Statistical Theory Commons^™

On Two-Stage Hypothesis Testing Procedures Via Asymptotically Independent Statistics, James Dai, Charles Kooperberg, Michael L. Leblanc, Ross Prentice

UW Biostatistics Working Paper Series

Kooperberg and LeBlanc (2008) proposed a two-stage testing procedure to screen for significant interactions in genome-wide association (GWA) studies by a soft threshold on marginal associations (MA), though its theoretical properties and generalization have not been elaborated. In this article, we discuss conditions that are required to achieve strong control of the Family-Wise Error Rate (FWER) by such procedures for low or high-dimensional hypothesis testing. We provide proof of asymptotic independence of marginal association statistics and interaction statistics in linear regression, logistic regression, and Cox proportional hazard models in a randomized clinical trial (RCT) with a rare event. In case-control …

Stratifying Subjects For Treatment Selection With Censored Event Time Data From A Comparative Study, Lihui Zhao, Tianxi Cai, Lu Tian, Hajime Uno, Scott D. Solomon, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

On Two-Stage Hypothesis Testing Procedures Via Asymptotically Independent Statistics, James Y. Dai, Charles Kooperberg, Michael Leblanc, Ross L. Prentice

UW Biostatistics Working Paper Series

Kooperberg08 proposed a two-stage testing procedure to screen for significant interactions in genome-wide association (GWA) studies by a soft threshold on marginal associations (MA), though its theoretical properties and generalization have not been elaborated. In this article, we discuss conditions that are required to achieve strong control of the Family-Wise Error Rate (FWER) by such procedures for low or high-dimensional hypothesis testing. We provide proof of asymptotic independence of marginal association statistics and interaction statistics in linear regression, logistic regression, and Cox proportional hazard models in a randomized clinical trial (RCT) with a rare event. In case-control studies nested within …

A Perturbation Method For Inference On Regularized Regression Estimates, Jessica Minnier, Lu Tian, Tianxi Cai

Harvard University Biostatistics Working Paper Series

No abstract provided.

Principled Sure Independence Screening For Cox Models With Ultra-High-Dimensional Covariates, Sihai Dave Zhao, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Optimizing Randomized Trial Designs To Distinguish Which Subpopulations Benefit From Treatment, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

It is a challenge to evaluate experimental treatments where it is suspected that the treatment effect may only be strong for certain subpopulations, such as those having a high initial severity of disease, or those having a particular gene variant. Standard randomized controlled trials can have low power in such situations. They also are not optimized to distinguish which subpopulations benefit from a treatment. With the goal of overcoming these limitations, we consider randomized trial designs in which the criteria for patient enrollment may be changed, in a preplanned manner, based on interim analyses. Since such designs allow data-dependent changes …

The Strength Of Statistical Evidence For Composite Hypotheses: Inference To The Best Explanation, David R. Bickel

COBRA Preprint Series

A general function to quantify the weight of evidence in a sample of data for one hypothesis over another is derived from the law of likelihood and from a statistical formalization of inference to the best explanation. For a fixed parameter of interest, the resulting weight of evidence that favors one composite hypothesis over another is the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function over the parameter of interest. Since the weight of evidence is generally only known up to a nuisance parameter, it is approximated by replacing the likelihood function with …

Model-Robust Regression And A Bayesian `Sandwich' Estimator, Adam A. Szpiro, Kenneth M. Rice, Thomas Lumley

UW Biostatistics Working Paper Series

The published version of this paper in Annals of Applied Statistics (Vol. 4, No. 4 (2010), 2099–2113) is available from the journal web site at http://dx.doi.org/10.1214/10-AOAS362.

We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber-White sandwich estimator. The sandwich estimator is known to provide asymptotically correct frequentist inference, even when standard modeling assumptions such as linearity and homoscedasticity in the data-generating mechanism are violated. Our derivation provides a compelling Bayesian justification for using this simple and popular tool, and it also clarifies what is being estimated …

Asymptotic Properties Of The Sequential Empirical Roc And Ppv Curves, Joseph S. Koopmeiners, Ziding Feng

UW Biostatistics Working Paper Series

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three common measures of performance for a diagnostic biomarker. The independent increments covariance structure assumption is common in the group sequential study design literature. Showing that summary measures of the ROC, PPV and NPV curves have an independent increments covariance structure will provide the theoretical foundation for designing group sequential diagnostic biomarker studies. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. In this paper we derive asymptotic theory …

