Takeshi Emura

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.

This publication addresses copula approaches to competing risks models for dependent latent failure times. It will establish the fundamentals on dependent competing risks models, as well as a range of recent developments to identifiability and estimation using copulas. Readers will learn from the presentation of theory, in relation to its applications in different subject areas in economics, engineering, and medicine. The comprehensive knowledge provided in this book gives readers an overview of existing models for dependent competing risks, which are not found in other books. The book covers basic statistical ideas, such as “parametric latent failure time models”, theoretical issues, such as “identifiability of the competing risks model”, and model comparisons, such as comparative studies for “different copulas and different models for hazard functions”. Aside from the introductory materials, the authors cover new and recently developed methodologies. The new solutions address the identifiability problems in competing risks models that rely on copula modelling. Copula models and other competing risks models are presented in unified theoretical framework and illustrated with data from various disciplines (such as economics, engineering, and medicine). The book also includes applications with real data and the code (written by R and/or Stata) will be made available for easy practice purposes. A selection of exercises and their solutions will be available online. This book serves as a good reading for senior undergraduates and postgraduate students studying in such courses as “Multivariate Survival Analysis”, “Survival Data Analysis” or “Advanced Econometrics”. This book would also serve as a useful reference for empirical researchers in a wide range of disciplines.

This publication addresses copula approaches to competing risks models for dependent latent failure times. It will establish the fundamentals on dependent competing risks models, as well as a range of recent developments to identifiability and estimation using copulas. Readers will learn from the presentation of theory, in relation to its applications in different subject areas in economics, engineering, and medicine. The comprehensive knowledge provided in this book gives readers an overview of existing models for dependent competing risks, which are not found in other books. The book covers basic statistical ideas, such as “parametric latent failure time models”, theoretical issues, such as “identifiability of the competing risks model”, and model comparisons, such as comparative studies for “different copulas and different models for hazard functions”. Aside from the introductory materials, the authors cover new and recently developed methodologies. The new solutions address the identifiability problems in competing risks models that rely on copula modelling. Copula models and other competing risks models are presented in unified theoretical framework and illustrated with data from various disciplines (such as economics, engineering, and medicine). The book also includes applications with real data and the code (written by R and/or Stata) will be made available for easy practice purposes. A selection of exercises and their solutions will be available online. This book serves as a good reading for senior undergraduates and postgraduate students studying in such courses as “Multivariate Survival Analysis”, “Survival Data Analysis” or “Advanced Econometrics”. This book would also serve as a useful reference for empirical researchers in a wide range of disciplines.

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.

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.

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.