Statistics and Probability Commons^™

An Extended General Location Model For Causal Inference From Data Subject To Noncompliance And Missing Values, Yahong Peng, Rod Little, Trivellore E. Raghuanthan

The University of Michigan Department of Biostatistics Working Paper Series

Noncompliance is a common problem in experiments involving randomized assignment of treatments, and standard analyses based on intention-to treat or treatment received have limitations. An attractive alternative is to estimate the Complier-Average Causal Effect (CACE), which is the average treatment effect for the subpopulation of subjects who would comply under either treatment (Angrist, Imbens and Rubin, 1996, henceforth AIR). We propose an Extended General Location Model to estimate the CACE from data with non-compliance and missing data in the outcome and in baseline covariates. Models for both continuous and categorical outcomes and ignorable and latent ignorable (Frangakis and Rubin, 1999) …

Inference For The Population Total From Probability-Proportional-To-Size Samples Based On Predictions From A Penalized Spline Nonparametric Model, Hui Zheng, Rod Little

The University of Michigan Department of Biostatistics Working Paper Series

Inference about the finite population total from probability-proportional-to-size (PPS) samples is considered. In previous work (Zheng and Little, 2003), penalized spline (p-spline) nonparametric model-based estimators were shown to generally outperform the Horvitz-Thompson (HT) and generalized regression (GR) estimators in terms of the root mean squared error. In this article we develop model-based, jackknife and balanced repeated replicate variance estimation methods for the p-spline based estimators. Asymptotic properties of the jackknife method are discussed. Simulations show that p-spline point estimators and their jackknife standard errors lead to inferences that are superior to HT or GR based inferences. This suggests that nonparametric …

On The Formation Of Weighting Adjustment Cells For Unit Nonresponse, Sonya Vartivarian, Rod Little

The University of Michigan Department of Biostatistics Working Paper Series

A method is proposed for weighting adjustments for unit nonresponse based on a crossclassification by the estimated propensity to respond and by the predicted mean of a survey outcome. Simulations to assess the performance of the method are described.

Spearman Rank Regression, Jason C. Parcon

Dissertations

The main purpose of this dissertation is to obtain an estimate of the slope parameter in a regression model that is robust to outlying values in both the x - and Y-spaces. The least squares method, though known to be optimal for normal errors, can yield estimates with infinitely large MSE's if the error distribution is thick-tailed. Regular rank-based methods like the Wilcoxon method are known to be robust to outlying values in the Y -space, but it is still grossly affected by outlying values in x -space.

This dissertation derives an estimate of the slope from an estimating …

Locally Efficient Estimation Of Nonparametric Causal Effects On Mean Outcomes In Longitudinal Studies, Romain Neugebauer, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Marginal Structural Models (MSM) have been introduced by Robins (1998a) as a powerful tool for causal inference as they directly model causal curves of interest, i.e. mean treatment-specific outcomes possibly adjusted for baseline covariates. Two estimators of the corresponding MSM parameters of interest have been proposed, see van der Laan and Robins (2002): the Inverse Probability of Treatment Weighted (IPTW) and the Double Robust (DR) estimators. A parametric MSM approach to causal inference has been favored since the introduction of MSM. It relies on correct specification of a parametric MSM to consistently estimate the parameter of interest using the IPTW …

Adjusting For Non-Ignorable Verification Bias In Clinical Studies For Alzheimer’S Disease, Xiao-Hua Zhou, Pete Castelluccio

UW Biostatistics Working Paper Series

A common problem for comparing the relative accuracy of two screening tests for Alzheimer’s disease (D) in a two-stage design study is verification bias. If the verification bias can be assumed to be ignorable, Zhou and Higgs (2000) have proposed a maximum likelihood approach to compare the relative accuracy of screening tests in a two-stage design study. However, if the verification mechanism also depends on the unobserved disease status, the ignorable assumption does not hold. In this paper, we discuss how to use a profile likelihood approach to compare the relative accuracy of two screening tests for AD without assuming …

Behavioral Evaluation Of The Psychological Welfare And Environmental Requirements Of Agricultural Research Animals: Theory, Measurement, Ethics, And Practical Implications, Lesley A. King

Experimentation Collection

The welfare of agricultural research animals relies not only on measures of good health but also on the presence of positive emotional states and the absence of aversive or unpleasant subjective states such as fear, frustration, or association with pain. Although subjective states are not inherently observable, their interaction with motivational states can be measured through assessment of motivated behavior, which indicates the priority animals place on obtaining or avoiding specific environmental stimuli and thus allows conclusions regarding the impact of housing, husbandry, and experimental procedures on animal welfare. Preference tests and consumer demand models demonstrate that animal choices are …

On Adaptive Estimation In Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss

Mathematics and Statistics Faculty Publications

A simple method is provided to construct a general class of individual and simultaneous confidence intervals for the effects in orthogonal saturated designs. These intervals use the data adaptively, maintain the confidence levels sharply at 1 - α at the least favorable parameter configuration, work effectively under effect sparsity, and include the intervals by Wang and Voss (2001) as a special case.

