Missing covariate data often arise in various settings, including surveys, clinical trials, epidemiological studies, biological studies and environmental studies. Large scale studies often have large fractions of missing data, which can present serious problems to the data analyst. Motivated by real data applications, this dissertation addresses several aspects in modeling and analyzing data with missing covariates. First, we propose Bayesian methods for estimating parameters in generalized linear models (GLM's) with nonignorably missing covariate data. We specify a parametric distribution for the response variable given the covariates (GLM), a parametric distribution for the missing covariates, and a parametric multinomial selection model for the missing data mechanism. Then we characterize general conditions for the propriety of the joint posterior distribution of the parameters and extend two model selection criteria, weighted L measure and Deviance Information Criterion for model comparison in the presence of missing covariates. Second, we develop a novel modeling strategy for analyzing data with repeated binary responses over time as well as with time-dependent missing covariates. We use the generalized linear mixed logistic model for the repeated binary responses and then propose a joint model for time-dependent missing covariates using information from different sources. The Monte Carlo EM algorithm is developed for computing the maximum likelihood estimates. An extended version of the AIC criterion is proposed to identify factors of interest that may disrupt the cyclical pattern of flowering. Third, we develop an efficient Gibbs sampling algorithm to sample from the joint posterior distribution for the generalized linear mixed logistic model. Moreover, we propose a novel Monte Carlo method to compute a Bayesian model comparison criterion, DIC, for any variable subset model using a single Markov Chain Monte Carlo sample from the full model without sampling from the posterior distribution under each subset model. In the end, we provide a brief discussion of future research.

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.

A modern and practical guide to the essential concepts and ideas for analyzing data with missing observations in the field of biostatistics With an emphasis on hands-on applications, Applied Missing Data Analysis in the Health Sciences outlines the various modern statistical methods for the analysis of missing data. The authors acknowledge the limitations of established techniques and provide newly-developed methods with concrete applications in areas such as causal inference methods and the field of diagnostic medicine. Organized by types of data, chapter coverage begins with an overall introduction to the existence and limitations of missing data and continues into traditional techniques for missing data inference, including likelihood-based, weighted GEE, multiple imputation, and Bayesian methods. The book’s subsequently covers cross-sectional, longitudinal, hierarchical, survival data. In addition, Applied Missing Data Analysis in the Health Sciences features: Multiple data sets that can be replicated using the SAS®, Stata®, R, and WinBUGS software packages Numerous examples of case studies in the field of biostatistics to illustrate real-world scenarios and demonstrate applications of discussed methodologies Detailed appendices to guide readers through the use of the presented data in various software environments Applied Missing Data Analysis in the Health Sciences is an excellent textbook for upper-undergraduate and graduate-level biostatistics courses as well as an ideal resource for health science researchers and applied statisticians.

Due to recent theoretical findings and advances in statistical computing, there has been a rapid development of techniques and applications in the area of missing data analysis. Statistical Methods for Handling Incomplete Data covers the most up-to-date statistical theories and computational methods for analyzing incomplete data. Features Uses the mean score equation as a building block for developing the theory for missing data analysis Provides comprehensive coverage of computational techniques for missing data analysis Presents a rigorous treatment of imputation techniques, including multiple imputation fractional imputation Explores the most recent advances of the propensity score method and estimation techniques for nonignorable missing data Describes a survey sampling application Updated with a new chapter on Data Integration Now includes a chapter on Advanced Topics, including kernel ridge regression imputation and neural network model imputation The book is primarily aimed at researchers and graduate students from statistics, and could be used as a reference by applied researchers with a good quantitative background. It includes many real data examples and simulated examples to help readers understand the methodologies.

Multiple Imputation of Missing Data in Practice: Basic Theory and Analysis Strategies provides a comprehensive introduction to the multiple imputation approach to missing data problems that are often encountered in data analysis. Over the past 40 years or so, multiple imputation has gone through rapid development in both theories and applications. It is nowadays the most versatile, popular, and effective missing-data strategy that is used by researchers and practitioners across different fields. There is a strong need to better understand and learn about multiple imputation in the research and practical community. Accessible to a broad audience, this book explains statistical concepts of missing data problems and the associated terminology. It focuses on how to address missing data problems using multiple imputation. It describes the basic theory behind multiple imputation and many commonly-used models and methods. These ideas are illustrated by examples from a wide variety of missing data problems. Real data from studies with different designs and features (e.g., cross-sectional data, longitudinal data, complex surveys, survival data, studies subject to measurement error, etc.) are used to demonstrate the methods. In order for readers not only to know how to use the methods, but understand why multiple imputation works and how to choose appropriate methods, simulation studies are used to assess the performance of the multiple imputation methods. Example datasets and sample programming code are either included in the book or available at a github site (https://github.com/he-zhang-hsu/multiple_imputation_book). Key Features Provides an overview of statistical concepts that are useful for better understanding missing data problems and multiple imputation analysis Provides a detailed discussion on multiple imputation models and methods targeted to different types of missing data problems (e.g., univariate and multivariate missing data problems, missing data in survival analysis, longitudinal data, complex surveys, etc.) Explores measurement error problems with multiple imputation Discusses analysis strategies for multiple imputation diagnostics Discusses data production issues when the goal of multiple imputation is to release datasets for public use, as done by organizations that process and manage large-scale surveys with nonresponse problems For some examples, illustrative datasets and sample programming code from popular statistical packages (e.g., SAS, R, WinBUGS) are included in the book. For others, they are available at a github site (https://github.com/he-zhang-hsu/multiple_imputation_book)