Statistics and Probability Commons^™

Covariate Specific Roc Curve With Survival Outcome, Xiao Song, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

The receiver operating characteristic (ROC) curve has been extended to survival data recently, including the nonparametric approach by Heagerty, Lumley and Pepe (2000) and the semiparametric approach by Heagerty and Zheng (2005) using standard survival analysis techniques based on two different time-dependent ROC curve definitions. However, both approaches cannot adjust for the effect of covariates on the accuracy of the biomarker. To account for the covariate effect, we propose semiparametric models for covariate specific ROC curves corresponding to the two time-dependent ROC curve definitions, respectively. We show that the estimators are consistent and converge to Gaussian processes. In the case …

Conditional Likelihood Methods For Haplotype-Based Association Analysis Using Matched Case-Control Data, Jinbo Chen, Carmen Rodriguez

UPenn Biostatistics Working Papers

Genetic epidemiologists routinely assess disease susceptibility in relation to haplotypes, i.e., combinations of alleles on a single chromosome. We study statistical methods for inferring haplotype-related disease risk using SNP genotype data from matched case-control studies, where controls are individually matched to cases on some selected factors. Assuming a logistic regression model for haplotype-disease association, we propose two conditional likelihood approaches that address the issue that haplotypes cannot be inferred with certainty from SNP genotype data (phase ambiquity). One approach is based on the likelihood of disease status conditioned on the total number of cases, genotypes, and other covariates within each …

Generalized Confidence Intervals For The Ratio Or Difference Of Two Means For Lognormal Populations With Zeros, Yea-Hung Chen, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

We discuss in this article methods for analyzing lognormal data that may include zeros. Specifically, we are interested in interval estimation for the ratio or difference of the population means. We propose here two generalized pivotal (GP) approaches: a ``true'' GP method and an ``approximate'' GP method. Additionally, we propose two likelihood-based approaches: a signed log-likelihood ratio (SLLR) method and a modified SLLR method. Our simulation studies suggest that the approximate generalized pivotal approach outperforms all other known methods; it results in highly accurate coverage frequencies and fairly low bias, even in small sample settings.

Multiple Imputation - Review Of Theory, Implementation And Software, Ofer Harel, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Missing data is a common complication in data analysis. In many medical settings missing data can cause difficulties in estimation, precision and inference. Multiple imputation (MI) \cite{Rubin87} is a simulation based approach to deal with incomplete data. Although there are many different methods to deal with incomplete data, MI has become one of the leading methods. Since the late 80's we observed a constant increase in the use and publication of MI related research. This tutorial does not attempt to cover all the material concerning MI, but rather provides an overview and combines together the theory behind MI, the implementation …

Multiple Imputation For The Comparison Of Two Screening Tests In Two-Phase Alzheimer Studies, Ofer Harel, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

Two-phase designs are common in epidemiological studies of dementia, and especially in Alzheimer research. In the first phase, all subjects are screened using a common screening test(s), while in the second phase, only a subset of these subjects is tested using a more definitive verification assessment, i.e. golden standard test. When comparing the accuracy of two screening tests in a two-phase study of dementia, inferences are commonly made using only the verified sample. It is well documented that in that case, there is a risk for bias, called verification bias. When the two screening tests have only two values (e.g. …

Improved Generalized Estimating Equation Analysis Via Xtqls For Implementation Of Quasi-Least Squares In Stata, Justine Shults, Sarah J. Ratcliffe, Mary Leonard

UPenn Biostatistics Working Papers

No abstract provided.

Generalized Monotonic Functional Mixed Models With Application To Modeling Normal Tissue Complications , Matthew Schipper, Jeremy Taylor, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

Normal tissue complications are a common side effect of radiation therapy. They are the consequence of the dose of radiation received by the normal tissue surrounding the tumor site. It is not known what function of the dose distribution to the normal tissue drives the presence and severity of the complications. Regarding the density of the dose distribution as a curve, a summary measure is obtained by integrating a weighting function of dose (w(d)) over the dose density. For biological reasons the weight function should be monotonic. We propose to study the dose effect on a clinical outcome using a …

Predicting Future Responses Based On Possibly Misspecified Working Models, Tianxi Cai, Lu Tian, Scott D. Solomon, L.J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Permutation Methods In Relative Risk Regression Models, Wenyu Jiang, Jack Kalbfleisch

The University of Michigan Department of Biostatistics Working Paper Series

In this paper, we develop a weighted permutation (WP) method to construct confidence intervals for regression parameters in relative risk regression models. The WP method is a generalized permutation approach. It constructs a resampled history which mimics the observed history for individuals under study. Inference procedures are based on studentized score statistics that are insensitive to the forms of the relative risk function. This makes the WP method appealing in the general framework of the relative risk regression model. First order accuracy of the WP method is established using the counting process approach with a partial likelihood filtration. A simulation …

