Digital Commons Network^™

Teaching Random Assignment: Do You Believe It Works?, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

Textbook authors admonish students to check on the comparability of two randomly assigned groups by conducting statistical tests on pretest means to determine if randomization worked. A Monte Carlo study was conducted on a sample of n = 2 per group, where each participant’s personality profile was represented by 7,500 randomly selected and assigned scores. Independent samples t tests were conducted and the results demonstrated that random assignment was successful in equating the two groups on 7,467 variables. The students’ focus is redirected from the ability of random assignment to create comparable groups to the testing of the claims of …

A Comparison Of Bayesian And Frequentist Statistics As Applied In A Simple Repeated Measures Example, Jan Perkins, Daniel Wang

Journal of Modern Applied Statistical Methods

Clinicians see Bayesian and frequentist analysis in published research papers, and need a basic understanding of both. A repeated measures data set was analyzed using both approaches. Assumptions underlying each method and conclusions reached were contrasted. The Bayesian approach is a viable alternative to frequentist statistical analysis for many clinical projects.

Jmasm10: A Fortran Routine For Sieve Bootstrap Prediction Intervals, Andrés M. Alonso

Journal of Modern Applied Statistical Methods

A Fortran routine for constructing nonparametric prediction intervals for a general class of linear processes is described. The approach uses the sieve bootstrap procedure of Bühlmann (1997) based on residual resampling from an autoregressive approximation to the given process.

A Resistant Estimator Of Multivariate Location And Dispersion, David J. Olive

Articles and Preprints

This paper presents a simple resistant estimator of multivariate location and dispersion. The DD plot is a plot of Mahalanobis distances from the classical estimator versus the distances from a resistant estimator and can be used to detect outliers and as a diagnostic for multivariate normality. The new estimator can be used in the DD plot, is easy to compute and provides insights about several useful robust algorithm techniques.

A Comparison Of Methods For Longitudinal Analysis With Missing Data, James Algina, H. J. Keselman

Journal of Modern Applied Statistical Methods

In a longitudinal two-group randomized trials design, also referred to as randomized parallel-groups design or split-plot repeated measures design, the important hypothesis of interest is whether there are differential rates of change over time, that is, whether there is a group by time interaction. Several analytic methods have been presented in the literature for testing this important hypothesis when data are incomplete. We studied these methods for the case in which the missing data pattern is non-monotone. In agreement with earlier work on monotone missing data patterns, our results on bias, sampling variability, Type I error and power support the …

On Polynomial Transformations For Simulating Multivariate Non-Normal Distributions, Todd C. Headrick

Journal of Modern Applied Statistical Methods

Procedures are introduced and discussed for increasing the computational and statistical efficiency of polynomial transformations used in Monte Carlo or simulation studies. Comparisons are also made between polynomials of order three and five in terms of (a) computational and statistical efficiency, (b) the skew and kurtosis boundary, and (c) boundaries for Pearson correlations. It is also shown how ranked data can be simulated for specified Spearman correlations and sample sizes. Potential consequences of nonmonotonic transformations on rank correlations are also discussed.

An Alternative Q Chart Incorporating A Robust Estimator Of Scale, Michael B. C. Khoo

Journal of Modern Applied Statistical Methods

In overcoming the shortcomings of the classical control charts in a short runs production, Quesenberry (1991 & 1995a – d) proposed Q charts for attributes and variables data. An approach to enhance the performance of a variable Q chart based on individual measurements using a robust estimator of scale is proposed. Monte carlo simulations are conducted to show that the proposed robust Q chart is superior to the present Q chart.

Quantifying The Proportion Of Cases Attributable To An Exposure, Camil Fuchs, Vance W. Berger

Journal of Modern Applied Statistical Methods

The attributable fraction and the average attributable fractions, which are commonly used to assess the relative effect of several exposures to the prevalence of a disease, do not represent the proportion of cases caused by each exposure. Furthermore, the sum of attributable fractions over all exposures generally exceeds not only the attributable fraction for all exposures taken together, but also 100%. Other measures are discussed here, including the directly attributable fraction and the confounding fraction, that may be more suitable in defining the fraction directly attributable to an exposure.

The Robustness Of Factor Analyses When The Data Does Not Conform To Standard Parametric Requirements, Haisong Peng

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Objective: To access the robustness of factor analyses when the data does not conform to standard parametric requirements.

