The Statistical Analysis of Multivariate Failure Time Data: A Marginal Modeling Approach

Abstract

This book written by Prentice and Zhao brings advances in the specialized field of failure time data analysis. In the existing literature, an extensive study of statistical methods for univariate failure time analysis has been performed. These methods include Kaplan-Meier (KM) estimator, Cox regression, and censored data rank test, etc. However, to my best knowledge, the effort on multivariate failure time data analysis is insufficient. Multivariate failure time data arise when failure times for individuals in a study cohort have a dependent feature, which exists in a number of situations, including epidemiologic studies and clinical trials, etc. The development of statistical methods for multivariate data deserves more research attention. Even though there are several books tackling the problem, they devote the analysis either for select types of multivariate data or have an emphasis on a specific method. Compared with these works, this book makes a summary of the latest innovative research results both deeply and extensively. Overall, the logic of this book is very clear. Chapter 1 gives an overview of the subsequent chapters. It covers a brief introduction to the models and tools and also provides some good application settings. Readers who are not familiar with the topic may read this chapter to grasp the motivation of the study quickly. Chapter 2 describes some core methods that are used to model univariate failure time data. It serves as a solid foundation for the extension to multivariate data analysis; therefore, readers need to pay much attention to this chapter. Chapters 3 and 4 provide tools for analyzing bivariate failure time data from the nonparametric and regression perspectives, respectively. In Chapters 5 and 6, the aforementioned models and tools are extended to cover the scenario of three or more failure time variates. Chapter 7 further considers the case of recurrent event data. Finally, the book concludes with Chapter 8, which discusses approaches to handling more general assumptions, such as dependent censorship and mismeasured covariate data. As implied by the title, the marginal modeling approach is the most important and unique feature of this book. This approach has been described in detail by Sections 4.6, 5.4, and 6.5. Under this approach, a Cox-type model for the marginal double or triple or multiple failure hazard rates is utilized to explain the effects of time-dependent covariates. Some strengths provided by this approach make it distinct from the three conventional approaches: 1) the frailty approach, 2) the copula approach, and 3) the counting process intensity modeling. For example, the copula approach imposes a strong assumption on the dependencies among failure times and doesn’t allow such dependencies to depend on covariates. In contrast, the marginal approach provides robustness by conducting semiparametric estimates of the dependency. In short, the contributions of this book consist of