The Statistical Analysis of Multivariate Failure Time Data

A Marginal Modeling Approach

Ross L. Prentice, Shanshan Zhao

• Publisher: Chapman and Hall/CRC
• Year: 2019
• eBook ISBN: 9780429529702
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

Chapter 1

Introduction and Characterization of Multivariate Failure Time Distributions

1.1 Failure Time Data and Distributions

1.2 Bivariate Failure Time Data and Distributions

1.3 Bivariate Failure Time Regression Modeling

1.4 Higher Dimensional Failure Time Data and Distributions

1.5 Multivariate Response Data: Modeling and Analysis

1.6 Recurrent Event Characterization and Modeling

1.7 Some Application Settings

1.7.1 Aplastic anemia clinical trial

1.7.2 Australian twin data

1.7.3 Women's Health Initiative hormone therapy trial

1.7.4 Bladder tumor recurrence data

1.7.5 Women’s Health Initiative dietary modification trial

1.1 Failure Time Data and Distributions

This book is concerned with methods for the analysis of time-to-event data, with events generically referred to as failures. Typically there is an underlying study population from which a cohort of individuals is selected and followed forward to observe the times to occurrences of events of interest. Data analysis goals may include estimation of the failure time distribution, and study of dependencies of failure times on study subject characteristics, exposures, or treatments, generically referred to as covariates. The nature and strength of dependencies among the failure times themselves may be also of interest in some settings. The types of mean and covariance models used for the analysis of multivariate quantitative response data more generally can be considered for multivariate failure time data analyses, but there are some important features of multivariate time to response data that need to be acknowledged, as is elaborated below.

Failure time methods have application in many subject matter and research areas, including biomedical, behavioral, physical, and engineering sciences, and various industrial settings. Most of the illustrations in this book will be drawn from the biomedical research area in which the authors are engaged.

A major reason for specialized statistical methods for failure time data analysis is the usual presence of right censoring since some, or perhaps most, study subjects will not have experienced the event or events of interest at the cutoff date for data analysis, and some may have discontinued participation in study follow-up procedures used to ascertain failures prior to such cutoff date. The usual assumption about censoring is that of independence, which requires the set of subjects who are uncensored and con...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• 1 Introduction and Characterization of Multivariate Failure Time Distributions
• 2 Univariate Failure Time Data Analysis Methods
• 3 Nonparametric Estimation of the Bivariate Survivor Function
• 4 Regression Analysis of Bivariate Failure Time Data
• 5 Trivariate Failure Time Data Modeling and Analysis
• 6 Higher Dimensional Failure Time Data Modeling and Estimation
• 7 Recurrent Event Data Analysis Methods
• 8 Additional Important Multivariate Failure Time Topics
• Glossary of Notation
• Appendix A: Technical Materials
• Appendix B: Software and Data
• Bibliography
• Author Index
• Subject Index