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 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 Bayesian Nonparametrics for Causal Inference and Missing Data written by Michael J. Daniels and published by CRC Press. This book was released on 2023-08-23 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Nonparametrics for Causal Inference and Missing Data provides an overview of flexible Bayesian nonparametric (BNP) methods for modeling joint or conditional distributions and functional relationships, and their interplay with causal inference and missing data. This book emphasizes the importance of making untestable assumptions to identify estimands of interest, such as missing at random assumption for missing data and unconfoundedness for causal inference in observational studies. Unlike parametric methods, the BNP approach can account for possible violations of assumptions and minimize concerns about model misspecification. The overall strategy is to first specify BNP models for observed data and then to specify additional uncheckable assumptions to identify estimands of interest. The book is divided into three parts. Part I develops the key concepts in causal inference and missing data and reviews relevant concepts in Bayesian inference. Part II introduces the fundamental BNP tools required to address causal inference and missing data problems. Part III shows how the BNP approach can be applied in a variety of case studies. The datasets in the case studies come from electronic health records data, survey data, cohort studies, and randomized clinical trials. Features • Thorough discussion of both BNP and its interplay with causal inference and missing data • How to use BNP and g-computation for causal inference and non-ignorable missingness • How to derive and calibrate sensitivity parameters to assess sensitivity to deviations from uncheckable causal and/or missingness assumptions • Detailed case studies illustrating the application of BNP methods to causal inference and missing data • R code and/or packages to implement BNP in causal inference and missing data problems The book is primarily aimed at researchers and graduate students from statistics and biostatistics. It will also serve as a useful practical reference for mathematically sophisticated epidemiologists and medical researchers.

Download or read book Flexible Imputation of Missing Data Second Edition written by Stef van Buuren and published by CRC Press. This book was released on 2018-07-17 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Missing data pose challenges to real-life data analysis. Simple ad-hoc fixes, like deletion or mean imputation, only work under highly restrictive conditions, which are often not met in practice. Multiple imputation replaces each missing value by multiple plausible values. The variability between these replacements reflects our ignorance of the true (but missing) value. Each of the completed data set is then analyzed by standard methods, and the results are pooled to obtain unbiased estimates with correct confidence intervals. Multiple imputation is a general approach that also inspires novel solutions to old problems by reformulating the task at hand as a missing-data problem. This is the second edition of a popular book on multiple imputation, focused on explaining the application of methods through detailed worked examples using the MICE package as developed by the author. This new edition incorporates the recent developments in this fast-moving field. This class-tested book avoids mathematical and technical details as much as possible: formulas are accompanied by verbal statements that explain the formula in accessible terms. The book sharpens the reader’s intuition on how to think about missing data, and provides all the tools needed to execute a well-grounded quantitative analysis in the presence of missing data.

Download or read book Applied Bayesian Modeling and Causal Inference from Incomplete Data Perspectives written by Andrew Gelman and published by John Wiley & Sons. This book was released on 2004-09-03 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a collection of articles on statistical methods relating to missing data analysis, including multiple imputation, propensity scores, instrumental variables, and Bayesian inference. Covering new research topics and real-world examples which do not feature in many standard texts. The book is dedicated to Professor Don Rubin (Harvard). Don Rubin has made fundamental contributions to the study of missing data. Key features of the book include: Comprehensive coverage of an imporant area for both research and applications. Adopts a pragmatic approach to describing a wide range of intermediate and advanced statistical techniques. Covers key topics such as multiple imputation, propensity scores, instrumental variables and Bayesian inference. Includes a number of applications from the social and health sciences. Edited and authored by highly respected researchers in the area.

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 Missing Data in Longitudinal Studies written by Michael J. Daniels and published by CRC Press. This book was released on 2008-03-11 with total page 324 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

