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2005

Statistical Theory

UW Biostatistics Working Paper Series

Articles 1 - 16 of 16

Full-Text Articles in Physical Sciences and Mathematics

Alleviating Linear Ecological Bias And Optimal Design With Subsample Data, Adam Glynn, Jon Wakefield, Mark Handcock, Thomas Richardson Dec 2005

Alleviating Linear Ecological Bias And Optimal Design With Subsample Data, Adam Glynn, Jon Wakefield, Mark Handcock, Thomas Richardson

UW Biostatistics Working Paper Series

In this paper, we illustrate that combining ecological data with subsample data in situations in which a linear model is appropriate provides three main benefits. First, by including the individual level subsample data, the biases associated with linear ecological inference can be eliminated. Second, by supplementing the subsample data with ecological data, the information about parameters will be increased. Third, we can use readily available ecological data to design optimal subsampling schemes, so as to further increase the information about parameters. We present an application of this methodology to the classic problem of estimating the effect of a college degree …

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Empirical Likelihood Inference For The Area Under The Roc Curve, Gengsheng Qin, Xiao-Hua Zhou Dec 2005

Empirical Likelihood Inference For The Area Under The Roc Curve, Gengsheng Qin, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

For a continuous-scale diagnostic test, the most commonly used summary index of the receiver operating characteristic (ROC) curve is the area under the curve (AUC) that measures the accuracy of the diagnostic test. In this paper we propose an empirical likelihood approach for the inference of AUC. We first define an empirical likelihood ratio for AUC and show that its limiting distribution is a scaled chi-square distribution. We then obtain an empirical likelihood based confidence interval for AUC using the scaled chi-square distribution. This empirical likelihood inference for AUC can be extended to stratified samples and the resulting limiting distribution …

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Interval Estimation For The Ratio And Difference Of Two Lognormal Means, Yea-Hung Chen, Xiao-Hua Zhou Dec 2005

Interval Estimation For The Ratio And Difference Of Two Lognormal Means, Yea-Hung Chen, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Health research often gives rise to data that follow lognormal distributions. In two sample situations, researchers are likely to be interested in estimating the difference or ratio of the population means. Several methods have been proposed for providing confidence intervals for these parameters. However, it is not clear which techniques are most appropriate, or how their performance might vary. Additionally, methods for the difference of means have not been adequately explored. We discuss in the present article five methods of analysis. These include two methods based on the log-likelihood ratio statistic and a generalized pivotal approach. Additionally, we provide and …

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Inferences In Censored Cost Regression Models With Empirical Likelihood, Xiao-Hua Zhou, Gengsheng Qin, Huazhen Lin, Gang Li Dec 2005

Inferences In Censored Cost Regression Models With Empirical Likelihood, Xiao-Hua Zhou, Gengsheng Qin, Huazhen Lin, Gang Li

UW Biostatistics Working Paper Series

In many studies of health economics, we are interested in the expected total cost over a certain period for a patient with given characteristics. Problems can arise if cost estimation models do not account for distributional aspects of costs. Two such problems are 1) the skewed nature of the data and 2) censored observations. In this paper we propose an empirical likelihood (EL) method for constructing a confidence region for the vector of regression parameters and a confidence interval for the expected total cost of a patient with the given covariates. We show that this new method has good theoretical …

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Confidence Intervals For Predictive Values Using Data From A Case Control Study, Nathaniel David Mercaldo, Xiao-Hua Zhou, Kit F. Lau Dec 2005

Confidence Intervals For Predictive Values Using Data From A Case Control Study, Nathaniel David Mercaldo, Xiao-Hua Zhou, Kit F. Lau

UW Biostatistics Working Paper Series

The accuracy of a binary-scale diagnostic test can be represented by sensitivity (Se), specificity (Sp) and positive and negative predictive values (PPV and NPV). Although Se and Sp measure the intrinsic accuracy of a diagnostic test that does not depend on the prevalence rate, they do not provide information on the diagnostic accuracy of a particular patient. To obtain this information we need to use PPV and NPV. Since PPV and NPV are functions of both the intrinsic accuracy and the prevalence of the disease, constructing confidence intervals for PPV and NPV for a particular patient in a population with …