Methods: Data were simulated in package R. Maximum likelihood was used to fit and assess the factor models. Chi-square statistics were obtained to test hypotheses about the correct number of factors in simulated settings where the true number of factors was known. The number of true factors varied between 1 and 3; the number of observed variables was either 6 (for 1 factor) or 3 per factor for 2 or more factors.

Results: With standard normal factor populations, and normal errors added …

Does Weighting For Nonresponse Increase The Variance Of Survey Means?, Rod Little, Sonya L. Vartivarian

The University of Michigan Department of Biostatistics Working Paper Series

Nonresponse weighting is a common method for handling unit nonresponse in surveys. A widespread view is that the weighting method is aimed at reducing nonresponse bias, at the expense of an increase in variance. Hence, the efficacy of weighting adjustments becomes a bias-variance trade-off. This note suggests that this view is an oversimplification -- nonresponse weighting can in fact lead to a reduction in variance as well as bias. A covariate for a weighting adjustment must have two characteristics to reduce nonresponse bias - it needs to be related to the probability of response, and it needs to be related …

Resampling Methods For Estimating Functions With U-Statistic Structure, Wenyu Jiang, Jack Kalbfleisch

The University of Michigan Department of Biostatistics Working Paper Series

Suppose that inference about parameters of interest is to be based on an unbiased estimating function that is U-statistic of degree 1 or 2. We define suitable studentized versions of such estimating functions and consider asymptotic approximations as well as an estimating function bootstrap (EFB) method based on resampling the estimated terms in the estimating functions. These methods are justified asymptotically and lead to confidence intervals produced directly from the studentized estimating functions. Particular examples in this class of estimating functions arise in La estimation as well as Wilcoxon rank regression and other related estimation problems. The proposed methods are …

One- And Two-Sample Nonparametric Inference Procedures In The Presence Of Dependent Censoring, Yuhyun Park, Lu Tian, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Covariate Adjustment In The Analysis Of Microarray Data From Clinical Studies, Debashis Ghosh, Arul Chinnaiyan

The University of Michigan Department of Biostatistics Working Paper Series

There is tremendous scientific interest in the analysis of gene expression data in clinical settings, such as oncology. In this paper, we describe the importance of adjusting for confounders and other prognostic factors in order to select for differentially expressed genes for followup validation studies. We develop two approaches to the analysis of microarray data in nonrandomized clinical settings. The first is an extension of the current significance analysis of microarray procedures, where other covariates are taken into account. The second is a novel covariate-adjusted regression modelling based on the receiver operating characteristic curve for the analysis of gene expression …

Evaluating Markers For Selecting A Patient's Treatment, Xiao Song, Margaret S. Pepe

UW Biostatistics Working Paper Series

Selecting the best treatment for a patient's disease may be facilitated by evaluating clinical characteristics or biomarker measurements at diagnosis. We consider how to evaluate the potential of such measurements to impact on treatment selection algorithms. For example, magnetic resonance neurographic imaging is potentially useful for deciding whether a patient should be treated surgically for carpal tunnel syndrome or if he/she should receive less invasive conservative therapy. We propose a graphical display, the selection impact (SI) curve, that shows the population response rate as a function of treatment selection criteria based on the marker. The curve can be useful for …

Nonparametric Control Chart For The Range, Arnold J. Stromberg

Statistics Faculty Patents

The method comprises establishing the number of subsets of a dataset that have a range of the difference between any two datapoints within the dataset, and computing a control chart for the range based thereon. In another aspect, a software program for accomplishing the method of the present invention is provided. The method of the invention allows monitoring variability of a product being produced by a particular piece of machinery, of a process conducted by the machinery, or of a product stream generated thereby, accurately detecting changes in variability in real time. The true distribution of the data is reflected, …

Mathematical And Empirical Modeling Of Chemical Reactions In A Microreactor, Jing Hu

Doctoral Dissertations

This dissertation is concerned with mathematical and empirical modeling to simulate three important chemical reactions (cyclohexene hydrogenation and dehydrogenation, preferential oxidation of carbon monoxide, and the Fischer-Tropsch (F-T) synthesis in a microreaction system.

Empirical modeling and optimization techniques based on experimental design (Central Composite Design (CCD)) and response surface methodology were applied to these three chemical reactions. Regression models were built, and the operating conditions (such as temperature, the ratio of the reactants, and total flow rate) which maximize reactant conversion and product selectivity were determined for each reaction.

