Statistics and Probability Commons^™

The Design And Sample Size Requirement For A Cluster Randomized Non-Inferiority Trial With Two Binary Co-Primary Outcomes., William F. Mccarthy

COBRA Preprint Series

This paper will discuss the design and sample size requirement for a cluster randomized non-inferiority trial with two binary co-primary outcomes. A hypothetical study (the EXAMPLE Trial) will be considered.

Lets assume the EXAMPLE Trial will consist of two separate binomial non-inferiority two-sample trials. Trial 1: the Coronary Artery Disease known population (co-primary 1) and Trial 2: the Coronary Artery Disease unknown population (co-primary 2). A physician-month cluster randomization scheme will be used. That is, for each trial (trial 1 and trial 2) every month for a 12-month period, each physician participating in the EXAMPLE Trial will be allocated a …

Bayesian Inference For Smoking Cessation With A Latent Cure State, Sheng Luo, Ciprian M. Crainiceanu, Thomas A. Louis, Nilanjan Chatterjee

Johns Hopkins University, Dept. of Biostatistics Working Papers

We present a Bayesian approach to modeling dynamic smoking addiction behavior processes when cure is not directly observed due to censoring. Subject-specic probabilities model the stochastic transitions among three behavioral states: smoking, transient quitting, and permanent quitting (absorbent state). A multivariate normal distribution for random e ects is used to account for the potential correlation among the subject-specic transition probabilities. Inference is conducted using a Bayesian framework via Markov Chain Monte Carlo simulation. This framework provides various measures of subject-specic predictions, which are useful for policy making, intervention development, and evaluation. Simulations are used to validate our Bayesian methodology, and …

Semiparametric And Nonparametric Methods For Evaluating Risk Prediction Markers In Case-Control Studies, Ying Huang, Margaret Pepe

UW Biostatistics Working Paper Series

The performance of a well calibrated risk model, Risk(Y)=P(D=1|Y), can be characterized by the population distribution of Risk(Y) and displayed with the predictiveness curve. Better performance is characterized by a wider distribution of Risk(Y), since this corresponds to better risk stratification in the sense that more subjects are identified at low and high risk for the outcome D=1. Although methods have been developed to estimate predictiveness curves from cohort studies, most studies to evaluate novel risk prediction markers employ case-control designs. Here we develop semiparametric and nonparametric methods that accommodate case-control data and assume apriori knowledge of P(D=1). Large and …

On The Designation Of The Patterned Associations For Longitudinal Bernoulli Data: Weight Matrix Versus True Correlation Structure?, Hanjoo Kim, Joseph M. Hilbe, Justine Shults

UPenn Biostatistics Working Papers

Due to potential violation of standard constraints for the correlation for binary data, it has been argued recently that the working correlation matrix should be viewed as a weight matrix that should not be confused with the true correlation structure. We propose two arguments to support our view to the contrary for the first-order autoregressive AR(1) correlation matrix. First, we prove that the standard constraints are not unduly restrictive for the AR(1) structure that is plausible for longitudinal data; furthermore, for the logit link function the upper boundary value only depends on the regression parameter and the change in covariate …

Bringing Game Theory To Hypothesis Testing: Establishing Finite Sample Bounds On Inference, Karl H. Schlag

COBRA Preprint Series

Small sample properties are of fundamental interest when only limited data is available. Exact inference is limited by constraints imposed by specific nonrandomized tests and of course also by lack of more data. These effects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a fictitious game against nature. We use this method to investigate sequential …

Estimation And Testing For The Effect Of A Genetic Pathway On A Disease Outcome Using Logistic Kernel Machine Regression Via Logistic Mixed Models, Dawei Liu, Debashis Ghosh, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Powerful And Flexible Multilocus Association Test For Quantitative Traits, Lydia Coulter Kwee, Dawei Liu, Xihong Lin, Debashis Ghosh, Michael P. Epstein

Harvard University Biostatistics Working Paper Series

No abstract provided.

Nonparametric Regression Using Local Kernel Estimating Equations For Correlated Failure Time Data, Zhangsheng Yu, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Comparison Of Methods For Estimating The Causal Effect Of A Treatment In Randomized Clinical Trials Subject To Noncompliance, Rod Little, Qi Long, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Semiparametric Maximum Likelihood Estimation In Normal Transformation Models For Bivariate Survival Data, Yi Li, Ross L. Prentice, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Accounting For Errors From Predicting Exposures In Environmental Epidemiology And Environmental Statistics, Adam A. Szpiro, Lianne Sheppard, Thomas Lumley

UW Biostatistics Working Paper Series

PLEASE NOTE THAT AN UPDATED VERSION OF THIS RESEARCH IS AVAILABLE AS WORKING PAPER 350 IN THE UNIVERSITY OF WASHINGTON BIOSTATISTICS WORKING PAPER SERIES (http://www.bepress.com/uwbiostat/paper350).