On The Potential For Ill-Logic With Logically Defined Outcomes, Xianbin Li, Brian S. Caffo, Daniel O. Scharfstein

Johns Hopkins University, Dept. of Biostatistics Working Papers

Logically defined outcomes are commonly used in medical diagnoses and epidemiological research. When missing values in the original outcomes exist, the method of handling the missingness can have unintended consequences, even if the original outcomes are missing completely at random. Complicating the issue is that the default behavior of standard statistical packages yields different results. In this paper, we consider two binary original outcomes, which are missing completely at random. For estimating the prevalence of a logically defined "or" outcome, we discuss the properties of four estimators: complete case estimator, all-available case estimator, maximum likelihood estimator (MLE), and moment-based estimator. …

Evaluating Causal Effect Predictiveness Of Candidate Surrogate Endpoints, Peter B. Gilbert, Michael Hudgens

UW Biostatistics Working Paper Series

Most methods for evaluating surrogate endpoints measure validity in terms of net effects (i.e., treatment effects adjusted for the biomarker measured after randomization). Frangakis and Rubin (2002, Biometrics) criticized these approaches because net effects may reflect selection bias, and suggested an alternative definition of a surrogate endpoint (a "principal" surrogate) based on causal effects. For evaluating principal surrogates we introduce a causal effect predictiveness (CEP) surface, which quantifies how well causal treatment effects on the biomarker predict causal treatment effects on the clinical endpoint. The CEP surface is not identifiable in general due to missing potential outcomes. However, by incorporating …

Causal Comparisons In Randomized Trials Of Two Active Treatments: The Effect Of Supervised Exercise To Promote Smoking Cessation, Jason Roy, Joseph W. Hogan

COBRA Preprint Series

In behavioral medicine trials, such as smoking cessation trials, two or more active treatments are often compared. Noncompliance by some subjects with their assigned treatment poses a challenge to the data analyst. Causal parameters of interest might include those defined by subpopulations based on their potential compliance status under each assignment, using the principal stratification framework (e.g., causal effect of new therapy compared to standard therapy among subjects that would comply with either intervention). Even if subjects in one arm do not have access to the other treatment(s), the causal effect of each treatment typically can only be identified from …

Efficient Unbiased Estimating Equations For Analyzing Structured Correlation Matrices, Yihao Deng

Mathematics & Statistics Theses & Dissertations

Analysis of dependent continuous and discrete data has become an active area of research. For normal data, correlations fully quantify the dependence. And historically, maximum likelihood method has been very successful to estimate the correlations and unbiased estimating equation approach has become a popular alternative when there may be a departure from normality. In this thesis we show that the optimal unbiased estimating equation coincides with the likelihood equations for normal data. We then introduce a general class of weighted unbiased estimating equations to estimate parameters in a structured correlation matrix. We derive expressions for asymptotic covariance of the estimates, …

Age- And Sex-Specific Transformations Of Health Status Measures To Incorporate Death, Ann M. Derleth, Paula Diehr

UW Biostatistics Working Paper Series

Introduction: Measures of health status and physical function do not usually include a specific code for death. This can cause problems in longitudinal studies because analyses limited to survivors may bias the results. One approach is to recode the status variables to include a reasonable value for death. One method that has been used is to replace each scale value with the estimated probability that a person with this value will be “healthy”. “Healthy” has been defined as being above a particular threshold on the variable of interest one year later, or alternatively as being in excellent, very good, or …

Integrating The Predictiveness Of A Marker With Its Performance As A Classifier, Margaret S. Pepe, Ziding Feng, Ying Huang, Gary M. Longton, Ross Prentice, Ian M. Thompson, Yingye Zheng

UW Biostatistics Working Paper Series

There are two popular statistical approaches to biomarker evaluation. One models the risk of disease (or disease outcome) using, for example, logistic regression. A marker is useful if it has a strong effect on risk. The second evaluates classification performance using measures such as sensitivity, specificity, predictive values and ROC curves. There is controversy about which approach is most appropriate. Moreover, the two approaches often give contradictory results on the same data. We present a new graphic, the predictiveness curve, that complements the risk modeling approach. It assesses the usefulness of a risk model when applied to the population. In …

A Data Gathering Toolkit For Biological Information Integration, Munira Lokhandwala

Theses

SYSTERS is a biological information integration system containing protein sequences from many protein databases such as Swiss-Prot and TrEMBL and also protein sequences from complete genomes available at Ensembl, The Arabidopsis Information Resource, SGD and GeneDB. For some protein sequences their encoding nucleotide sequences can be found in their corresponding websites. However, for some protein sequences their encoding nucleotide sequences are missing.

