Statistical Theory Commons^™

The Effect Of Correlation In False Discovery Rate Estimation, Armin Schwartzman, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Spatial Cluster Detection For Repeatedly Measured Outcomes While Accounting For Residential History, Andrea J. Cook, Diane Gold, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Marginalized Frailty Models For Multivariate Survival Data, Megan Othus, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Spatial Cluster Detection For Weighted Outcomes Using Cumulative Geographic Residuals, Andrea J. Cook, Yi Li, David Arterburn, Ram C. Tiwari

Harvard University Biostatistics Working Paper Series

No abstract provided.

On The C-Statistics For Evaluating Overall Adequacy Of Risk Prediction Procedures With Censored Survival Data, Hajime Uno, Tianxi Cai, Michael J. Pencina, Ralph B. D'Agostino, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Estimating Subject-Specific Dependent Competing Risk Profile With Censored Event Time Observations, Yi Li, Lu Tian, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

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.

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 …

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.

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 …

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 …

The Highest Confidence Density Region And Its Usage For Inferences About The Survival Function With Censored Data, Lu Tian, Rui Wang, Tianxi Cai, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Change-Point Problem And Regression: An Annotated Bibliography, Ahmad Khodadadi, Masoud Asgharian

COBRA Preprint Series

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as "the change-point problem" or, in the Eastern literature, as "disorder".

The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis.

Numerous methodological approaches …

The Strength Of Statistical Evidence For Composite Hypotheses With An Application To Multiple Comparisons, David R. Bickel

COBRA Preprint Series

The strength of the statistical evidence in a sample of data that favors one composite hypothesis over another may be quantified by the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function. Unlike the p-value and the Bayes factor, this measure of evidence is coherent in the sense that it cannot support a hypothesis over any hypothesis that it entails. Further, when comparing the hypothesis that the parameter lies outside a non-trivial interval to the hypotheses that it lies within the interval, the proposed measure of evidence almost always asymptotically favors the correct hypothesis …

Calibrating Parametric Subject-Specific Risk Estimation, Tianxi Cai, Lu Tian, Hajime Uno, Scott D. Solomon, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Evaluating Subject-Level Incremental Values Of New Markers For Risk Classification Rule, Tianxi Cai, Lu Tian, Donald M. Lloyd-Jones, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Generalized Multilevel Functional Regression, Ciprian M. Crainiceanu, Ana-Maria Staicu, Chongzhi Di

Johns Hopkins University, Dept. of Biostatistics Working Papers

We introduce Generalized Multilevel Functional Linear Models (GMFLM), a novel statistical framework motivated by and applied to the Sleep Heart Health Study (SHHS), the largest community cohort study of sleep. The primary goal of SHHS is to study the association between sleep disrupted breathing (SDB) and adverse health effects. An exposure of primary interest is the sleep electroencephalogram (EEG), which was observed for thousands of individuals at two visits, roughly 5 years apart. This unique study design led to the development of models where the outcome, e.g. hypertension, is in an exponential family and the exposure, e.g. sleep EEG, is …

Measurement Error Caused By Spatial Misalignment In Environmental Epidemiology, Alexandros Gryparis, Christopher J. Paciorek, Ariana Zeka, Joel Schwartz, Brent A. Coull

Harvard University Biostatistics Working Paper Series

No abstract provided.

Practical Large-Scale Spatio-Temporal Modeling Of Particulate Matter Concentrations, Christopher J. Paciorek, Jeff D. Yanosky, Robin C. Puett, Francine Laden, Helen H. Suh

Harvard University Biostatistics Working Paper Series

The last two decades have seen intense scientific and regulatory interest in the health effects of particulate matter (PM). Influential epidemiological studies that characterize chronic exposure of individuals rely on monitoring data that are sparse in space and time, so they often assign the same exposure to participants in large geographic areas and across time. We estimate monthly PM during 1988-2002 in a large spatial domain for use in studying health effects in the Nurses' Health Study. We develop a conceptually simple spatio-temporal model that uses a rich set of covariates. The model is used to estimate concentrations of PM10 …

Confidence Intervals For Negative Binomial Random Variables Of High Dispersion, David Shilane, Alan E. Hubbard, S N. Evans

U.C. Berkeley Division of Biostatistics Working Paper Series

This paper considers the problem of constructing confidence intervals for the mean of a Negative Binomial random variable based upon sampled data. When the sample size is large, we traditionally rely upon a Normal distribution approximation to construct these intervals. However, we demonstrate that the sample mean of highly dispersed Negative Binomials exhibits a slow convergence to the Normal in distribution as a function of the sample size. As a result, standard techniques (such as the Normal approximation and bootstrap) that construct confidence intervals for the mean will typically be too narrow and significantly undercover in the case of high …

A New Method For Constructing Exact Tests Without Making Any Assumptions, Karl H. Schlag

COBRA Preprint Series

We present a new method for constructing exact distribution-free tests (and con…fidence intervals) for variables that can generate more than two possible outcomes. This method separates the search for an exact test from the goal to create a non- randomized test. Randomization is used to extend any exact test relating to means of variables with fi…nitely many outcomes to variables with outcomes belonging to a given bounded set. Tests in terms of variance and covariance are reduced to tests relating to means. Randomness is then eliminated in a separate step. This method is used to create con…fidence intervals for the …

Trading Bias For Precision: Decision Theory For Intervals And Sets, Kenneth M. Rice, Thomas Lumley, Adam A. Szpiro

UW Biostatistics Working Paper Series

Interval- and set-valued decisions are an essential part of statistical inference. Despite this, the justification behind them is often unclear, leading in practice to a great deal of confusion about exactly what is being presented. In this paper we review and attempt to unify several competing methods of interval-construction, within a formal decision-theoretic framework. The result is a new emphasis on interval-estimation as a distinct goal, and not as an afterthought to point estimation. We also see that representing intervals as trade-offs between measures of precision and bias unifies many existing approaches -- as well as suggesting interpretable criteria to …

Fdr Controlling Procedure For Multi-Stage Analyses, Catherine Tuglus, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Multiple testing has become an integral component in genomic analyses involving microarray experiments where large number of hypotheses are tested simultaneously. However before applying more computationally intensive methods, it is often desirable to complete an initial truncation of the variable set using a simpler and faster supervised method such as univariate regression. Once such a truncation is completed, multiple testing methods applied to any subsequent analysis no longer control the appropriate Type I error rates. Here we propose a modified marginal Benjamini \& Hochberg step-up FDR controlling procedure for multi-stage analyses (FDR-MSA), which correctly controls Type I error in terms …