Download or read book Bayesian Variable Selection for the Cox Regression Model with Missing Covariates written by Joseph George Ibrahim and published by . This book was released on 2008 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics on Bayesian Analysis of Missing Data written by Yun Kai Jiang and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation focuses on model selection in logistic regression with incompletely observed data. In particular, methods are presented for using Markov Chain Monte Carlo imputation and Bayesian variable selection to model a binary outcome. We consider multivariate missing covariates, with different types of predictors, such as continuous, counts, and categorical variables. Such type of data is considered in the analysis of Project Talent recorded from a longitudinal study. Roughly 400,000 were selected for the study from United States high school students in grades 9 through 12 during the year 1960; follow-up surveys were conducted 1, 5, and 11 years after graduation. We extend a methodology developed by Yang, Belin, and Boscardin (2005), to this Project Talent for a logistic regression model with incomplete covariates. The idea is to use data information as much as possible to fill in the missing values and study associations between a binary response variable and covariates. According to Yang, Belin, and Boscardin, one approach under a multivariate normal assumption for data, is to conduct Bayesian variable selection and missing data imputation simultaneously within one Gibbs Sampling process, called "Simultaneously Impute And Select" (SIAS). A modified strategy of SIAS is extended to a mixed data structure that allows for categorical, counts, and continuous variables. The first chapter consists of an introduction to some approaches to variable selection for missing data. The fact that missing data arise commonly in statistical analyses, leads to a variety of methods to handle missing data. The missing data mechanism needs to be considered in imputations. The multiple imputation methods and Markov Chain Mote Carlo (MCMC) algorithms are presented as general statistical approaches to missing data analysis. In the MCMC computational toolbox, various implementation methods for imputation are discussed: Metropolis-Hasting, Gibbs Sampler, and Data Augmentation. Compared to model selection methods in frequentist and likelihood inference, Bayesian inference takes an entirely different approach. The frequentist approach only looks at the current data to make inference. The Bayesian approach requires the specification of the prior distribution, which can come from historical data or expert opinion. Stochastic Search Variable Selection (SSVS) and Gibbs Variable Selection (GVS) are reviewed for model selection. Two alternative strategies, Impute Then Select (ITS) and Simultaneously Impute And Select (SIAS), are studied. In the second chapter, imputation and Bayesian variable selection methods for linear regression are extended to a binary response variable that is completely observed, but some covariates have missing values. We focus on extending SIAS strategy to logistic regression models via two alternative imputations, decomposition and Fully Conditional Specification (FCS). The decomposition method breaks a multivariate distribution into a series of univariate ones by decomposing the joint density function p(Y, X1, ..., X[p]) into the product of conditional distributions, using the factorization p(A, B) = p(A[vertical line]B)p(B). The FCS aims to involve iteratively sampling from the conditional distributions for one random variable, given all the others. These two methods are implemented in the imputation step of the SIAS procedure then applied to the Project Talent data. Simulations are also performed to validate these results and demonstrate the superiority of FCS over the decomposition method under certain circumstances. The third chapter presents a new approach for incorporating the sampling weight into imputation and Bayesian variable selection in logistic regression models. We develop the approach that extends SIAS by a Bayesian version of iterative weighted least squares algorithm to include a sampling step based on Gibbs sampler. This approach is illustrated using both simulation studies and Project Talent data.

Download or read book Handbook of Bayesian Variable Selection written by Mahlet G. Tadesse and published by CRC Press. This book was released on 2021-12-24 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material

Download or read book Bayesian Variable Selection in Parametric and Semiparametric High Dimensional Survival Analysis written by Kyu Ha Lee and published by . This book was released on 2011 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we propose several Bayesian variable selection schemes forBayesian parametric and semiparametric survival models for right-censored survivaldata. In the rst chapter we introduce a special shrinkage prior on the coe cients corresponding to the predictor variables. The shrinkage prior is obtained through a scale mixture representation of Normal and Gamma distributions. The likelihood functionis constructed based on the Cox proportional hazards model framework, where the cumulative baseline hazard function is modeled a priori by a gamma process. In the second chapter we extend the idea of the shrinkage prior such that it can incorporate the existing grouping structure among the covariates. Our selected priors are similar to the elastic-net, group lasso, and fused lasso penalty. The proposed models are highly useful when we want to take into consideration the grouping structure. In the third chapter we propose a Bayesian variable selection method for high dimensional survival analysis in the context of parametric accelerated failure time (AFT) model. To identify subsets of relevant covariates the regression coe cients are assumed to follow the conditional Laplace distribution as in the rst chapter. We used a data augmentation approach to impute the survival times of censored subjects.