The goal of this thesis is to. collect all nucleotide sequences for the protein sequences in SYSTERS and store them in a common database. There are two cases. The first case is that if the nucleotide sequences can …

Network Activity Arising From Optimal Diameters Of Neuronal Processes, Juliane Gansert

Theses

Electrical coupling provides an important pathway for signal transmission between neurons. In several regions of the mammalian brain electrical synapses have been detected, and their role in the synchronization of neural networks and the generation of oscillations has been studied theoretically. Recently, it has been found that the amplitude of the postsynaptic potential is maximized for a specific diameter of the postsynaptic fiber.

In this thesis, the impact of the fiber's diameter on the success or failure of the action potential initiation and propagation is studied theoretically. Systems of two coupled neurons, as well as small networks, are investigated. The …

Comparative Analysis Of Parametric, Nonparametric And Permutation Methods For Differential Expression, Rahul Patil

Theses

DNA microarrays permit us to study the expression of thousands of genes simultaneously. They are now used in many different contexts to compare mRNA levels between two or more samples of cells. Microarray experiments typically give us expression measurements on a large number of genes. Increasing popularity of microarray technology has resulted in a number of tests being proposed to detect differentials expression.

The purpose of study is to compare the parametric, non parametric and permutation tests when applied to microarray data for differential expression analysis. t test (parametric), Mann Whitney test (nonparametric) and Significance of analysis (permutation ) test …

Posterior Simulation In The Generalized Linear Model With Semiparmetric Random Effects, Subharup Guha

Harvard University Biostatistics Working Paper Series

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP …

Bounded Search For De Novo Identification Of Degenerate Cis-Regulatory Elements, Jonathan M. Carlson, Arijit Chakravarty, Radhika S. Khetani, Robert H. Gross

Dartmouth Scholarship

The identification of statistically overrepresented sequences in the upstream regions of coregulated genes should theoretically permit the identification of potential cis-regulatory elements. However, in practice many cis-regulatory elements are highly degenerate, precluding the use of an exhaustive word-counting strategy for their identification. While numerous methods exist for inferring base distributions using a position weight matrix, recent studies suggest that the independence assumptions inherent in the model, as well as the inability to reach a global optimum, limit this approach.

Semiparametric Bayesian Modeling Of Multivariate Average Bioequivalence, Pulak Ghosh Dr., Mithat Gonen

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

Bioequivalence trials are usually conducted to compare two or more formulations of a drug. Simultaneous assessment of bioequivalence on multiple endpoints is called multivariate bioequivalence. Despite the fact that some tests for multivariate bioequivalence are suggested, current practice usually involves univariate bioequivalence assessments ignoring the correlations between the endpoints such as AUC and Cmax. In this paper we develop a semiparametric Bayesian test for bioequivalence under multiple endpoints. Specifically, we show how the correlation between the endpoints can be incorporated in the analysis and how this correlation affects the inference. Resulting estimates and posterior probabilities ``borrow strength'' from one another …

Combining Information From Two Surveys To Estimate County-Level Prevalence Rates Of Cancer Risk Factors And Screening, Trivellore E. Raghuanthan, Dawei Xie, Nathaniel Schenker, Van Parsons, William W. Davis, Kevin W. Dodd, Eric J. Feuer

The University of Michigan Department of Biostatistics Working Paper Series

Cancer surveillance requires estimates of the prevalence of cancer risk factors and screening for small areas such as counties. Two popular data sources are the Behavioral Risk Factor Surveillance System (BRFSS), a telephone survey conducted by state agencies, and the National Health Interview Survey (NHIS), an area probability sample survey conducted through face-to-face interviews. Both data sources have advantages and disadvantages. The BRFSS is a larger survey, and almost every county is included in the survey; but it has lower response rates as is typical with telephone surveys, and it does not include subjects who live in households with no …

Semiparametric Latent Variable Regression Models For Spatio-Temporal Modeling Of Mobile Source Particles In The Greater Boston Area, Alexandros Gryparis, Brent A. Coull, Joel Schwartz, Helen H. Suh

Harvard University Biostatistics Working Paper Series

Traffic particle concentrations show considerable spatial variability within a metropolitan area. We consider latent variable semiparametric regression models for modeling the spatial and temporal variability of black carbon and elemental carbon concentrations in the greater Boston area. Measurements of these pollutants, which are markers of traffic particles, were obtained from several individual exposure studies conducted at specific household locations as well as 15 ambient monitoring sites in the city. The models allow for both flexible, nonlinear effects of covariates and for unexplained spatial and temporal variability in exposure. In addition, the different individual exposure studies recorded different surrogates of traffic …

Empirical Bayes Approach To Controlling Familywise Error: An Application To Hiv Resistance Data, Rhoderick N. Machekano, Alan E. Hubbard