Robust Regression With High Coverage, David J. Olive, Douglas M. Hawkins

Articles and Preprints

An important parameter for several high breakdown regression algorithm estimators is the number of cases given weight one, called the coverage of the estimator. Increasing the coverage is believed to result in a more stable estimator, but the price paid for this stability is greatly decreased resistance to outliers. A simple modification of the algorithm can greatly increase the coverage and hence its statistical performance while maintaining high outlier resistance.

On The Stability Of The Positive Radial Steady States For A Semilinear Cauchy Problem, Yinbin Deng, Yi Li, Yi Liu

Mathematics and Statistics Faculty Publications

No abstract provided.

What Is A Reasonable Attorney Fee? An Empirical Study Of Class Action Settlements, Theodore Eisenberg, Geoffrey P. Miller

Cornell Law Faculty Publications

Determining an appropriate fee is a difficult task facing trial court judges in class action litigation. But courts rarely rely on empirical research to assess a fee’s reasonableness, due, at least in part, to the relative paucity of available information. Existing empirical studies of attorney fees in class action cases are limited in scope, and generally do not control for important variables. To help fill this gap, we analyzed data from all state and federal class actions with reported fee decisions from 1993 to 2002 in which the fee and class recovery could be determined with reasonable confidence.

We find …

Estimation Of Parameters In Replicated Time Series Regression Models, Genming Shi

Mathematics & Statistics Theses & Dissertations

The time series regression model was widely studied in the literature by several authors. However, statistical analysis of replicated time series regression models has received little attention. In this thesis, we study the application of quasi-least squares, a relatively new method, to estimate the parameters in replicated time series models with general ARMA( p, q) correlation structure. We also study several established methods for estimating the parameters in those models, including the maximum likelihood, method of moments, and the GEE method. Asymptotic comparisons of the methods are made bV fixing the number of repeated measurements in each series, and …

Analysis Of Multivariate Data Using Kotz Type Distribution, Kusaya Plungpongpun

Mathematics & Statistics Theses & Dissertations

Most of the inferential statistical methods for multivariate data are developed under the fundamental assumption that the data are from a multivariate normal distribution. Unfortunately, one can never be sure a set of data is really from a multivariate normal distribution. There are numerous methods for checking (testing) multivariate normality, but based on many published and our own simulation studies, provided in the first chapter of this dissertation, we observe that these tests are generally not very powerful, especially for smaller sample sizes. Hence it is always beneficial to have alternative multivariate distributions available along with the methodology for using …

Geographic Variation In The Morphology Of Crotalus Horridus (Serpentes: Viperidae), John Robert Allsteadt

Biological Sciences Theses & Dissertations

The Timber Rattlesnake (Crotalus horridus) occurs in discontinuous populations throughout the eastern and central United States. The species exhibits high levels of polymorphism in morphological traits, especially in coloration and pattern. Previous studies recognized either distinct northern and southern subspecies or three regional morphs (northern, southern, and western), but conflicting data sets and limited geographic sampling of previous studies have left the relationships among those regional variants unclear. In this study, univariate and multivariate statistics, together with a geographic information system, were used to analyze geographic variation in 36 morphological characters recorded from 2,420 specimens of C. horridus …

Resampling-Based Multiple Testing: Asymptotic Control Of Type I Error And Applications To Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We define a general statistical framework for multiple hypothesis testing and show that the correct null distribution for the test statistics is obtained by projecting the true distribution of the test statistics onto the space of mean zero distributions. For common choices of test statistics (based on an asymptotically linear parameter estimator), this distribution is asymptotically multivariate normal with mean zero and the covariance of the vector influence curve for the parameter estimator. This test statistic null distribution can be estimated by applying the non-parametric or parametric bootstrap to correctly centered test statistics. We prove that this bootstrap estimated null …

Statistical Implications Of Pooling Rna Samples For Microarray Experiments, Xuejun Peng, Constance L. Wood, Eric M. Blalock, Kuey Chu Chen, Philip W. Landfield, Arnold J. Stromberg

Statistics Faculty Publications

BACKGROUND: Microarray technology has become a very important tool for studying gene expression profiles under various conditions. Biologists often pool RNA samples extracted from different subjects onto a single microarray chip to help defray the cost of microarray experiments as well as to correct for the technical difficulty in getting sufficient RNA from a single subject. However, the statistical, technical and financial implications of pooling have not been explicitly investigated.

