem And Regression: An Annotated Bibliography, Ahmad Khodadadi, Masoud Asgharian

COBRA Preprint Series

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as "the change-point problem" or, in the Eastern literature, as "disorder".

The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis.

Numerous methodological approaches …

A Simple Index Of Smoking, Abhaya Indrayan Dr., Rajeev Kumar Mr., Shridhar Dwivedi Dr.

COBRA Preprint Series

Background: Cigarette smoking is implicated in a large number of diseases and other adverse health conditions. Among the dimensions of smoking are number of cigarettes smoked per day, duration of smoking, passive smoking, smoking of filter cigarettes, age at start, and duration elapsed since quitting by ex-smokers. The practice so far is to study most of these separately. We develop a simple index that integrates these dimensions of smoking into a single metric, and suggest that this index be developed further. Method: The index is developed under a series of natural assumptions. Broadly, these are (i) the burden of smoking …

The Strength Of Statistical Evidence For Composite Hypotheses With An Application To Multiple Comparisons, David R. Bickel

COBRA Preprint Series

The strength of the statistical evidence in a sample of data that favors one composite hypothesis over another may be quantified by the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function. Unlike the p-value and the Bayes factor, this measure of evidence is coherent in the sense that it cannot support a hypothesis over any hypothesis that it entails. Further, when comparing the hypothesis that the parameter lies outside a non-trivial interval to the hypotheses that it lies within the interval, the proposed measure of evidence almost always asymptotically favors the correct hypothesis …

Multi-Group Confirmatory Factor Analysis For Testing Measurement Invariance In Mixed Item Format Data, Kim H. Koh, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

This simulation study investigated the empirical Type I error rates of using the maximum likelihood estimation method and Pearson covariance matrix for multi-group confirmatory factor analysis (MGCFA) of full and strong measurement invariance hypotheses with mixed item format data that are ordinal in nature. The results indicate that mixed item formats and sample size combinations do not result in inflated empirical Type I error rates for rejecting the true measurement invariance hypotheses. Therefore, although the common methods are in a sense sub-optimal, they don’t lead to researchers claiming that measures are functioning differently across groups – i.e., a lack of …

Estimating Explanatory Power In A Simple Regression Model Via Smoothers, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

Consider the regression model Y = γ(X) + ε , where γ(X) is some conditional measure of location associated with Y , given X. Let Υ̂ be some estimate of Y, given X, and let τ² (Y) be some measure of variation. Explanatory power is η² = τ² (Υ̂) /τ²(Y) . When γ(X) = β₀ + β₁X and τ²(Y) is the variance of Y , η² = ρ² , …

Data Mining Ceo Compensation, Susan M. Adams, Atul Gupta, Dominique M. Haughton, John D. Leeth

Journal of Modern Applied Statistical Methods

The need to pre-specify expected interactions between variables is an issue in multiple regression. Theoretical and practical considerations make it impossible to pre-specify all possible interactions. The functional form of the dependent variable on the predictors is unknown in many cases. Two ways are described in which the data mining technique Multivariate Adaptive Regression Splines (MARS) can be utilized: first, to obtain possible improvements in model specification, and second, to test for the robustness of findings from a regression analysis. An empirical illustration is provided to show how MARS can be used for both purposes.

Least Squares Percentage Regression, Chris Tofallis

Journal of Modern Applied Statistical Methods

In prediction, the percentage error is often felt to be more meaningful than the absolute error. We therefore extend the method of least squares to deal with percentage errors, for both simple and multiple regression. Exact expressions are derived for the coefficients, and we show how such models can be estimated using standard software. When the relative error is normally distributed, least squares percentage regression is shown to provide maximum likelihood estimates. The multiplicative error model is linked to least squares percentage regression in the same way that the standard additive error model is linked to ordinary least squares regression.

Application Of Dynamic Poisson Models To Japanese Cancer Mortality Data, Shuichi Midorikawa, Etsuo Miyaoka, Bruce Smith

Journal of Modern Applied Statistical Methods

A dynamic Poisson model is used with a Bayesian approach to modeling to predict cancer mortality. The complexity of the posterior distribution prohibits direct evaluation of the posterior, and so parameters are estimated by using a Markov Chain Monte Carlo method. The model is applied to analyze lung and stomach cancer data which have been collected in Japan.

A Randomization Method To Control The Type I Error Rates In Best Subset Regression, Yasser A. Shehata, Paul White

Journal of Modern Applied Statistical Methods

A randomization method for the assessment of statistical significance for best subsets regression is given. The procedure takes into account the number of potential predictors and the inter-dependence between predictors. The approach corrects a non-trivial problem with Type I errors and can be used to assess individual variable significance.