A probability model for predicting the probability that a certain species …

Fisheries Occasional Publication No. 6 - Anglers Guide To Assessing Reproductive Stage In Fish, Kim Smith, Mike Mackie, Department Of Fisheries Western Australia

Fisheries Occasional Publications

What is a gonad?

"Gonad" is a general term for a reproductive organ, and is used to describe both ovaries and testes. In male and female fish, the gonad is an elongated organ lying along the upper wall of the gut cavity (i.e. running immediately under the vertebral column). The gonad gonad has 2 lobes. Both lobes are attached to the body near the anus and extend forward inside the gut cavity.

As fish gonads ripen, they become larger, heavier and change colour. Immature and undeveloped adult gonads are very small, strap-like in shape, pinkish in colour and translucent (i.e. …

On Leverage In A Stochastic Volatility Model, Jun Yu

Research Collection School Of Economics

This paper is concerned with specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications co-exist in the literature. One is the Euler approximation to the well known continuous time SV model with leverage effect and the other is the discrete time SV model of Jacquier, Polson and Rossi (2004, Journal of Econometrics, forthcoming). Using a Gaussian nonlinear state space form with uncorrelated measurement and transition errors, I show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain the leverage effect …

Regulatory Motif Finding By Logic Regression, Sunduz Keles, Mark J. Van Der Laan, Chris Vulpe

U.C. Berkeley Division of Biostatistics Working Paper Series

Multiple transcription factors coordinately control transcriptional regulation of genes in eukaryotes. Although multiple computational methods consider the identification of individual transcription factor binding sites (TFBSs), very few focus on the interactions between these sites. We consider finding transcription factor binding sites and their context specific interactions using microarray gene expression data. We devise a hybrid approach called LogicMotif composed of a TFBS identification method combined with the new regression methodology logic regression of Ruczinski et al. (2003). LogicMotif has two steps: First potential binding sites are identified from transcription control regions of genes of interest. Various available methods can be …

Latest Tools For Viewing And Quality Checking Arm Data, S. Moore, Gary B. Hughes

Statistics

The DOE Atmospheric Radiation Measurement (ARM) program has acquired an incredibly large quantity of data over its period of operation, all of which must be reviewed in some manner in order to ensure that the data is of “known and reasonable” quality (ARM Science Plan). To accomplish this, Mission Research Corporation (MRC) coordinates with the ARM Data Quality Office to develop software tools that quality-check data products in a timely and continuous fashion. These tools work with the Data Quality Health and Status (DQ HandS) Explorer (Peppler et al. 2004) by analyzing ARM data streams, providing assessments of data quality …

A Statistical Method For Constructing Transcriptional Regulatory Networks Using Gene Expression And Sequence Data , Biao Xing, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Transcriptional regulation is one of the most important means of gene regulation. Uncovering transcriptional regulatory network helps us to understand the complex cellular process. In this paper, we describe a comprehensive statistical approach for constructing the transcriptional regulatory network using data of gene expression, promoter sequence, and transcription factor binding sites. Our simulation studies show that the overall and false positive error rates in the estimated transcriptional regulatory network are expected to be small if the systematic noise in the constructed feature matrix is small. Our analysis based on 658 microarray experiments on yeast gene expression programs and 46 transcription …

Causal Inference In Hybrid Intervention Trials Involving Treatment Choice, Qi Long, Rod Little, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

Randomized allocation of treatments is a cornerstone of experimental design, but has drawbacks when a limited set of individuals are willing to be randomized, or the act of randomization undermines the success of the treatment. Choice-based experimental designs allow a subset of the participants to choose their treatments. We discuss here causal inferences for experimental designs where some participants are randomly allocated to treatments and others receive their treatment preference. This paper was motivated by the “Women Take Pride” (WTP) study (Janevic et al., 2001), a doubly randomized preference trail (DRPT) to assess behavioral interventions for women with heart disease. …

Error Models For Microarray Intensities, Wolfgang Huber, Anja Von Heydebreck, Martin Vingron

Bioconductor Project Working Papers

We derive the additive-multiplicative error model for microarray intensities, and describe two applications. For the detection of differentially expressed genes, we obtain a statistic whose variance is approximately independent of the mean intensity. For the post hoc calibration (normalization) of data with respect to experimental factors, we describe a method for parameter estimation.

