Series:

SpringerBriefs in Statistics

5 total works

Cover of Copula-Based Markov Models for Time Series

This book provides statistical methodologies for time series data, focusing on copula-based Markov chain models for serially correlated time series. It also includes data examples from economics, engineering, finance, sport and other disciplines to illustrate the methods presented. An accessible textbook for students in the fields of economics, management, mathematics, statistics, and related fields wanting to gain insights into the statistical analysis of time series data using copulas, the book also features stand-alone chapters to appeal to researchers.

As the subtitle suggests, the book highlights parametric models based on normal distribution, t-distribution, normal mixture distribution, Poisson distribution, and others. Presenting likelihood-based methods as the main statistical tools for fitting the models, the book details the development of computing techniques to find the maximum likelihood estimator. It also addresses statistical process control, as well as Bayesian and regression methods. Lastly, to help readers analyze their data, it provides computer codes (R codes) for most of the statistical methods.

Cover of Analysis of Doubly Truncated Data

This book introduces readers to statistical methodologies used to analyze doubly truncated data. The first book exclusively dedicated to the topic, it provides likelihood-based methods, Bayesian methods, non-parametric methods, and linear regression methods. These procedures can be used to effectively analyze continuous data, especially survival data arising in biostatistics and economics. Because truncation is a phenomenon that is often encountered in non-experimental studies, the methods presented here can be applied to many branches of science. The book provides R codes for most of the statistical methods, to help readers analyze their data. Given its scope, the book is ideally suited as a textbook for students of statistics, mathematics, econometrics, and other fields.

Cover of Survival Analysis with Correlated Endpoints

This book introduces readers to advanced statistical methods for analyzing survival data involving correlated endpoints. In particular, it describes statistical methods for applying Cox regression to two correlated endpoints by accounting for dependence between the endpoints with the aid of copulas. The practical advantages of employing copula-based models in medical research are explained on the basis of case studies.

In addition, the book focuses on clustered survival data, especially data arising from meta-analysis and multicenter analysis. Consequently, the statistical approaches presented here employ a frailty term for heterogeneity modeling. This brings the joint frailty-copula model, which incorporates a frailty term and a copula, into a statistical model. The book also discusses advanced techniques for dealing with high-dimensional gene expressions and developing personalized dynamic prediction tools under the joint frailty-copula model.

To help readers apply the statistical methods to real-world data, the book provides case studies using the authors' original R software package (freely available in CRAN). The emphasis is on clinical survival data, involving time-to-tumor progression and overall survival, collected on cancer patients. Hence, the book offers an essential reference guide for medical statisticians and provides researchers with advanced, innovative statistical tools. The book also provides a concise introduction to basic multivariate survival models.

Cover of Estimation and Selection in High-Dimensional Genomic Studies
This book provides an overview of the statistical methods used in genome-wide screening of relevant genomic features or genes. Gene screening can facilitate deeper understanding of disease biology at the molecular level, possibly leading to discovery of new molecular targets for developing new treatments and developing diagnostic tests to predict patients' prognosis or response to treatment. The most common approach to such gene screening studies is to apply multiple univariate analysis based on separate statistical tests for individual genes to test the null hypothesis of no association with clinical variables. This book first provides an overview of the state of the art of such multiple testing methodologies for gene screening, including frequentist multiple tests, empirical Bayes, and full-Bayes model-based methods for controlling the family-wise error rate or false discovery rate. Optimal discovery procedures and model-based variants are also discussed. Although great endeavor has been directed toward developing multiple testing methods, there are other, more relevant and effective analyses that should be given much attention in gene screening, including gene ranking, estimation of effect sizes, and classification accuracy based on selected genes. The core contents of this book provide a framework for integrated gene screening analysis based on hierarchical mixture modeling and empirical Bayes. Within this framework effective tools for multiple testing, ranking, estimation of effect size, and classification accuracy are derived. Methods for sample size determination for gene screening studies are also provided. With this content, the book is certain to expand the existing framework of statistical analysis based on multiple testing for gene screening to one based on estimation and selection.

Cover of Analysis of Survival Data with Dependent Censoring

This book introduces readers to copula-based statistical methods for analyzing survival data involving dependent censoring. Primarily focusing on likelihood-based methods performed under copula models, it is the first book solely devoted to the problem of dependent censoring.

The book demonstrates the advantages of the copula-based methods in the context of medical research, especially with regard to cancer patients’ survival data. Needless to say, the statistical methods presented here can also be applied to many other branches of science, especially in reliability, where survival analysis plays an important role.

The book can be used as a textbook for graduate coursework or a short course aimed at (bio-) statisticians. To deepen readers’ understanding of copula-based approaches, the book provides an accessible introduction to basic survival analysis and explains the mathematical foundations of copula-based survival models.