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A scientific and educational journal not only for professional statisticians but also for economists, business executives, research directors, government officials, university professors, and others who are seriously interested in the application of statistical methods to practical problems, in the development of more useful methods, and in the improvement of basic statistical data.
Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.
This dissertation focuses on developing statistical methods for semiparametric inference and its applications. Semiparametric theory provides statistical tools that are flexible and robust to model misspecification. Utilizing the theory, this work proposes robust estimation approaches that are applicable to several scenarios with mild conditions, and establishes their asymptotic properties for inference. Chapter 1 provides a brief review of the literature related to this work. It first introduces the concept of semiparametric models and the efficiency bound. It further discusses two nonparametric techniques employed in the following chapters, kernel regression and B-spline approximation. The chapter then addresses the concept of dataset shift. In Chapter 2, novel estimators of causal effects for categorical and continuous treatments are proposed by using an optimal covariate balancing strategy for inverse probability weighting. The resulting estimators are shown to be consistent for causal contrasts and asymptotically normal, when either the model explaining the treatment assignment is correctly specified, or the correct set of bases for the outcome models has been chosen and the assignment model is sufficiently rich. Asymptotic results are complemented with simulations illustrating the finite sample properties. A data analysis suggests a nonlinear effect of BMI on self-reported health decline among the elderly. In Chapter 3, we consider a semiparametric generalized linear model and study estimation of both marginal mean effects and marginal quantile effects in this model. We propose an approximate maximum likelihood estimator and rigorously establish the consistency, the asymptotic normality, and the semiparametric efficiency of our method in both the marginal mean effect and the marginal quantile effect estimation. Simulation studies are conducted to illustrate the finite sample performance, and we apply the new tool to analyze non-labor income data and discover a new interesting predictor. In Chapter 4, we propose a procedure to select the best training subsample for a classification model. Identifying patient's disease status from electronic health records (EHR) is a frequently encountered task in EHR related research. However, assessing patient's phenotype is costly and labor intensive, hence a proper selection of EHR as a training set is desired. We propose a procedure to tailor the training subsample for a classification model minimizing its mean squared error (MSE). We provide theoretical justification on its optimality in terms of MSE. The performance gain from our method is illustrated through simulation and a real data example, and is found often satisfactory under criteria beyond mean squared error. In Chapter 5, we study label shift assumption and propose robust estimators for quantities of interest. In studies ranging from clinical medicine to policy research, the quantity of interest is often sought for a population from which only partial data is available, based on complete data from a related but different population. In this work, we consider this setting under the so-called label shift assumption. We propose an estimation procedure that only needs standard nonparametric techniques to approximate a conditional expectation, while by no means needs estimates for other model components. We develop the large sample theory for the proposed estimator, and examine its finite-sample performance through simulation studies, as well as an application to the MIMIC-III database.
A comprehensive overview of environmetric research and its applications... Environmetrics covers the development and application of quantitative methods in the environmental sciences. It provides essential tools for understanding, predicting, and controlling the impacts of agents, both man-made and natural, which affect the environment. Basic and applied research in this area covers a broad range of topics. Primary among these are the quantitative sciences, such as statistics, probability and applied mathematics, chemometrics, and econometrics. Applications are also important, for example in, ecology and environmental biology, public health, atmospheric science, geology, engineering, risk management, and regulatory/governmental policy amongst others. * Divided into 12 sections, the Encyclopedia brings together over 600 detailed articles which have been carefully selected and reviewed through the collaborative efforts of the Editors-in-Chief and the appropriate Section Editor * Presented in alphabetical order all the articles will include an explanatory introduction, extensive cross-referencing and an up-to-date bibliography providing literature references for further reading. Presenting state of the art information in a readable, highly accessible style, the scope and coverage provided by the Encyclopedia of Environmetrics will ensure its place as the landmark reference for the many scientists, educators, and decision-makers working across this multidisciplinary field. An essential reference tool for university libraries, research laboratories, government institutions and consultancies concerned with the environmental sciences, the Encyclopedia of Environmetrics brings together for the first time, comprehensive coverage of the full range of topics, techniques and applications covered by this multidisciplinary field. There is currently no central reference source which addresses the needs of this multidisciplinary community. This new Encyclopedia will fill this gap by providing a comprehensive source of relevant fundamental concepts in environmetric research, development and applications for statisticians, mathematicians, economists, environmentalists, ecologist, government officials and policy makers.
The Statistical Analysis of Multivariate Failure Time Data: A Marginal Modeling Approach provides an innovative look at methods for the analysis of correlated failure times. The focus is on the use of marginal single and marginal double failure hazard rate estimators for the extraction of regression information. For example, in a context of randomized trial or cohort studies, the results go beyond that obtained by analyzing each failure time outcome in a univariate fashion. The book is addressed to researchers, practitioners, and graduate students, and can be used as a reference or as a graduate course text. Much of the literature on the analysis of censored correlated failure time data uses frailty or copula models to allow for residual dependencies among failure times, given covariates. In contrast, this book provides a detailed account of recently developed methods for the simultaneous estimation of marginal single and dual outcome hazard rate regression parameters, with emphasis on multiplicative (Cox) models. Illustrations are provided of the utility of these methods using Women’s Health Initiative randomized controlled trial data of menopausal hormones and of a low-fat dietary pattern intervention. As byproducts, these methods provide flexible semiparametric estimators of pairwise bivariate survivor functions at specified covariate histories, as well as semiparametric estimators of cross ratio and concordance functions given covariates. The presentation also describes how these innovative methods may extend to handle issues of dependent censorship, missing and mismeasured covariates, and joint modeling of failure times and covariates, setting the stage for additional theoretical and applied developments. This book extends and continues the style of the classic Statistical Analysis of Failure Time Data by Kalbfleisch and Prentice. Ross L. Prentice is Professor of Biostatistics at the Fred Hutchinson Cancer Research Center and University of Washington in Seattle, Washington. He is the recipient of COPSS Presidents and Fisher awards, the AACR Epidemiology/Prevention and Team Science awards, and is a member of the National Academy of Medicine. Shanshan Zhao is a Principal Investigator at the National Institute of Environmental Health Sciences in Research Triangle Park, North Carolina.