Estimating Causal Effects In Trials Involving Multi-Treatment Arms Subject To Non-Compliance: A Bayesian Frame-Work, Qi Long, Roderick J. Little, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Super Learner In Prediction, Eric C. Polley, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Super learning is a general loss based learning method that has been proposed and analyzed theoretically in van der Laan et al. (2007). In this article we consider super learning for prediction. The super learner is a prediction method designed to find the optimal combination of a collection of prediction algorithms. The super learner algorithm finds the combination of algorithms minimizing the cross-validated risk. The super learner framework is built on the theory of cross-validation and allows for a general class of prediction algorithms to be considered for the ensemble. Due to the previously established oracle results for the cross-validation …

Assessing Noninferiority In A Three-Arm Trial Using The Bayesian Approach, Pulak Ghosh, Farouk S. Nathoo, Mithat Gonen, Ram C. Tiwari

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm clinical trial is usually recommended for non-inferiority trials by the Food and Drug Administration (FDA). The three-arm trial consists of a placebo, a reference, and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with …

Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations, Lu Wang, Andrea Rotnitzky, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Simple Examples Of Estimating Causal Effects Using Targeted Maximum Likelihood Estimation, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We present a brief overview of targeted maximum likelihood for estimating the causal effect of a single time point treatment and of a two time point treatment. We focus on simple examples demonstrating how to apply the methodology developed in (van der Laan and Rubin, 2006; Moore and van der Laan, 2007; van der Laan, 2010a,b). We include R code for the single time point case.

Likelihood Ratio Testing For Admixture Models With Application To Genetic Linkage Analysis, Chong-Zhi Di, Kung-Yee Liang

Johns Hopkins University, Dept. of Biostatistics Working Papers

We consider likelihood ratio tests (LRT) and their modifications for homogeneity in admixture models. The admixture model is a special case of two component mixture model, where one component is indexed by an unknown parameter while the parameter value for the other component is known. It has been widely used in genetic linkage analysis under heterogeneity, in which the kernel distribution is binomial. For such models, it is long recognized that testing for homogeneity is nonstandard and the LRT statistic does not converge to a conventional 2 distribution. In this paper, we investigate the asymptotic behavior of the LRT for …

Graphical Procedures For Evaluating Overall And Subject-Specific Incremental Values From New Predictors With Censored Event Time Data, Hajime Uno, Tianxi Cai, Lu Tian, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

A New Class Of Dantzig Selectors For Censored Linear Regression Models, Yi Li, Lee Dicker, Sihai Dave Zhao

Harvard University Biostatistics Working Paper Series

No abstract provided.

Penalized Functional Regression, Jeff Goldsmith, Jennifer Feder, Ciprian M. Crainiceanu, Brian Caffo, Daniel Reich

Johns Hopkins University, Dept. of Biostatistics Working Papers

We develop fast fitting methods for generalized functional linear models. An undersmooth of the functional predictor is obtained by projecting on a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. Our method can be applied to many functional data designs including functions measured with and without error, sparsely or densely sampled. The methods also extend to the case of multiple functional predictors or functional predictors with a natural multilevel structure. Our approach can be implemented using standard mixed effects software and is computationally fast. Our methodology is motivated by a diffusion tensor imaging …

Regression Adjustment And Stratification By Propensty Score In Treatment Effect Estimation, Jessica A. Myers, Thomas A. Louis

Johns Hopkins University, Dept. of Biostatistics Working Papers

Propensity score adjustment of effect estimates in observational studies of treatment is a common technique used to control for bias in treatment assignment. In situations where matching on propensity score is not possible or desirable, regression adjustment and stratification are two options. Regression adjustment is used most often and can be highly efficient, but it can lead to biased results when model assumptions are violated. Validity of the stratification approach depends on fewer model assumptions, but is less efficient than regression adjustment when the regression assumptions hold. To investigate these issues, by simulation we compare stratification and regression adjustments. We …

Pragmatic Estimation Of A Spatio-Temporal Air Quality Model With Irregular Monitoring Data, Paul D. Sampson, Adam A. Szpiro, Lianne Sheppard, Johan Lindström, Joel D. Kaufman

UW Biostatistics Working Paper Series

Statistical analyses of the health effects of air pollution have increasingly used GIS-based covariates for prediction of ambient air quality in “land-use” regression models. More recently these regression models have accounted for spatial correlation structure in combining monitoring data with land-use covariates. The current paper builds on these concepts to address spatio-temporal prediction of ambient concentrations of particulate matter with aerodynamic diameter less than 2.5 μm (PM2.5) on the basis of a model representing spatially varying seasonal trends and spatial correlation structures. Our hierarchical methodology provides a pragmatic approach that fully exploits regulatory and other supplemental monitoring data which jointly …

On The Behaviour Of Marginal And Conditional Akaike Information Criteria In Linear Mixed Models, Sonja Greven, Thomas Kneib

Johns Hopkins University, Dept. of Biostatistics Working Papers

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive …

Survival Analysis With Error-Prone Time-Varying Covariates: A Risk Set Calibration Approach, Xiaomei Liao, David M. Zucker, Yi Li, Donna Spiegelman

Harvard University Biostatistics Working Paper Series

No abstract provided.