Download or read book The Prevention and Treatment of Missing Data in Clinical Trials written by National Research Council and published by National Academies Press. This book was released on 2010-12-21 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Randomized clinical trials are the primary tool for evaluating new medical interventions. Randomization provides for a fair comparison between treatment and control groups, balancing out, on average, distributions of known and unknown factors among the participants. Unfortunately, these studies often lack a substantial percentage of data. This missing data reduces the benefit provided by the randomization and introduces potential biases in the comparison of the treatment groups. Missing data can arise for a variety of reasons, including the inability or unwillingness of participants to meet appointments for evaluation. And in some studies, some or all of data collection ceases when participants discontinue study treatment. Existing guidelines for the design and conduct of clinical trials, and the analysis of the resulting data, provide only limited advice on how to handle missing data. Thus, approaches to the analysis of data with an appreciable amount of missing values tend to be ad hoc and variable. The Prevention and Treatment of Missing Data in Clinical Trials concludes that a more principled approach to design and analysis in the presence of missing data is both needed and possible. Such an approach needs to focus on two critical elements: (1) careful design and conduct to limit the amount and impact of missing data and (2) analysis that makes full use of information on all randomized participants and is based on careful attention to the assumptions about the nature of the missing data underlying estimates of treatment effects. In addition to the highest priority recommendations, the book offers more detailed recommendations on the conduct of clinical trials and techniques for analysis of trial data.

Download or read book Bayesian Nonparametrics for Causal Inference and Missing Data written by Michael Joseph Daniels and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Nonparametrics for Causal Inference and Missing Data provides an overview of flexible Bayesian nonparametric (BNP) methods for modeling joint or conditional distributions and functional relationships, and their interplay with causal inference and missing data. This book emphasizes the importance of making untestable assumptions to identify estimands of interest, such as missing at random assumption for missing data and unconfoundedness for causal inference in observational studies. Unlike parametric methods, the BNP approach can account for possible violations of assumptions and minimize concerns about model misspecification. The overall strategy is to first specify BNP models for observed data and then to specify additional uncheckable assumptions to identify estimands of interest. The book is divided into three parts. Part I develops the key concepts in causal inference and missing data and reviews relevant concepts in Bayesian inference. Part II introduces the fundamental BNP tools required to address causal inference and missing data problems. Part III shows how the BNP approach can be applied in a variety of case studies. The datasets in the case studies come from electronic health records data, survey data, cohort studies, and randomized clinical trials. Features Thorough discussion of both BNP and its interplay with causal inference and missing data How to use BNP and g-computation for causal inference and non-ignorable missingness How to derive and calibrate sensitivity parameters to assess sensitivity to deviations from uncheckable causal and/or missingness assumptions Detailed case studies illustrating the application of BNP methods to causal inference and missing data R code and/or packages to implement BNP in causal inference and missing data problems The book is primarily aimed at researchers and graduate students from statistics and biostatistics. It will also serve as a useful practical reference for mathematically sophisticated epidemiologists and medical researchers.

Download or read book Bayesian Data Analysis Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Download or read book Elements of Causal Inference written by Jonas Peters and published by MIT Press. This book was released on 2017-11-29 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise and self-contained introduction to causal inference, increasingly important in data science and machine learning. The mathematization of causality is a relatively recent development, and has become increasingly important in data science and machine learning. This book offers a self-contained and concise introduction to causal models and how to learn them from data. After explaining the need for causal models and discussing some of the principles underlying causal inference, the book teaches readers how to use causal models: how to compute intervention distributions, how to infer causal models from observational and interventional data, and how causal ideas could be exploited for classical machine learning problems. All of these topics are discussed first in terms of two variables and then in the more general multivariate case. The bivariate case turns out to be a particularly hard problem for causal learning because there are no conditional independences as used by classical methods for solving multivariate cases. The authors consider analyzing statistical asymmetries between cause and effect to be highly instructive, and they report on their decade of intensive research into this problem. The book is accessible to readers with a background in machine learning or statistics, and can be used in graduate courses or as a reference for researchers. The text includes code snippets that can be copied and pasted, exercises, and an appendix with a summary of the most important technical concepts.

Download or read book Analysis of Incomplete Multivariate Data written by J.L. Schafer and published by CRC Press. This book was released on 1997-08-01 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last two decades have seen enormous developments in statistical methods for incomplete data. The EM algorithm and its extensions, multiple imputation, and Markov Chain Monte Carlo provide a set of flexible and reliable tools from inference in large classes of missing-data problems. Yet, in practical terms, those developments have had surprisingly little impact on the way most data analysts handle missing values on a routine basis. Analysis of Incomplete Multivariate Data helps bridge the gap between theory and practice, making these missing-data tools accessible to a broad audience. It presents a unified, Bayesian approach to the analysis of incomplete multivariate data, covering datasets in which the variables are continuous, categorical, or both. The focus is applied, where necessary, to help readers thoroughly understand the statistical properties of those methods, and the behavior of the accompanying algorithms. All techniques are illustrated with real data examples, with extended discussion and practical advice. All of the algorithms described in this book have been implemented by the author for general use in the statistical languages S and S Plus. The software is available free of charge on the Internet.

