Biostatistics Commons^™

Lehmann Family Of Roc Curves, Mithat Gonen, Glenn Heller

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

Receiver operating characteristic (ROC) curves are useful in evaluating the ability of a continuous marker in discriminating between the two states of a binary outcome such as diseased/not diseased. The most popular parametric model for an ROC curve is the binormal model which assumes that the marker is normally distributed conditional on the outcome. Here we present an alternative to the binormal model based on the Lehmann family, also known as the proportional hazards specification. The resulting ROC curve and its functionals (such as the area under the curve) have simple analytic forms. We derive closed-form expressions for the asymptotic …

A Likelihood Based Method For Real Time Estimation Of The Serial Interval And Reproductive Number Of An Epidemic, Laura Forsberg White, Marcello Pagano

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Semiparametric Approach For The Nonparametric Transformation Survival Model With Multiple Covariates, Xiao Song, Shuangge Ma, Jian Huang, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

The nonparametric transformation model for survival time that makes no parametric assumptions on both the transformation function and the error is appealing in its flexibility. The nonparametric transformation model makes no assumption on the forms of the transformation function and the error distribution. This model is appealing in its flexibility for modeling censored survival data. Current approaches for estimation of the regression parameters involve maximizing discontinuous objective functions, which are numerically infeasible to implement in the case of multiple covariates. Based on the partial rank estimator (Khan & Tamer, 2004), we propose a smoothed partial rank estimator which maximizes a …

Semiparametric Regression Of Multi-Dimensional Genetic Pathway Data: Least Squares Kernel Machines And Linear Mixed Models, Dawei Liu, Xihong Lin, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

SUMMARY. We consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway, where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least squares kernel machines (LSKMs). This unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way. This semiparametric model …

Semiparametric Regression Of Multi-Dimensional Genetic Pathway Data: Least Squares Kernel Machines And Linear Mixed Models, Dawei Liu, Xihong Lin, Debashis Ghosh

Harvard University Biostatistics Working Paper Series

No abstract provided.

Analysis Of Case-Control Age-At-Onset Data Using A Modified Case-Cohort Method, Bin Nan, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

Case-control designs are widely used in rare disease studies. In a typical case-control study, data are collected from a sample of all available subjects who have experienced a disease (cases) and a sub-sample of subjects who have not experienced the disease (controls) in a study cohort. Cases are often oversampled in case-control studies. Logistic regression is a common tool to estimate the relative risks of the disease and a set of covariates. Very often in such a study, information of ages-at-onset of the disease for all cases and ages at survey of controls are known. Standard logistic regression analysis using …

Doubly Penalized Buckley-James Method For Survival Data With High-Dimensional Covariates, Sijian Wang, Bin Nan, Ji Zhu, David G. Beer

The University of Michigan Department of Biostatistics Working Paper Series

Recent interest in cancer research focuses on predicting patients' survival by investigating gene expression profiles based on microarray analysis. We propose a doubly penalized Buckley-James method for the semiparametric accelerated failure time model to relate high-dimensional genomic data to censored survival outcomes, which uses a mixture of L₁-norm and L₂-norm penalties. Similar to the elastic-net method for linear regression model with uncensored data, the proposed method performs automatic gene selection and parameter estimation, where highly correlated genes are able to be selected (or removed) together. The two-dimensional tuning parameter is determined by cross-validation and uniform design. …

Exploiting Gene-Environment Independence For Analysis Of Case-Control Studies: An Empirical Bayes Approach To Trade Off Between Bias And Efficiency, Bhramar Mukherjee, Nilanjan Chatterjee

The University of Michigan Department of Biostatistics Working Paper Series

Standard prospective logistic regression analysis of case-control data often leads to very imprecise estimates of gene-environment interactions due to small numbers of cases or controls in cells of crossing genotype and exposure. In contrast, under the assumption of gene-environment independence, modern “retrospective” methods, including the “case-only” approach, can estimate the interaction parameters much more precisely, but they can be seriously biased when the underlying assumption of gene-environment independence is violated. In this article, we propose a novel approach to analyze case-control data that can relax the gene-environment independence assumption using an empirical Bayes framework. In the special case, involving a …

A Note On Bias Due To Fitting Prospective Multivariate Generalized Linear Models To Categorical Outcomes Ignoring Retrospective Sampling Schemes, Bhramar Mukherjee, Ivy Liu

The University of Michigan Department of Biostatistics Working Paper Series

Outcome dependent sampling designs are commonly used in economics, market research and epidemiological studies. Case-control sampling design is a classic example of outcome dependent sampling, where exposure information is collected on subjects conditional on their disease status. In many situations, the outcome under consideration may have multiple categories instead of a simple dichotomization. For example, in a case-control study, there may be disease sub-classification among the “cases” based on progression of the disease, or in terms of other histological and morphological characteristics of the disease. In this note, we investigate the issue of fitting prospective multivariate generalized linear models to …

Indeks Sosio-Ekonomi Menggunakan Principal Component Analysis, Iwan Ariawan

Kesmas

Pada penelitian survei, kita dapat mengukur tingkat status sosio-ekonomi rumah tangga melalui pemasukan, pengeluaran dan kepemilikan barang-barang berharga. Penggunaan variabel pemasukan dan pengeluaran di negara berkembang memiliki banyak kelemahan, sehingga banyak peneliti lebih suka menggunakan variabel kepemilikan barang berharga untuk mengukur status sosio-ekonomi. Namun, penggunaan variabel kepemilikan barang berharga menimbulkan masalah lain, yaitu banyaknya variabel untuk mengukur status sosio-ekonomi. Tujuan penulisan ini adalah menyederhanakan banyak variabel kepemilikan barang berharga menjadi 1 indeks sosio-ekonomi. Data yang digunakan adalah data Survei Demografi Kesehatan Indonesia 2002-2003 yang memiliki 7 variabel binomial tentang kepemilikan barang berharga dan 3 variabel ordinal tentang keadaan rumah untuk …

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 …

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 …

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 …

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.