A New Class Of Minimum Power Divergence Estimators With Applications To Cancer Surveillance, Nirian Martin, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Quasi-Least Squares With Mixed Linear Correlation Structures, Jichun Xie, Justine Shults, Jon Peet, Dwight Stambolian, Mary F. Cotch

UPenn Biostatistics Working Papers

Quasi-least squares (QLS) is a two-stage computational approach for estimation of the correlation parameters in the framework of generalized estimating equations (GEE). We prove two general results for the class of mixed linear correlation structures: namely, that the stage one QLS estimate of the correlation parameter always exists and is feasible (yields a positive definite estimated correlation matrix) for any correlation structure, while the stage two estimator exists and is unique (and therefore consistent) with probability one, for the class of mixed linear correlation structures. Our general results justify the implementation of QLS for particular members of the class of …

Readings In Targeted Maximum Likelihood Estimation, Mark J. Van Der Laan, Sherri Rose, Susan Gruber

U.C. Berkeley Division of Biostatistics Working Paper Series

This is a compilation of current and past work on targeted maximum likelihood estimation. It features the original targeted maximum likelihood learning paper as well as chapters on super (machine) learning using cross validation, randomized controlled trials, realistic individualized treatment rules in observational studies, biomarker discovery, case-control studies, and time-to-event outcomes with censored data, among others. We hope this collection is helpful to the interested reader and stimulates additional research in this important area.

Causal Inference For Nested Case-Control Studies Using Targeted Maximum Likelihood Estimation, Sherri Rose, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

A nested case-control study is conducted within a well-defined cohort arising out of a population of interest. This design is often used in epidemiology to reduce the costs associated with collecting data on the full cohort; however, the case control sample within the cohort is a biased sample. Methods for analyzing case-control studies have largely focused on logistic regression models that provide conditional and not marginal causal estimates of the odds ratio. We previously developed a Case-Control Weighted Targeted Maximum Likelihood Estimation (TMLE) procedure for case-control study designs, which relies on the prevalence probability q0. We propose the use of …

Targeted Maximum Likelihood Estimation: A Gentle Introduction, Susan Gruber, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

This paper provides a concise introduction to targeted maximum likelihood estimation (TMLE) of causal effect parameters. The interested analyst should gain sufficient understanding of TMLE from this introductory tutorial to be able to apply the method in practice. A program written in R is provided. This program implements a basic version of TMLE that can be used to estimate the effect of a binary point treatment on a continuous or binary outcome.

Comparing Risk Scoring Systems Beyond The Roc Paradigm In Survival Analysis, Hajime Uno, Lu Tian, Tianxi Cai, Isaac S. Kohane, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Combinational Mixtures Of Multiparameter Distributions, Valeria Edefonti, Giovanni Parmigiani

Johns Hopkins University, Dept. of Biostatistics Working Papers

We introduce combinatorial mixtures - a flexible class of models for inference on mixture distributions whose component have multidimensional parameters. The key idea is to allow each element of the component-specific parameter vectors to be shared by a subset of other components. This approach allows for mixtures that range from very flexible to very parsimonious, and unifies inference on component-specific parameters with inference on the number of components. We develop Bayesian inference and computation approaches for this class of distributions, and illustrate them in an application. This work was originally motivated by the analysis of cancer subtypes: in terms of …

Shrinkage Estimation Of Expression Fold Change As An Alternative To Testing Hypotheses Of Equivalent Expression, Zahra Montazeri, Corey M. Yanofsky, David R. Bickel

COBRA Preprint Series

Research on analyzing microarray data has focused on the problem of identifying differentially expressed genes to the neglect of the problem of how to integrate evidence that a gene is differentially expressed with information on the extent of its differential expression. Consequently, researchers currently prioritize genes for further study either on the basis of volcano plots or, more commonly, according to simple estimates of the fold change after filtering the genes with an arbitrary statistical significance threshold. While the subjective and informal nature of the former practice precludes quantification of its reliability, the latter practice is equivalent to using a …