In environmental epidemiology and related problems in environmental statistics, it is typically not practical to directly measure the exposure for each subject. Environmental monitoring is employed with a statistical model to assign exposures to individuals. The result is a form of exposure misspecification that can result in complicated errors in the health effect estimates if the exposure is naively treated as known. The exposure error is neither “classical” nor “Berkson”, so standard regression calibration methods …

Supervised Distance Matrices: Theory And Applications To Genomics, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a new approach to studying the relationship between a very high dimensional random variable and an outcome. Our method is based on a novel concept, the supervised distance matrix, which quantifies pairwise similarity between variables based on their association with the outcome. A supervised distance matrix is derived in two stages. The first stage involves a transformation based on a particular model for association. In particular, one might regress the outcome on each variable and then use the residuals or the influence curve from each regression as a data transformation. In the second stage, a choice of distance …

Analysis Of Subgroup Effects In Randomized Trials When Subgroup Membership Is Informatively Missing: Application To The Madit Ii Study, Daniel O. Scharfstein, Georgiana Onicescu, Steven Goodman

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper, we develop and implement a general sensitivity analysis methodology for drawing inference about subgroup effects in a two-arm randomized trial when subgroup status is only known for a non-random sample in one of the trial arms. The methodology is developed in the context of the MADIT II study, a randomized trial designed to evaluate the effectiveness of implantable defibrillators on survival.

Causal Inference In Observational Studies With Outcome-Dependent Sampling, Weiwei Wang, Daniel Scharfstein, Zhiqiang Tan, Ellen J. Mackenzie

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper, we consider estimation of the causal effect of a treatment on an outcome from observational data collected in two phases. In the first phase, a simple random sample of individuals are drawn from a population. On these individuals, information is obtained on treatment, outcome, and a few low-dimensional confounders. These individuals are then stratified according to these factors. In the second phase, a random sub-sample of individuals are drawn from each stratum, with known, stratum-specific selection probabilities. On these individuals, a rich set of confounding factors are collected. In this setting, we introduce four estimators: (1) simple …

Model-Based Clustering Of Methylation Array Data: A Recursive-Partitioning Algorithm For High-Dimensional Data Arising As A Mixture Of Beta Distributions, E. Andres Houseman, Brock C. Christensen, Ru-Fang Yeh, Carmen J. Marsit, Margaret R. Karagas, Margaret Wrensch, Heather H. Nelson, Joseph Wiemels, Shichun Zheng, John K. Wiencke, Karl T. Kelsey

Harvard University Biostatistics Working Paper Series

No abstract provided.

Confidence Intervals For The Population Mean Tailored To Small Sample Sizes, With Applications To Survey Sampling, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

The validity of standard confidence intervals constructed in survey sampling is based on the central limit theorem. For small sample sizes, the central limit theorem may give a poor approximation, resulting in confidence intervals that are misleading. We discuss this issue and propose methods for constructing confidence intervals for the population mean tailored to small sample sizes.

We present a simple approach for constructing confidence intervals for the population mean based on tail bounds for the sample mean that are correct for all sample sizes. Bernstein's inequality provides one such tail bound. The resulting confidence intervals have guaranteed coverage probability …

Doubly Robust Ecological Inference, Daniel B. Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

The ecological inference problem is a famous longstanding puzzle that arises in many disciplines. The usual formulation in epidemiology is that we would like to quantify an exposure-disease association by obtaining disease rates among the exposed and unexposed, but only have access to exposure rates and disease rates for several regions. The problem is generally intractable, but can be attacked under the assumptions of King's (1997) extended technique if we can correctly specify a model for a certain conditional distribution. We introduce a procedure that it is a valid approach if either this original model is correct or if we …

Estimation Based On Case-Control Designs With Known Incidence Probability, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Case-control sampling is an extremely common design used to generate data to estimate effects of exposures or treatments on a binary outcome of interest when the proportion of cases (i.e., binary outcome equal to 1) in the population of interest is low. Case-control sampling represents a biased sample of a target population of interest by sampling a disproportional number of cases. Case-control studies are also commonly employed to estimate the effects of genetic markers or biomarkers on phenotypes. The typical approach used in practice is to fit (conditional) logistic regression models, ignoring the case-control sampling, in order to estimate the …

A Guide To Causal Parameters In Case-Control Designs: Targeted Maximum Likelihood Estimation, Sherri Rose, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Researchers of uncommon diseases are often interested in assessing potential risk factors. Given the low incidence of disease, these studies are frequently case-control in design, as this allows for a sufficient number of cases to be obtained without extensive sampling and can increase efficiency. However, these case-control samples are then biased since the proportion of cases in the sample is not the same as the population of interest. Methods for analyzing case-control studies have focused on utilizing logistic regression models that provide conditional and not causal estimates of the odds ratio. This article will demonstrate the use of the prevalence …

Semiparametric Methods For Evaluating The Covariate-Specific Predictiveness Of Continuous Markers In Matched Case-Control Studies, Ying Huang, Margaret S. Pepe