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 Data Analysis Using Regression and Multilevel Hierarchical Models written by Andrew Gelman and published by Cambridge University Press. This book was released on 2007 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2007, is for the applied researcher performing data analysis using linear and nonlinear regression and multilevel models.

Download or read book Bayesian Nonparametric Methods for Causal Inference and Prediction written by Bret Michael Zeldow and published by . This book was released on 2017 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we present novel approaches to regression and causal inference using popular Bayesian nonparametric methods. Bayesian Additive Regression Trees (BART) is a Bayesian machine learning algorithm in which the conditional distribution is modeled as a sum of regression trees. We extend BART into a semiparametric generalized linear model framework so that a portion of the covariates are modeled nonparametrically using BART and a subset of the covariates have parametric form. This presents an attractive option for research in which only a few covariates are of scientific interest but there are other covariates must be controlled for. Under certain causal assumptions, this model can be used as a structural mean model. We demonstrate this method by examining the effect of initiating certain antiretroviral medications has on mortality among HIV/HCV coinfected subjects. In later chapters, we propose a joint model for a continuous longitudinal outcome and baseline covariates using penalized splines and an enriched Dirichlet process (EDP) prior. This joint model decomposes into local linear mixed models for the outcome given the covariates and marginals for the covariates. The EDP prior that is placed on the regression parameters and the parameters on the covariates induces clustering among subjects determined by similarity in their regression parameters and nested within those clusters, sub-clusters based on similarity in the covariate space. When there are a large number of covariates, we find improved prediction over the same model with Dirichlet process (DP) priors. Since the model clusters based on regression parameters, this model also serves as a functional clustering algorithm where one does not have to choose the number of clusters beforehand. We use the method to estimate incidence rates of diabetes when longitudinal laboratory values from electronic health records are used to augment diagnostic codes for outcome identification. We later extend this work by using our EDP model in a causal inference setting using the parametric g-formula. We demonstrate this using electronic health record data consisting of subjects initiating second generation antipsychotics.

Download or read book Bayesian and Frequentist Regression Methods written by Jon Wakefield and published by Springer Science & Business Media. This book was released on 2013-01-04 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian and Frequentist Regression Methods provides a modern account of both Bayesian and frequentist methods of regression analysis. Many texts cover one or the other of the approaches, but this is the most comprehensive combination of Bayesian and frequentist methods that exists in one place. The two philosophical approaches to regression methodology are featured here as complementary techniques, with theory and data analysis providing supplementary components of the discussion. In particular, methods are illustrated using a variety of data sets. The majority of the data sets are drawn from biostatistics but the techniques are generalizable to a wide range of other disciplines.

Download or read book Statistical Analysis with Missing Data written by Roderick J. A. Little and published by John Wiley & Sons. This book was released on 2019-03-21 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, comprehensive treatment of a classic text on missing data in statistics The topic of missing data has gained considerable attention in recent decades. This new edition by two acknowledged experts on the subject offers an up-to-date account of practical methodology for handling missing data problems. Blending theory and application, authors Roderick Little and Donald Rubin review historical approaches to the subject and describe simple methods for multivariate analysis with missing values. They then provide a coherent theory for analysis of problems based on likelihoods derived from statistical models for the data and the missing data mechanism, and then they apply the theory to a wide range of important missing data problems. Statistical Analysis with Missing Data, Third Edition starts by introducing readers to the subject and approaches toward solving it. It looks at the patterns and mechanisms that create the missing data, as well as a taxonomy of missing data. It then goes on to examine missing data in experiments, before discussing complete-case and available-case analysis, including weighting methods. The new edition expands its coverage to include recent work on topics such as nonresponse in sample surveys, causal inference, diagnostic methods, and sensitivity analysis, among a host of other topics. An updated “classic” written by renowned authorities on the subject Features over 150 exercises (including many new ones) Covers recent work on important methods like multiple imputation, robust alternatives to weighting, and Bayesian methods Revises previous topics based on past student feedback and class experience Contains an updated and expanded bibliography The authors were awarded The Karl Pearson Prize in 2017 by the International Statistical Institute, for a research contribution that has had profound influence on statistical theory, methodology or applications. Their work "has been no less than defining and transforming." (ISI) Statistical Analysis with Missing Data, Third Edition is an ideal textbook for upper undergraduate and/or beginning graduate level students of the subject. It is also an excellent source of information for applied statisticians and practitioners in government and industry.