Download or read book Objective Bayesian Variable Selection for Censored Data written by Silvia Perra and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of survival analysis is to explain and predict the survival, usually defined along the time domain. In this work we study it by means of regression models. In statistical data analysis it is common to consider the regression set up in which a given response variable depends on some factors and/or covariates. The model selection problem mainly consists in choosing the covariates which better explain the dependent variable in a precise and hopefully fast manner. This process usually has several steps: the first one is to collect considerations from an expert about the set of covariates, then the statistician derives a prior on model parameters and constructs a tool to solve the model selection problem. We consider the model selection problem in survival analysis when the response variable is the time to event. Under an objective Bayesian approach, some commonly used tools in literature are the Intrinsic Bayes factor (IBF) and the Fractional Bayes factor (FBF). In this thesis we deal with the variable selection problem for censored data.

Download or read book Cox Regression with Survival time dependent Missing Covariate Values written by Yanyao Yi and published by . This book was released on 2019 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis with time-to-event data in clinical and epidemiological studies often encounters missing covariate values and the missing at random assumption is commonly adopted (e.g., Qi et al., 2005), which assumes that missingness depends on the observed data, including the observed outcome which is the minimum of survival and censoring time. However, it is conceivable that in certain settings, missingness of covariate values is related to the survival time but not to the censoring time (Rathouz, 2007). This is especially so when covariate missingness is related with an unmeasured variable that is affected by survival time but does not causally affect survival. If this is the case, then the covariate missingness is not at random as the survival time is censored, and it creates a challenge in data analysis. In this article, we propose an approach to deal with such survival-time-dependent covariate missingness based on the well known Cox proportional hazard model. Our method is based on inverse propensity weighting with the propensity estimated by nonparametric kernel regression. Our estimators are consistent and asymptotically normal, and their finite- sample performance is examined through simulation. An application to a real-data example is included for illustration.

Download or read book Bayesian Methods to Impute Missing Covariates for Causal Inference and Model Selection written by Robin Mitra and published by . This book was released on 2008 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents new approaches to deal with missing covariate data in two situations; matching in observational studies and model selection for generalized linear models.

Download or read book Multiple Imputation and its Application written by James Carpenter and published by John Wiley & Sons. This book was released on 2012-12-21 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical guide to analysing partially observeddata. Collecting, analysing and drawing inferences from data iscentral to research in the medical and social sciences.Unfortunately, it is rarely possible to collect all the intendeddata. The literature on inference from the resultingincomplete data is now huge, and continues to grow both asmethods are developed for large and complex data structures, and asincreasing computer power and suitable software enable researchersto apply these methods. This book focuses on a particular statistical method foranalysing and drawing inferences from incomplete data, calledMultiple Imputation (MI). MI is attractive because it is bothpractical and widely applicable. The authors aim is to clarify theissues raised by missing data, describing the rationale for MI, therelationship between the various imputation models and associatedalgorithms and its application to increasingly complex datastructures. Multiple Imputation and its Application: Discusses the issues raised by the analysis of partiallyobserved data, and the assumptions on which analyses rest. Presents a practical guide to the issues to consider whenanalysing incomplete data from both observational studies andrandomized trials. Provides a detailed discussion of the practical use of MI withreal-world examples drawn from medical and social statistics. Explores handling non-linear relationships and interactionswith multiple imputation, survival analysis, multilevel multipleimputation, sensitivity analysis via multiple imputation, usingnon-response weights with multiple imputation and doubly robustmultiple imputation. Multiple Imputation and its Application is aimed atquantitative researchers and students in the medical and socialsciences with the aim of clarifying the issues raised by theanalysis of incomplete data data, outlining the rationale for MIand describing how to consider and address the issues that arise inits application.