RESULTS: Modeling the resulting gene expression from sample pooling as a mixture of individual responses, we derived expressions for the experimental error and provided both upper and lower bounds for …

The Consequences Of Race-Blindness: Revisiting Prediction Models With Current Law School Data, Linda F. Wightman

Journal of Legal Education

No abstract provided.

Maximization By Parts In Likelihood Inference, Peter Xuekun Song, Yanqin Fan, Jack Kalbfleisch

The University of Michigan Department of Biostatistics Working Paper Series

This paper presents and examines a new algorithm for solving a score equation for the maximum likelyhood estimate in certain problems of practical interest. The method circumvents the need to compute second order derivaties of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log likelihood from a simply analyzed model and the second part is used to update estimates from the first. Convergence properties of this fixed point algorithm are examined and asymptotics are derived for estimators obtained …

Design Considerations For Efficient And Effective Microarray Studies, M. Kathleen Kerr

UW Biostatistics Working Paper Series

This paper describes the theoretical and practical issues in experimental design for gene expression microarrays. Specifically, this paper (1) discusses the basic principles of design (randomization, replication, and blocking) as they pertain to microarrays, and (2) provides some general guidelines for statisticians designing microarray studies.

Cluster Stability Scores For Microarray Data In Cancer Studies, Mark Smolkin, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

A potential benefit of profiling of tissue samples using microarrays is the generation of molecular fingerprints that will define subtypes of disease. Hierarchical clustering has been the primary analytical tool used to define disease subtypes from microarray experiments in cancer settings. Assessing cluster reliability poses a major complication in analyzing output from these procedures. While much work has been done on assessing the global question of number of clusters in a dataset, relatively little research exists on assessing stability of individual clusters. A potential benefit of profiling of tissue samples using microarrays is the generation of molecular fingerprints that will …

Double Robust Estimation In Longitudinal Marginal Structural Models, Zhuo Yu, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Consider estimation of causal parameters in a marginal structural model for the discrete intensity of the treatment specific counting process (e.g. hazard of a treatment specific survival time) based on longitudinal observational data on treatment, covariates and survival. We assume the sequential randomization assumption (SRA) on the treatment assignment mechanism and the so called experimental treatment assignment assumption which is needed to identify the causal parameters from the observed data distribution. Under SRA, the likelihood of the observed data structure factorizes in the auxiliary treatment mechanism and the partial likelihood consisting of the product over time of conditional distributions of …

A New Confidence Interval For The Difference Between Two Binomial Proportions Of Paired Data, Xiao-Hua Zhou, Gengsheng Qin

UW Biostatistics Working Paper Series

Motivated by a study on comparing sensitivities and specificities of two diagnostic tests in a paired design when the sample size is small, we first derived an Edgeworth expansion for the studentized difference between two binomial proportions of paired data. The Edgeworth expansion can help us understand why the usual Wald interval for the difference has poor coverage performance in the small sample size. Based on the Edgeworth expansion, we then derived a transformation based confidence interval for the difference. The new interval removes the skewness in the Edgeworth expansion; the new interval is easy to compute, and its coverage …

The Effect Of Ultrasonics On Fibroblast Cells, Sheila A. Harris

Loma Linda University Electronic Theses, Dissertations & Projects

The field of dentistry uses the debriding properties of ultrasonic vibration. It is unknown if this property is detrimental to the periodontal ligament (PDL) of an avulsed tooth. This information is important when a clinician is faced with a debris-covered avulsed tooth following a traumatic event. The purpose of this study was to determine the effect that ultrasonic vibration has on those PDL cells most numerous and most vital to a successful tooth replantation, namely, the fibroblasts.