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Optimal Feature Selection For Nearest Centroid Classifiers, With Applications To Gene Expression Microarrays, Alan R. Dabney, John D. Storey Nov 2005

Optimal Feature Selection For Nearest Centroid Classifiers, With Applications To Gene Expression Microarrays, Alan R. Dabney, John D. Storey

UW Biostatistics Working Paper Series

Nearest centroid classifiers have recently been successfully employed in high-dimensional applications. A necessary step when building a classifier for high-dimensional data is feature selection. Feature selection is typically carried out by computing univariate statistics for each feature individually, without consideration for how a subset of features performs as a whole. For subsets of a given size, we characterize the optimal choice of features, corresponding to those yielding the smallest misclassification rate. Furthermore, we propose an algorithm for estimating this optimal subset in practice. Finally, we investigate the applicability of shrinkage ideas to nearest centroid classifiers. We use gene-expression microarrays for …

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A New Approach To Intensity-Dependent Normalization Of Two-Channel Microarrays, Alan R. Dabney, John D. Storey Nov 2005

A New Approach To Intensity-Dependent Normalization Of Two-Channel Microarrays, Alan R. Dabney, John D. Storey

UW Biostatistics Working Paper Series

A two-channel microarray measures the relative expression levels of thousands of genes from a pair of biological samples. In order to reliably compare gene expression levels between and within arrays, it is necessary to remove systematic errors that distort the biological signal of interest. The standard for accomplishing this is smoothing "MA-plots" to remove intensity-dependent dye bias and array-specific effects. However, MA methods require strong assumptions. We review these assumptions and derive several practical scenarios in which they fail. The "dye-swap" normalization method has been much less frequently used because it requires two arrays per pair of samples. We show …

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Estimating A Treatment Effect With Repeated Measurements Accounting For Varying Effectiveness Duration, Ying Qing Chen, Jingrong Yang, Su-Chun Cheng Nov 2005

Estimating A Treatment Effect With Repeated Measurements Accounting For Varying Effectiveness Duration, Ying Qing Chen, Jingrong Yang, Su-Chun Cheng

UW Biostatistics Working Paper Series

To assess treatment efficacy in clinical trials, certain clinical outcomes are repeatedly measured for same subject over time. They can be regarded as function of time. The difference in their mean functions between the treatment arms usually characterises a treatment effect. Due to the potential existence of subject-specific treatment effectiveness lag and saturation times, erosion of treatment effect in the difference may occur during the observation period of time. Instead of using ad hoc parametric or purely nonparametric time-varying coefficients in statistical modeling, we first propose to model the treatment effectiveness durations, which are the varying time intervals between the …

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The Optimal Discovery Procedure: A New Approach To Simultaneous Significance Testing, John D. Storey Sep 2005

The Optimal Discovery Procedure: A New Approach To Simultaneous Significance Testing, John D. Storey

UW Biostatistics Working Paper Series

Significance testing is one of the main objectives of statistics. The Neyman-Pearson lemma provides a simple rule for optimally testing a single hypothesis when the null and alternative distributions are known. This result has played a major role in the development of significance testing strategies that are used in practice. Most of the work extending single testing strategies to multiple tests has focused on formulating and estimating new types of significance measures, such as the false discovery rate. These methods tend to be based on p-values that are calculated from each test individually, ignoring information from the other tests. As …

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The Optimal Discovery Procedure For Large-Scale Significance Testing, With Applications To Comparative Microarray Experiments, John D. Storey, James Y. Dai, Jeffrey T. Leek Sep 2005

The Optimal Discovery Procedure For Large-Scale Significance Testing, With Applications To Comparative Microarray Experiments, John D. Storey, James Y. Dai, Jeffrey T. Leek

UW Biostatistics Working Paper Series

As much of the focus of genetics and molecular biology has shifted toward the systems level, it has become increasingly important to accurately extract biologically relevant signal from thousands of related measurements. The common property among these high-dimensional biological studies is that the measured features have a rich and largely unknown underlying structure. One example of much recent interest is identifying differentially expressed genes in comparative microarray experiments. We propose a new approach aimed at optimally performing many hypothesis tests in a high-dimensional study. This approach estimates the Optimal Discovery Procedure (ODP), which has recently been introduced and theoretically shown …

