Statistics and Probability Commons^™

Resampling-Based Multiple Hypothesis Testing With Applications To Genomics: New Developments In The R/Bioconductor Package Multtest, Houston N. Gilbert, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

The multtest package is a standard Bioconductor package containing a suite of functions useful for executing, summarizing, and displaying the results from a wide variety of multiple testing procedures (MTPs). In addition to many popular MTPs, the central methodological focus of the multtest package is the implementation of powerful joint multiple testing procedures. Joint MTPs are able to account for the dependencies between test statistics by effectively making use of (estimates of) the test statistics joint null distribution. To this end, two additional bootstrap-based estimates of the test statistics joint null distribution have been developed for use in the …

A Class Of Semiparametric Mixture Cure Survival Models With Dependent Censoring, Megan Othus, Yi Li, Ram C. Tiwari

Harvard University Biostatistics Working Paper Series

No abstract provided.

Application Of Time-To-Event Methods In The Assessment Of Safety In Clinical Trials, Kelly L. Moore, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Since randomized controlled trials (RCT) are typically designed and powered for efficacy rather than safety, power is an important concern in the analysis of the effect of treatment on the occurrence of adverse events (AE). These outcomes are often time-to-event outcomes which will naturally be subject to right-censoring due to early patient withdrawals. In the analysis of the treatment effect on such an outcome, gains in efficiency, and thus power, can be achieved by exploiting covariate information. We apply the targeted maximum likelihood methodology to the estimation of treatment specific survival at a fixed end point for right-censored survival outcomes. …

Interval Estimation For The Difference In Paired Areas Under The Roc Curves In The Absence Of A Gold Standard Test, Hsin-Neng Hsieh, Hsiu-Yuan Su, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Receiver operating characteristic (ROC) curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The most commonly used measure for the overall diagnostic accuracy of diagnostic tests is the area under the ROC curve (AUC). A gold standard test on the true disease status is required to estimate the AUC. However, a gold standard test may sometimes be too expensive or infeasible. Therefore, in many medical research studies, the true disease status of the subjects may remain unknown. Under the normality assumption on test results from each disease group of subjects, using the expectation-maximization …

Collaborative Targeted Maximum Likelihood Estimation, Mark J. Van Der Laan, Susan Gruber

U.C. Berkeley Division of Biostatistics Working Paper Series

Collaborative double robust targeted maximum likelihood estimators represent a fundamental further advance over standard targeted maximum likelihood estimators of causal inference and variable importance parameters. The targeted maximum likelihood approach involves fluctuating an initial density estimate, (Q), in order to make a bias/variance tradeoff targeted towards a specific parameter in a semi-parametric model. The fluctuation involves estimation of a nuisance parameter portion of the likelihood, g. TMLE and other double robust estimators have been shown to be consistent and asymptotically normally distributed (CAN) under regularity conditions, when either one of these two factors of the likelihood of the data is …

A Semi-Parametric Two-Part Mixed-Effects Heteroscedastic Transformation Model For Correlated Right-Skewed Semi-Continuous Data, Huazhen Lin, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

In longitudinal or hierarchical structure studies, we often encounter a semi-continuous variable that has a certain proportion of a single value and a continuous and skewed distribution among the rest of values. In the paper, we propose a new semi-parametric two-part mixed-effects transformation model to fit correlated skewed semi-continuous data. In our model, we allow the transformation to be non-parametric. Fitting the proposed model faces computational challenges due to intractable numerical integrations. We derive the estimates for the parameter and the transformation function based on an approximate likelihood, which has high order accuracy but less computational burden. We also propose …

Composite Likelihood Bayesian Information Criteria For Model Selection In High Dimensional Data, X Gao, Peter Xuekun Song

The University of Michigan Department of Biostatistics Working Paper Series

For high-dimensional data set with complicated dependency structures, the full likelihood approach often renders to intractable computational complexity. This imposes di±culty on model selection as most of the traditionally used information criteria require the evaluation of the full likelihood. We propose a composite likelihood version of the Bayesian information criterion (BIC) and establish its consistency property for the selection of the true underlying model. Under some mild regularity conditions, the proposed BIC is shown to be selection consistent, where the number of potential model parameters is allowed to increase to in¯nity at a certain rate of the sample size. Simulation …

Longitudinal Image Analysis Of Tumor/Brain Change In Contrast Uptake Induced By Radiation, Xiaoxi Zhang, Tim Johnson, Rod Little, Yue Cao

