Analysis of Survival Data with Dependent Censoring

Copula-Based Approaches

verfasst von: Prof. Takeshi Emura, Yi-Hau Chen

Verlag: Springer Singapore

Buchreihe : SpringerBriefs in Statistics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Setting the Scene

Abstract

This first chapter presents the purpose of the book. We first illustrate the issues of dependent censoring arising from medical research. We then explain several benefits of investigating dependent censoring. We finally illustrate how copula-based methods have been grown through the literature of survival analysis.

Takeshi Emura, Yi-Hau Chen

Chapter 2. Introduction to Survival Analysis

Abstract

This chapter provides a concise introduction to survival analysis. We review the essential tools in survival analysis, such as the survival function, Kaplan–Meier estimator, hazard function, log-rank test, Cox regression, and likelihood-based inference.

Takeshi Emura, Yi-Hau Chen

Chapter 3. Copula Models for Dependent Censoring

Abstract

This chapter provides mathematical infrastructures for copula models, focusing on applications to survival analysis involving dependent censoring. After reviewing the concept of copulas, we introduce measures of dependence, including Kendall’s tau and the cross-ratio function. We also introduce the idea of residual dependence that explains how dependence between event times arises and how it can be modeled by copulas. Finally, we apply copulas for modeling the effect of dependent censoring and analyze the bias of the Cox regression analysis owing to dependent censoring.

Takeshi Emura, Yi-Hau Chen

Chapter 4. Analysis of Survival Data Under an Assumed Copula

Abstract

This chapter introduces statistical methods for analyzing survival data subject to dependent censoring. We review the copula-graphic estimator, parametric likelihood methods, and semi-parametric likelihood methods developed under a variety of copula models. All these approaches employ an assumed copula, a copula function that is completely specified including its parameter value to avoid the non-identifiability.

Takeshi Emura, Yi-Hau Chen

Chapter 5. Gene Selection and Survival Prediction Under Dependent Censoring

Abstract

To select genes that are predictive of survival, univariate selection based on the Cox model has been routinely employed in biomedical research. However, this conventional approach relies on the independent censoring assumption, which is often an unrealistic assumption in many biomedical applications. We introduce an alternative approach to selecting genes by utilizing copulas to account for the effect of dependent censoring. We also introduce a method to construct a predictor based on the selected genes to predict patient survival. We use the non-small-cell lung cancer data to demonstrate the copula-based procedure for selecting genes, developing a predictor, and validating the predictor. We provide detailed instructions to implement the proposed statistical methods and to reproduce the real data analyses through the compound.Cox R package.

Takeshi Emura, Yi-Hau Chen

Chapter 6. Future Developments

Abstract

This final chapter introduces two open problems for future research. This might help find research topics for students and researchers.

Takeshi Emura, Yi-Hau Chen

Backmatter

Titel: Analysis of Survival Data with Dependent Censoring
verfasst von: Prof. Takeshi Emura
Yi-Hau Chen
Verlag: Springer Singapore
Electronic ISBN: 978-981-10-7164-5
Print ISBN: 978-981-10-7163-8
DOI: https://doi.org/10.1007/978-981-10-7164-5