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Linear Regression Of Censored Length-Biased Lifetimes, Ying Qing Chen, Yan Wang Jul 2005

Linear Regression Of Censored Length-Biased Lifetimes, Ying Qing Chen, Yan Wang

UW Biostatistics Working Paper Series

Length-biased lifetimes may be collected in observational studies or sample surveys due to biased sampling scheme. In this article, we use a linear regression model, namely, the accelerated failure time model, for the population lifetime distributions in regression analysis of the length-biased lifetimes. It is discovered that the associated regression parameters are invariant under the length-biased sampling scheme. According to this discovery, we propose the quasi partial score estimating equations to estimate the population regression parameters. The proposed methodologies are evaluated and demonstrated by simulation studies and an application to actual data set.

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On Additive Regression Of Expectancy, Ying Qing Chen Jun 2005

On Additive Regression Of Expectancy, Ying Qing Chen

UW Biostatistics Working Paper Series

Regression models have been important tools to study the association between outcome variables and their covariates. The traditional linear regression models usually specify such an association by the expectations of the outcome variables as function of the covariates and some parameters. In reality, however, interests often focus on their expectancies characterized by the conditional means. In this article, a new class of additive regression models is proposed to model the expectancies. The model parameters carry practical implication, which may allow the models to be useful in applications such as treatment assessment, resource planning or short-term forecasting. Moreover, the new model …

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An Empirical Process Limit Theorem For Sparsely Correlated Data, Thomas Lumley Jun 2005

An Empirical Process Limit Theorem For Sparsely Correlated Data, Thomas Lumley

UW Biostatistics Working Paper Series

We consider data that are dependent, but where most small sets of observations are independent. By extending Bernstein's inequality we prove a strong law of law numbers and an empirical process central limit theorem under bracketing entropy conditions.

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Multiple Imputation For Correcting Verification Bias, Ofer Harel, Xiao-Hua Zhou May 2005

Multiple Imputation For Correcting Verification Bias, Ofer Harel, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

In the case in which all subjects are screened using a common test, and only a subset of these subjects are tested using a golden standard test, it is well documented that there is a risk for bias, called verification bias. When the test has only two levels (e.g. positive and negative) and we are trying to estimate the sensitivity and specificity of the test, one is actually constructing a confidence interval for a binomial proportion. Since it is well documented that this estimation is not trivial even with complete data, we adopt Multiple imputation (MI) framework for verification bias …

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A Comparison Of Parametric And Coarsened Bayesian Interval Estimation In The Presence Of A Known Mean-Variance Relationship, Kent Koprowicz, Scott S. Emerson, Peter Hoff Apr 2005

A Comparison Of Parametric And Coarsened Bayesian Interval Estimation In The Presence Of A Known Mean-Variance Relationship, Kent Koprowicz, Scott S. Emerson, Peter Hoff

UW Biostatistics Working Paper Series

While the use of Bayesian methods of analysis have become increasingly common, classical frequentist hypothesis testing still holds sway in medical research - especially clinical trials. One major difference between a standard frequentist approach and the most common Bayesian approaches is that even when a frequentist hypothesis test is derived from parametric models, the interpretation and operating characteristics of the test may be considered in a distribution-free manner. Bayesian inference, on the other hand, is often conducted in a parametric setting where the interpretation of the results is dependent on the parametric model. Here we consider a Bayesian counterpart to …

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Bayesian Evaluation Of Group Sequential Clinical Trial Designs, Scott S. Emerson, John M. Kittelson, Daniel L. Gillen Mar 2005

Bayesian Evaluation Of Group Sequential Clinical Trial Designs, Scott S. Emerson, John M. Kittelson, Daniel L. Gillen

UW Biostatistics Working Paper Series

Clincal trial designs often incorporate a sequential stopping rule to serve as a guide in the early termination of a study. When choosing a particular stopping rule, it is most common to examine frequentist operating characteristics such as type I error, statistical power, and precision of confi- dence intervals (Emerson, et al. [1]). Increasingly, however, clinical trials are designed and analyzed in the Bayesian paradigm. In this paper we describe how the Bayesian operating characteristics of a particular stopping rule might be evaluated and communicated to the scientific community. In particular, we consider a choice of probability models and a …

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