The University of Michigan Department of Biostatistics Working Paper Series

This work is motivated by a quantitative Magnetic Resonance Imaging study of the differential tumor/healthy tissue change in contrast uptake induced by radiation. The goal is to determine the time in which there is maximal contrast uptake, a surrogate for permeability, in the tumor relative to healthy tissue. A notable feature of the data is its spatial heterogeneity. Zhang, Johnson, Little, and Cao (2008a and 2008b) discuss two parallel approaches to “denoise” a single image of change in contrast uptake from baseline to a single follow-up visit of interest. In this work we explore the longitudinal profile of the tumor/healthy …

Joint Multiple Testing Procedures For Graphical Model Selection With Applications To Biological Networks, Houston N. Gilbert, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

Gaussian graphical models have become popular tools for identifying relationships between genes when analyzing microarray expression data. In the classical undirected Gaussian graphical model setting, conditional independence relationships can be inferred from partial correlations obtained from the concentration matrix (= inverse covariance matrix) when the sample size n exceeds the number of parameters p which need to estimated. In situations where n < p, another approach to graphical model estimation may rely on calculating unconditional (zero-order) and first-order partial correlations. In these settings, the goal is to identify a lower-order conditional independence graph, sometimes referred to as a ‘0-1 graphs’. For either choice of graph, model selection may involve a multiple testing problem, in which edges in a graph are drawn only after rejecting hypotheses involving (saturated or lower-order) partial correlation parameters. Most multiple testing procedures applied in previously proposed graphical model selection algorithms rely on standard, marginal testing methods which do not take into account the joint distribution of the test statistics derived from (partial) correlations. We propose and implement a multiple testing framework useful when testing for edge inclusion during graphical model selection. Two features of our methodology include (i) a computationally efficient and asymptotically valid test statistics joint null distribution derived from influence curves for correlation-based parameters, and (ii) the application of empirical Bayes joint multiple testing procedures which can effectively control a variety of popular Type I error rates by incorpo- rating joint null distributions such as those described here (Dudoit and van der Laan, 2008). Using a dataset from Arabidopsis thaliana, we observe that the use of more sophisticated, modular approaches to multiple testing allows one to identify greater numbers of edges when approximating an undirected graphical model using a 0-1 graph. Our framework may also be extended to edge testing algorithms for other types of graphical models (e.g., for classical undirected, bidirected, and directed acyclic graphs).

The Importance Of Scale For Spatial-Confounding Bias And Precision Of Spatial Regression Estimators, Christopher J. Paciorek

Harvard University Biostatistics Working Paper Series

Increasingly, regression models are used when residuals are spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When the spatial residual is induced by an unmeasured confounder, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias …

Analysis Of Randomized Comparative Clinical Trial Data For Personalized Treatment Selections, Tianxi Cai, Lu Tian, Peggy H. Wong, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Correlated Binary Regression Using Orthogonalized Residuals, Richard C. Zink, Bahjat F. Qaqish

COBRA Preprint Series

This paper focuses on marginal regression models for correlated binary responses when estimation of the association structure is of primary interest. A new estimating function approach based on orthogonalized residuals is proposed. This procedure allows a new representation and addresses some of the difficulties of the conditional-residual formulation of alternating logistic regressions of Carey, Zeger & Diggle (1993). The new method is illustrated with an analysis of data on impaired pulmonary function.

Group Comparison Of Eigenvalues And Eigenvectors Of Diffusion Tensors, Armin Schwartzman, Robert F. Dougherty, Jonathan E. Taylor

Harvard University Biostatistics Working Paper Series

No abstract provided.

Relaxing Latent Ignorability In The Itt Analysis Of Randomized Studies With Missing Data And Noncompliance, L Taylor, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Abstract: In this paper we consider the problem in causal inference of estimating the local complier average causal effect (CACE) parameter in the setting of a randomized clinical trial with a binary outcome, cross-over noncompliance, and unintentional missing data on the responses. We focus on the development of a moment estimator that relaxes the assumption of latent ignorability and incorporates sensitivity parameters that represent the relationship between potential outcomes and associated potential response indicators. If conclusions are insensitive over a range of logically possible values of the sensitivity parameters, then the number of interpretations of the data is reduced, and …

Multiple Imputation Methods For Treatment Noncompliance And Nonresponse In Randomized Clinical Trials, Leslie Taylor, Xiao-Hua (Andrew) Zhou

UW Biostatistics Working Paper Series

Summary: Randomized clinical trials are a powerful tool for investigating causal treatment effects, but in human trials there are oftentimes problems of noncompliance which standard analyses, such as the intention-to-treat or as-treated analysis, either ignore or incorporate in such a way that the resulting estimand is no longer a causal effect. One alternative to these analyses is the complier average causal effect (CACE) which estimates the average causal treatment effect among a subpopulation that would comply under any treatment assigned. We focus on the setting of a randomized clinical trial with crossover treatment noncompliance (e.g., control subjects could receive the …

Selecting Optimal Treatments Based On Predictive Factors, Eric C. Polley, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

No abstract provided.