A Bayesian Hierarchical Approach To Multirater Correlated Roc Analysis, Tim Johnson, Valen Johnson

The University of Michigan Department of Biostatistics Working Paper Series

In a common ROC study design, several readers are asked to rate diagnostics of the same cases processed under different modalities. We describe a Bayesian hierarchical model that facilitates the analysis of this study design by explicitly modeling the three sources of variation inherent to it. In so doing, we achieve substantial reductions in the posterior uncertainty associated with estimates of the differences in areas under the estimated ROC curves and corresponding reductions in the mean squared error (MSE) of these estimates. Based on simulation studies, both the widths of confidence intervals and MSE of estimates of differences in the …

Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In van der Laan and Dudoit (2003) we propose and theoretically study a unified loss function based statistical methodology, which provides a road map for estimation and performance assessment. Given a parameter of interest which can be described as the minimizer of the population mean of a loss function, the road map involves as important ingredients cross-validation for estimator selection and minimizing over subsets of basis functions the empirical risk of the subset-specific estimator of the parameter of interest, where the basis functions correspond to a parameterization of a specified subspace of the complete parameter space. In this article we …

Explaining Death Row's Population And Racial Composition, John H. Blume, Theodore Eisenberg, Martin T. Wells

Cornell Law Faculty Publications

Twenty-three years of murder and death sentence data show how murder demographics help explain death row populations. Nevada and Oklahoma are the most death-prone states; Texas's death sentence rate is below the national mean. Accounting for the race of murderers establishes that black representation on death row is lower than black representation in the population of murder offenders. This disproportion results from reluctance to seek or impose death in black defendant-black victim cases, which more than offsets eagerness to seek and impose death in black defendant-white victim cases. Death sentence rates in black defendant-white victim cases far exceed those in …

Attorney Fees In Class Action Settlements: An Empirical Study, Theodore Eisenberg, Geoffrey P. Miller

Cornell Law Faculty Publications

Study of two comprehensive class action case data sets covering 1993-2002 shows that the amount of client recovery is overwhelmingly the most important determinant of the attorney fee award. Even in cases in which the courts engage in the lodestar calculation (the product of reasonable hours and a reasonable hourly rate), the client's recovery generally explains the pattern of awards better than the lodestar. Thus, the time and expense of a lodestar calculation may be wasteful. We also find no robust evidence that either recoveries for plaintiffs or fees of their attorneys increased overtime. The mean fee award in common …

An Investigation Of The Effects Of Correlation, Autocorrelation, And Sample Size In Classifier Fusion, Nathan J. Leap

Theses and Dissertations

This thesis extends the research found in Storm, Bauer, and Oxley, 2003. Data correlation effects and sample size effects on three classifier fusion techniques and one data fusion technique were investigated. Identification System Operating Characteristic Fusion (Haspert, 2000), the Receiver Operating Characteristic Within Fusion method (Oxley and Bauer, 2002), and a Probabilistic Neural Network were the three classifier fusion techniques; a Generalized Regression Neural Network was the data fusion technique. Correlation was injected into the data set both within a feature set (autocorrelation) and across feature sets for a variety of classification problems, and sample size was varied throughout. Total …

The Cross-Validated Adaptive Epsilon-Net Estimator, Mark J. Van Der Laan, Sandrine Dudoit, Aad W. Van Der Vaart

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose that we observe a sample of independent and identically distributed realizations of a random variable. Assume that the parameter of interest can be defined as the minimizer, over a suitably defined parameter space, of the expectation (with respect to the distribution of the random variable) of a particular (loss) function of a candidate parameter value and the random variable. Examples of commonly used loss functions are the squared error loss function in regression and the negative log-density loss function in density estimation. Minimizing the empirical risk (i.e., the empirical mean of the loss function) over the entire parameter space …

A Bayesian Chi-Squared Test For Goodness Of Fit, Valen Johnson

The University of Michigan Department of Biostatistics Working Paper Series

This article describes an extension of classical x 2 goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involvesevaluating Pearson's goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptoti-cally distributed as a x2 random variable on K-1 degrees of freedom, indepen-dently of the dimension of the underlying parameter vector. By averaging over the posterior distribution of this statistic, a global goodness-of-fit diagnostic is obtained. Advantages of this diagnostic{which may be interpreted as the area under an ROC curve{include ease of interpretation, computational conve-nience, and favorable power properties. The proposed …