Download or read book The Frailty Model written by Luc Duchateau and published by Springer Science & Business Media. This book was released on 2007-10-23 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.

Download or read book Case Studies in Bayesian Statistical Modelling and Analysis written by Clair L. Alston and published by John Wiley & Sons. This book was released on 2012-10-10 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an accessible foundation to Bayesian analysis using real world models This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises a description of the problem, the corresponding model, the computational method, results and inferences as well as the issues that arise in the implementation of these approaches. Case Studies in Bayesian Statistical Modelling and Analysis: Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems. Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods. Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing. Case Studies in Bayesian Statistical Modelling and Analysis is aimed at statisticians, researchers and practitioners who have some expertise in statistical modelling and analysis, and some understanding of the basics of Bayesian statistics, but little experience in its application. Graduate students of statistics and biostatistics will also find this book beneficial.

Download or read book Variable Selection in Cox Regression Models with Varying Coefficients written by Toshio Honda and published by . This book was released on 2017 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: We deal with two kinds of Cox regression models with varying coefficients. The coefficients vary with time in one model. In the other model, there is an important random variable called an index variable and the coefficients vary with the variable. In both models, we have p-dimensional covariates and p increases moderately. However, it is the case that only a small part of the covariates are relevant in these situations. We carry out variable selection and estimation of the coefficient functions by using the group SCAD-type estimator and the adaptive group Lasso estimator. We examine the theoretical properties of the estimators, especially the L2 convergence rate, the sparsity, and the oracle property. Simulation studies and a real data analysis show the performance of these new techniques.

Download or read book Bayesian Variable Selection and Covariance Selection in Gaussian Linear Regression written by Ed Cripps and published by . This book was released on 2005 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Existing Approaches and a New Weighted Method for Cox Regression in the Presence of Missing Covariates written by Qiang Xu and published by . This book was released on 2008 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Survival Analysis written by Joseph G. Ibrahim and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survival analysis arises in many fields of study including medicine, biology, engineering, public health, epidemiology, and economics. This book provides a comprehensive treatment of Bayesian survival analysis. It presents a balance between theory and applications, and for each class of models discussed, detailed examples and analyses from case studies are presented whenever possible. The applications are all from the health sciences, including cancer, AIDS, and the environment.

Download or read book Contemporary Multivariate Analysis and Design of Experiments written by Kaitai Fang and published by World Scientific. This book was released on 2005 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Index. Subject index -- Author index

Download or read book Handbook of Survival Analysis written by John P. Klein and published by CRC Press. This book was released on 2016-04-19 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Survival Analysis presents modern techniques and research problems in lifetime data analysis. This area of statistics deals with time-to-event data that is complicated by censoring and the dynamic nature of events occurring in time. With chapters written by leading researchers in the field, the handbook focuses on advances in survival analysis techniques, covering classical and Bayesian approaches. It gives a complete overview of the current status of survival analysis and should inspire further research in the field. Accessible to a wide range of readers, the book provides: An introduction to various areas in survival analysis for graduate students and novices A reference to modern investigations into survival analysis for more established researchers A text or supplement for a second or advanced course in survival analysis A useful guide to statistical methods for analyzing survival data experiments for practicing statisticians

Download or read book Missing Data in Longitudinal Studies written by Michael J. Daniels and published by Chapman and Hall/CRC. This book was released on 2008-03-11 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing from the authors’ own work and from the most recent developments in the field, Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis describes a comprehensive Bayesian approach for drawing inference from incomplete data in longitudinal studies. To illustrate these methods, the authors employ several data sets throughout that cover a range of study designs, variable types, and missing data issues. The book first reviews modern approaches to formulate and interpret regression models for longitudinal data. It then discusses key ideas in Bayesian inference, including specifying prior distributions, computing posterior distribution, and assessing model fit. The book carefully describes the assumptions needed to make inferences about a full-data distribution from incompletely observed data. For settings with ignorable dropout, it emphasizes the importance of covariance models for inference about the mean while for nonignorable dropout, the book studies a variety of models in detail. It concludes with three case studies that highlight important features of the Bayesian approach for handling nonignorable missingness. With suggestions for further reading at the end of most chapters as well as many applications to the health sciences, this resource offers a unified Bayesian approach to handle missing data in longitudinal studies.