Semiparametric Two-Part Models With Proportionality Constraints: Analysis Of The Multi-Ethnic Study Of Atherosclerosis (Mesa), Anna Liu, Richard Kronmal, Xiao-Hua Zhou, Shuangge Ma

UW Biostatistics Working Paper Series

SUMMARY. In this article, we analyze the coronary artery calcium (CAC) score in the Multi-Ethnic Study of Atherosclerosis (MESA), where about half of the CAC scores are zero and the rest are continuously distributed. When the observed data has a mixture distribution, two-part models can be the natural choice. With a two-part model, there are two covariate effects, with one in each part of the model. Determination of whether the two covariate effects are proportional can provide more insights into the process underlying development and progression of CAC. In this study, we model the CAC score using a semiparametric two-part …

Pooled Nucleic Acid Testing To Identify Antiretroviral Treatment Failure During Hiv Infection, Susanne May, Anthony Gamst, Richard Haubrich, Constance Benson, Davey Smith

UW Biostatistics Working Paper Series

Abstract Background: Pooling strategies have been used to reduce the costs of polymerase chain reaction based screening for acute HIV infection in populations where the prevalence of acute infection is low (<1%). Only limited research has been done for conditions where the prevalence of screening positivity is higher (>1%). Methods and Results: We present data on a variety of pooling strategies that incorporate the use of PCR-based quantitative measures to monitor for virologic failure among HIV-infected patients receiving antiretroviral therapy. For a prevalence of virologic failure between 1% and 25%, we demonstrate relative efficiency and accuracy of various strategies. These results could be used to choose the best strategy based on the requirements of individual laboratory …

Validation Of Differential Gene Expression Algorithms: Application Comparing Fold Change Estimation To Hypothesis Testing, David R. Bickel, Corey M. Yanofsky

COBRA Preprint Series

Sustained research on the problem of determining which genes are differentially expressed on the basis of microarray data has yielded a plethora of statistical algorithms, each justified by theory, simulation, or ad hoc validation and yet differing in practical results from equally justified algorithms. The widespread confusion on which method to use in practice has been exacerbated by the finding that simply ranking genes by their fold changes sometimes outperforms popular statistical tests.

Algorithms may be compared by quantifying each method's error in predicting expression ratios, whether such ratios are defined across microarray channels or between two independent groups. For …

Measures To Summarize And Compare The Predictive Capacity Of Markers, Wen Gu, Margaret Pepe

UW Biostatistics Working Paper Series

The predictive capacity of a marker in a population can be described using the population distribution of risk (Huang et al., 2007; Pepe et al., 2008a; Stern, 2008). Virtually all standard statistical summaries of predictability and discrimination can be derived from it (Gail and Pfeiffer, 2005). The goal of this paper is to develop methods for making inference about risk prediction markers using summary measures derived from the risk distribution. We describe some new clinically motivated summary measures and give new interpretations to some existing statistical measures. Methods for estimating these summary measures are described along with distribution theory that …

Weighting And Prediction In Sample Surveys, Rod Little

The University of Michigan Department of Biostatistics Working Paper Series

A fundamental technique in survey sampling is to weight included units by the inverse of their probability of inclusion, which may be known (as in the case of sampling weights) or estimated (as in the case of nonresponse weights). The technique is closely associated with the design-based approach to survey inference, with the idea that units in the sample are representing a certain number of units in the population. I discuss weighting from a modeling perspective. Some common misconceptions of weighting will be addressed, including the idea that modelers can ignore the sampling weights, or that weighting necessarily reduces bias …

Quantifying Uncertainty In Genotype Calls, Benilton Carvalho, Thomas A. Louis, Rafael A. Irizarry

Johns Hopkins University, Dept. of Biostatistics Working Papers

Genome-wide association studies (GWAS) are used to discover genes underlying complex, heritable disorders for which less powerful study designs have failed in the past. The number of GWAS has skyrocketed recently with findings reported in top journals and the mainstream media. Mircorarrays are the genotype calling technology of choice in GWAS as they permit exploration of more than a million single nucleotide polymorphisms (SNPs)simultaneously. The starting point for the statistical analyses used by GWAS, to determine association between loci and disease, are genotype calls (AA, AB, or BB). However, the raw data, microarray probe intensities, are heavily processed before arriving …

Sparse Linear Discriminant Analysis For Simultaneous Testing For The Significance Of A Gene Set/Pathway And Gene Selection, Michael C. Wu, Lingson Zhang, Zhaoxi Wang, David C. Christiani, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

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 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 …

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 …

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 …

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 …