UW Biostatistics Working Paper Series

To assess the value of a continuous marker in predicting the risk of a disease, a graphical tool called the predictiveness curve has been proposed. It characterizes the marker's predictiveness, or capacity to risk stratify the population by displaying the population distribution of risk endowed by the marker. Methods for making inference about the curve and for comparing curves in a general population have been developed. However, knowledge about a marker's performance in the general population only is not enough. Since a marker's effect on the risk model and its distribution can both differ across subpopulations, its predictiveness may vary …

Nonparametric Heteroscedastic Transformation Regression Models For Skewed Data With An Application To Health Care Costs, Xiao-Hua Zhou, Huazhen Lin, Eric Johnson

UW Biostatistics Working Paper Series

No abstract provided.

Semiparametric Inferential Procedures For Comparing Multivariate Roc Curves With Interaction Terms, Liansheng Tang, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Multivariate ROC curve models that include an interaction term be- tween biomarker type and false positive rate is important in comparative biomarker studies, because such interaction allows ROC curves of different biomarkers to cross each other. However, there has been limited work in drawing inference for comparing multivariate ROC curves, especially when the interaction terms are present. In this article we derive the asymptotic covariance of three estimators for multivariate ROC models. These covariance estimates have not been readily available in the literature, and bootstrap methods have to be used to obtain co- variance estimates. With the readily available variance …

Matrix Pooling: An Accurate And Cost Effective Testing Algorithm For Detection Of Acute Hiv Infection, Bethany L. Hedt, Marcello Pagano

Harvard University Biostatistics Working Paper Series

No abstract provided.

Semi-Parametric Maximum Likelihood Estimates For Roc Curves Of Continuous-Scale Tests, Xiao-Hua Zhou, Huazhen Lin

UW Biostatistics Working Paper Series

No abstract provided.

A Matrix Pooling Algorithm For Disease Detection, Bethany L. Hedt, Marcello Pagano

Harvard University Biostatistics Working Paper Series

No abstract provided.

Properties Of Monotonic Effects On Directed Acyclic Graphs, Tyler J. Vanderweele, James M. Robins

COBRA Preprint Series

Various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations. Counterexamples are provided to show that the results do not hold under less restrictive conditions. Monotonic effects are furthermore used to relate signed edges on a causal directed acyclic graph to qualitative effect modification. The theory is applied to an example concerning the direct effect of smoking on cardiovascular disease controlling for hypercholesterolemia. Monotonicity assumptions are used to construct a test for whether there is a variable that confounds the relationship between the mediator, hypercholesterolemia, and the outcome, cardiovascular disease.

Nonparametric Inference Procedure For Percentiles Of The Random Effect Distribution In Meta Analysis, Rui Wang, Lu Tian, Tianxi Cai, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Bayesian Approach To Modeling Associations Between Pulsatile Hormones, Nichole E. Carlson, Timothy D. Johnson, Morton B. Brown

The University of Michigan Department of Biostatistics Working Paper Series

Many hormones are secreted in pulses. The pulsatile relationship between hormones regulates many biological processes. To understand endocrine system regulation, time series of hormone concentrations are collected. The goal is to characterize pulsatile patterns and associations between hormones. Currently each hormone on each subject is fitted univariately. This leads to estimates of the number of pulses and estimates of the amount of hormone secreted; however, when the signal-to-noise ratio is small, pulse detection and parameter estimation remains di±cult with existing approaches. In this paper, we present a bivariate deconvolution model of pulsatile hormone data focusing on incorporating pulsatile associations. Through …

Parametric Non-Mixture Cure Models For Schedule-Finding Of Therapeutic Agents, Thomas M. Braun, Changying A. Liu

The University of Michigan Department of Biostatistics Working Paper Series

We propose a Phase I clinical trial design that seeks to determine the cumulative safety of a series of administrations of a fixed dose of an investigational agent. In contrast to traditional Phase I trials that are designed to solely find the maximum tolerated dose (MTD) of the agent, our design instead identifies a maximum tolerated schedule (MTS) that includes an MTD as well as a vector of recommended administration times. Our model is based upon a non-mixture cure model that constrains the probability of toxicity for all subjects to monotonically increase with both dose and the number of administrations …

Targeted Methods For Biomarker Discovery, The Search For A Standard, Catherine Tuglus, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

More often than not biomarker studies analyze large quantities of variables with complicated and generally unknown correlation structure. There are numerous statistical methods which attempt to unravel these variables and determine the underlying mechanism through identification of causally related biomarkers. Results from these methods are generally difficult to interpret and nearly impossible to compare across studies. The FDA has currently called for a standardization of methods and protocol for biomarker detection. In response, we propose targeted variable importance (tVIM) as a standardized method for biomarker discovery. Through the use of targeted Maximum Likelihood, tVIM provides double robust estimates of variable …