U.C. Berkeley Division of Biostatistics Working Paper Series

Statistical challenges arise in identifying meaningful patterns and structures from high dimensional genomic data sets. Relating HIV genotype (sequence of amino acids) to phenotypic resistance presents a typical problem. When the HIV virus is under antiretroviral drug pressure, unfavorable mutations of the target genes often lead to greatly increased resistance of the virus to drugs, including drugs the virus has not been exposed to. Identification of mutation combinations and their correlation to drug resistance is critical in guiding efficient prescription of HIV drugs. The identification of a subset of codons associated with drug resistance from a set of several hundreds …

Reliability, Effect Size, And Responsiveness And Intraclass Correlation Of Health Status Measures Used In Randomized And Cluster-Randomized Trials, Paula Diehr, Lu Chen, Donald L. Patrick, Ziding Feng, Yutaka Yasui

UW Biostatistics Working Paper Series

Background: New health status instruments are described by psychometric properties, such as Reliability, Effect Size, and Responsiveness. For cluster-randomized trials, another important statistic is the Intraclass Correlation for the instrument within clusters. Studies using better instruments can be performed with smaller sample sizes, but better instruments may be more expensive in terms of dollars, lost opportunities, or poorer data quality due to the response burden of longer instruments. Investigators often need to estimate the psychometric properties of a new instrument, or of an established instrument in a new setting. Optimal sample sizes for estimating these properties have not been studied …

Detecting Pulsatile Hormone Secretion Events: A Bayesian Approach, Tim Johnson

The University of Michigan Department of Biostatistics Working Paper Series

Many challenges arise in the analysis of pulsatile, or episodic, hormone concentration time series data. Among these challenges is the determination of the number and location of pulsatile events and the discrimination of events from noise. Analyses of these data are typically performed in two stages. In the first stage, the number and approximate location of the pulses are determined. In the second stage, a model (typically a deconvolution model) is fit to the data conditional on the number of pulses. Any error made in the first stage is carried over to the second stage. Furthermore, current methods, except two, …

Semiparametric Analysis For Correlated Recurrent And Terminal Events, Yining Ye, Jack Kalbfleisch, Doug E. Schaubel

The University of Michigan Department of Biostatistics Working Paper Series

In clinical and observational studies, recurrent event data (e.g. hospitalization) with a terminal event (e.g. death) are often encountered. In many instances, the terminal event is strongly correlated with the recurrent event process. In this article, we propose a semiparametric method to jointly model the recurrent and terminal event processes. The dependence is modeled by a shared gamma frailty that is included in both the recurrent event rate and terminal event hazard function. Marginal models are used to estimate the regression effects on the terminal and recurrent event processes and a Poisson model is used to estimate the dispersion of …

Adjusting For Covariate Effects On Classification Accuracy Using The Covariate-Adjusted Roc Curve, Holly Janes, Margaret S. Pepe

UW Biostatistics Working Paper Series

Recent scientific and technological innovations have produced an abundance of potential markers which are being investigated for their use in disease screen- ing and diagnosis. In evaluating these markers, it is often necessary to account for covariates which are associated with the marker of interest. These covariates may include subject characteristics, expertise of the test operator, test proce- dures, or aspects of specimen handling. In this paper, we propose the AROC, a covariate-adjusted measure of the classification accuracy. The AROC is the common covariate-specific ROC curve, when the covariate does not affect dis- crimination, and a weighted average of covariate-specific …

Genome Scanning Methods For Comparing Sequences Between Groups, With Application To Hiv Vaccine Trials, Peter B. Gilbert, Chunyuan Wu, David V. Jobes

UW Biostatistics Working Paper Series

Consider a placebo-controlled preventive HIV vaccine efficacy trial. An HIV amino acid sequence is measured from each volunteer who acquires HIV, and these sequences are aligned together with the reference HIV sequence represented in the vaccine. We develop genome scanning methods to identify HIV positions at which the amino acids in sequences from infected vaccine recipients tend to be more divergent from the corresponding reference amino acid than the amino acids in sequences from infected placebo recipients. We consider five two-sample test statistics, based on Euclidean, Mahalanobis, and Kullback-Leibler divergence measures. Weights are incorporated to reflect biological information contained in …

Multiple Tests Of Association With Biological Annotation Metadata, Sandrine Dudoit, Sunduz Keles, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a general and formal statistical framework for the multiple tests of associations between known fixed features of a genome and unknown parameters of the distribution of variable features of this genome in a population of interest. The known fixed gene-annotation profiles, corresponding to the fixed features of the genome, may concern Gene Ontology (GO) annotation, pathway membership, regulation by particular transcription factors, nucleotide sequences, or protein sequences. The unknown gene-parameter profiles, corresponding to the variable features of the genome, may be, for example, regression coefficients relating genome-wide transcript levels or DNA copy numbers to possibly censored biological and …