In many areas of science a basic task is to assess the influence of several factors on a quantity of interest. If this quantity is binary logistic, regression models provide a powerful tool for this purpose. This monograph presents an account of the use of logistic regression in the case where missing values in the variables prevent the use of standard techniques. Such situations occur frequently across a wide range of statistical applications. The emphasis of this book is on methods related to the classical maximum likelihood principle. The author reviews the essentials of logistic regression and discusses the variety of mechanisms which might cause missing values while the rest of the book covers the methods which may be used to deal with missing values and their effectiveness. Researchers across a range of disciplines and graduate students in statistics and biostatistics will find this a readable account of this.

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.

This is a second edition to the original published by Springer in 2006. The comprehensive volume takes a textbook approach systematically developing the field by starting from linear models and then moving up to generalized linear and non-linear mixed effects models. Since the first edition was published the field has grown considerably in terms of maturity and technicality. The second edition of the book therefore considerably expands with the addition of three new chapters relating to Bayesian models, Generalized linear and nonlinear mixed effects models, and Principles of simulation. In addition, many of the other chapters have been expanded and updated.

Causal effect estimation with observational data is subject to bias due to confounding. Although potential confounders could be adjusted for by fitting a multiple regression model, a more effective way to control for confounding is to use propensity score methods. Propensity scores are most commonly estimated from logistic regression with a binary exposure; generalized propensity scores could be estimated instead using linear regression if the exposure is continuous. One unresolved issue in propensity score estimation is handling of missing values in covariates. As covariates are only used for propensity score estimation but not for later outcome analysis, missing values in covariates may need to be handled differently from missing values in outcome analysis. Several approaches have been proposed for handling covariate missingness, including multiple imputation (MI), multiple imputation with missingness pattern (MIMP) and treatment mean imputation. There are other potentially useful approaches that have not been evaluated, including single imputation, single conditional mean imputation and Generalized Boosted Modeling (GBM), which is a nonparametric approach of estimating propensity scores and missing values are automatically accounted for in the estimation.To evaluate the performance of single imputation, single conditional mean imputation and GBM in comparison to the previously proposed approaches including treatment mean imputation, MI and MIMP, a simulation study is conducted with a binary exposure. Results suggest that when all confounders are included for propensity score estimation, single imputation, single conditional mean imputation, MI and MIMP perform almost equally well and better than treatment mean imputation and GBM. To examine whether the finding could be extended to a continuous exposure setting, another simulation study is conducted. Results suggest that single imputation, single conditional imputation, MI, MIMP and GBM with single conditional mean imputation have equally good and better performance than treatment mean imputation and GBM with incomplete data under scenario A (linearity and additivity). None of the approaches perform well under scenario G (nonlinearity and nonadditivity). These approaches are further demonstrated and compared through an empirical analysis with the Adolescent Alcohol Prevention Trial (AAPT). A similar pattern of results is observed as in the simulation study. It is recommended to impute missing covariates using different approaches and similar estimates help provide more confidence in the estimates.

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.

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.