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Full-Text Articles in Applied Mathematics

Resampling-Based Multiple Testing: Asymptotic Control Of Type I Error And Applications To Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan Jun 2003

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 …

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Maximization By Parts In Likelihood Inference, Peter Xuekun Song, Yanqin Fan, Jack Kalbfleisch Jun 2003

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 …

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Double Robust Estimation In Longitudinal Marginal Structural Models, Zhuo Yu, Mark J. Van Der Laan Jun 2003

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 …

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A Bootstrap Confidence Interval Procedure For The Treatment Effect Using Propensity Score Subclassification, Wanzhu Tu, Xiao-Hua Zhou May 2003

A Bootstrap Confidence Interval Procedure For The Treatment Effect Using Propensity Score Subclassification, Wanzhu Tu, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

In the analysis of observational studies, propensity score subclassification has been shown to be a powerful method for adjusting unbalanced covariates for the purpose of causal inferences. One practical difficulty in carrying out such an analysis is to obtain a correct variance estimate for such inferences, while reducing bias in the estimate of the treatment effect due to an imbalance in the measured covariates. In this paper, we propose a bootstrap procedure for the inferences concerning the average treatment effect; our bootstrap method is based on an extension of Efron’s bias-corrected accelerated (BCa) bootstrap confidence interval to a two-sample problem. …

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Estimating The Accuracy Of Polymerase Chain Reaction-Based Tests Using Endpoint Dilution, Jim Hughes, Patricia Totten Mar 2003

Estimating The Accuracy Of Polymerase Chain Reaction-Based Tests Using Endpoint Dilution, Jim Hughes, Patricia Totten

UW Biostatistics Working Paper Series

PCR-based tests for various microorganisms or target DNA sequences are generally acknowledged to be highly "sensitive" yet the concept of sensitivity is ill-defined in the literature on these tests. We propose that sensitivity should be expressed as a function of the number of target DNA molecules in the sample (or specificity when the target number is 0). However, estimating this "sensitivity curve" is problematic since it is difficult to construct samples with a fixed number of targets. Nonetheless, using serially diluted replicate aliquots of a known concentration of the target DNA sequence, we show that it is possible to disentangle …

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Simple Parallel Statistical Computing In R, Anthony Rossini, Luke Tierney, Na Li Mar 2003

Simple Parallel Statistical Computing In R, Anthony Rossini, Luke Tierney, Na Li

UW Biostatistics Working Paper Series

Theoretically, many modern statistical procedures are trivial to parallelize. However, practical deployment of a parallelized implementation which is robust and reliably runs on different computational cluster configurations and environments is far from trivial. We present a framework for the R statistical computing language that provides a simple yet powerful programming interface to a computational cluster. This interface allows the development of R functions that distribute independent computations across the nodes of the computational cluster. The resulting framework allows statisticians to obtain significant speed-ups for some computations at little additional development cost. The particular implementation can be deployed in heterogeneous computing …

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Literate Statistical Practice, Anthony Rossini, Friedrich Leisch Mar 2003

Literate Statistical Practice, Anthony Rossini, Friedrich Leisch

UW Biostatistics Working Paper Series

Literate Statistical Practice (LSP, Rossini, 2001) describes an approach for creating self-documenting statistical results. It applies literate programming (Knuth, 1992) and related techniques in a natural fashion to the practice of statistics. In particular, documentation, specification, and descriptions of results are written concurrently with writing and evaluation of statistical programs. We discuss how and where LSP can be integrated into practice and illustrate this with an example derived from an actual statistical consulting project. The approach is simplified through the use of a comprehensive, open source toolset incorporating Noweb, Emacs Speaks Statistics (ESS), Sweave (Ramsey, 1994; Rossini, et al, 2002; …

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Checking Assumptions In Latent Class Regression Models Via A Markov Chain Monte Carlo Estimation Approach: An Application To Depression And Socio-Economic Status, Elizabeth Garrett, Richard Miech, Pamela Owens, William W. Eaton, Scott L. Zeger Jan 2003

Checking Assumptions In Latent Class Regression Models Via A Markov Chain Monte Carlo Estimation Approach: An Application To Depression And Socio-Economic Status, Elizabeth Garrett, Richard Miech, Pamela Owens, William W. Eaton, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to …

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An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan Oct 2002

An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In non-randomized treatment studies a significant problem for statisticians is determining how best to adjust for confounders. Marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators are useful in analyzing the causal effect of treatment in observational studies. Given an IPTW estimator a doubly robust augmented IPTW (AIPTW) estimator orthogonalizes it resulting in a more e±cient estimator than the IPTW estimator. One purpose of this paper is to make a practical comparison between the IPTW estimator and the doubly robust AIPTW estimator via a series of Monte- Carlo simulations. We also consider the selection of the optimal …

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Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell Sep 2002

Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

In many applications, it is often of interest to estimate a bivariate distribution of two survival random variables. Complete observation of such random variables is often incomplete. If one only observes whether or not each of the individual survival times exceeds a common observed monitoring time C, then the data structure is referred to as bivariate current status data (Wang and Ding, 2000). For such data, we show that the identifiable part of the joint distribution is represented by three univariate cumulative distribution functions, namely the two marginal cumulative distribution functions, and the bivariate cumulative distribution function evaluated on the …

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A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan Feb 2002

A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan

U.C. Berkeley Division of Biostatistics Working Paper Series

Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …

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Maximum Likelihood Estimation Of Ordered Multinomial Parameters, Nicholas P. Jewell, John D. Kalbfleisch Oct 2001

Maximum Likelihood Estimation Of Ordered Multinomial Parameters, Nicholas P. Jewell, John D. Kalbfleisch

U.C. Berkeley Division 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. By making use of variants of the pool adjacent violator algorithm, we obtain a simple algorithm to compute the maximum likelihood estimator and demonstrate …

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Emacs Speaks Statistics: A Universal Interface For Statistical Analysis, Anthony Rossini, Martin Maechler, Kurt Hornik, Richard M. Heiberger, Rodney Sparapani Jul 2001

Emacs Speaks Statistics: A Universal Interface For Statistical Analysis, Anthony Rossini, Martin Maechler, Kurt Hornik, Richard M. Heiberger, Rodney Sparapani

UW Biostatistics Working Paper Series

Emacs Speaks Statistics (ESS) is a user interface for developing statistical applications and performing data analysis using any of several common statistical programming languages. ESS falls in the programming tools category of Integrated Development Environments (IDEs), which are approaches for developing and visualizing computer programs. We discuss how it works, the advantages of using it, and extensions for increasing statistical programming efficiency.

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