Several fibroblast cell sources were exposed to varying ultrasonic times. These included a commercially available cell line of human foreskin fibroblast (HFF), a …

Cultural And Psychological Influences On Diabetic Adherence, Keikilani Mcmillin-Williams

Loma Linda University Electronic Theses, Dissertations & Projects

Diabetes mellitus is a serious disease that poses a particular healthcare challenge because progression is considered controllable (Cox, et al, 1985; Vinicor, et al, 1996) yet treatment adherence, and thus outcome, is very poor (Gonder-Frederick, Cox, & Ritterband, 2002; Goodall, 1991). Culture is a lethal risk factor for diabetic contraction and treatment maintenance. Latinos within the United States are two-to-three times more likely to develop complications and die than non-Latinos (Haffner et al, 1996; Rubin, Peyrot, & Saudek, 1991) and are less likely to adhere to treatment (Lipton, Losey, Giachello, Mendez, & Girotti, 1998). Efforts to eliminate health disparities have …

Flow And Pressure Distributions In Vascular Networks Consisting Of Distensible Vessels, Gary S. Krenz, Christopher A. Dawson

Mathematics, Statistics and Computer Science Faculty Research and Publications

We examine the influence of vessel distensibility on the fraction of the total network flow passing through each vessel of a model vascular network. An exact computational methodology is developed yielding an analytic proof. For a class of structurally heterogeneous asymmetric vascular networks, if all the individual vessels share a common distensibility relation when the total network flow is changed, this methodology proves that each vessel will continue to receive the same fraction of the total network flow. This constant flow partitioning occurs despite a redistribution of pressures, which may result in a decrease in the diameter of one and …

A Monte Carlo Analysis Of Hedonic Models Using Traditional And Spatial Approaches, Helen R. Neill, David M. Hassenzahl, Djeto D. Assane

Public Policy and Leadership Faculty Research

Hedonic regression analysis of single family homes typically includes structural variables, locational variables and neighborhood quality characteristics. When nearby properties are related, Dubin (1988) reports that error terms are spatially autocorrelated. Estimation methods for these spatially autocorrelated error terms or hereafter, spatial approaches, include maximum likelihood estimation (MLE) and kriging techniques such as kriged maximum likelihood estimation (KMLE). Unfortunately these spatial methods require massive computer resources and are limited to significantly fewer observations than traditional ordinary least squares (OLS). This paper investigates the combination of spatial approaches and Monte Carlo analysis, a method that approximates large data sets. A question …

New Graphical Approach On The Analysis Of Experimental Data, Suha Sari

Dissertations

This study presents a new graphical method to identify significant effects in factorial experiments. The proposed methods are obtained for the different cases in which the design can be of full factorial or fractional factorial and the factor levels can be pure or mixed.

We focus on the different decomposition methods, for example orthogonal components system and orthogonal contrast method, to make use of the chisquare plot which requires that the sums of squares are of the same degrees of freedom. Examples and simulations illustrating the different cases of the procedure are presented.

A Comparison Of Different Schemes For Selecting And Estimating Score Functions Based On Residuals, Ali A. Al-Shomrani

Dissertations

In a linear model when the errors follow a normal distribution, least squares methodology is most powerful. However, when the assumption of normality of the error distribution is not met then there exist methods which are more powerful than least squares methods. Rank-based methods form one such class. These methods depend on the selection of a score function [varphi]( u ). The correct choice of [varphi] leads to an optimal (efficient) analysis, but its selection depends on the error distribution which is not known.

In this thesis, we explore different schemes for score selection. Some of these schemes are functions …

An Application In Bioinformatics : A Comparison Of Affymetrix And Compugen Human Genome Microarrays, Milind Misra

Theses

The human genome microarrays from Compugen® and Affymetrix® were compared in the context of the emerging field of computational biology. The two premier database servers for genomic sequence data, the National Center for Biotechnology Information and the European Bioinformatics Institute, were described in detail. The various databases and data mining tools available through these data servers were also discussed. Microarrays were examined from a historical perspective and their main current applications-expression analysis, mutation analysis, and comparative genomic hybridization-were discussed. The two main types of microarrays, cDNA spotted microarrays and high-density spotted microarrays were analyzed by exploring the human genome microarray …

Supervised Detection Of Regulatory Motifs In Dna Sequences, Sunduz Keles, Mark J. Van Der Laan, Sandrine Dudoit, Biao Xing, Michael B. Eisen

U.C. Berkeley Division of Biostatistics Working Paper Series

Identification of transcription factor binding sites (regulatory motifs) is a major interest in contemporary biology. We propose a new likelihood based method, COMODE, for identifying structural motifs in DNA sequences. Commonly used methods (e.g. MEME, Gibbs sampler) model binding sites as families of sequences described by a position weight matrix (PWM) and identify PWMs that maximize the likelihood of observed sequence data under a simple multinomial mixture model. This model assumes that the positions of the PWM correspond to independent multinomial distributions with four cell probabilities. We address supervising the search for DNA binding sites using the information derived from …