1st Edition
The Statistical Analysis of Multivariate Failure Time Data A Marginal Modeling Approach
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.
1. Introduction and Characterization of Multivariate Failure Time Distributions
Failure Time Data and Distributions
Bivariate Failure Time Data and Distributions
Bivariate Failure Time Regression Modeling
Higher Dimensional Failure Time Data and Distributions
Multivariate Response Data: Modeling and Analysis
Recurrent Event Characterization and Modeling
Some Application Settings
Aplastic anemia clinical trial
Australian twin data
Women’s Health Initiative hormone therapy trials
Bladder tumor recurrence data
Women’s Health Initiative dietary modification trial
2. Univariate Failure Time Data Analysis Methods
Overview
Nonparametric Survivor Function Estimation
Hazard Ratio Regression Estimation Using the Cox Model
Cox Model Properties and Generalizations
Censored Data Rank Tests
Cohort Sampling and Dependent Censoring
Aplastic Anemia Clinical Trial Application
WHI Postmenopausal Hormone Therapy Application
Asymptotic Distribution Theory
Additional Univariate Failure Time Models and Methods
Cox-Logistic Model for Failure Time Data
3. Nonparametric Estimation of the Bivariate Survivor Function
Introduction
Plug-In Nonparametric Estimators of F
The Volterra estimator
The Dabrowska and Prentice–Cai estimators
Simulation evaluation
Asymptotic distributional results
Maximum Likelihood and Estimating Equation Approaches
Nonparametric Assessment of Dependency
Cross ratio and concordance function estimators
Australian twin study illustration
Simulation evaluation
Additional Estimators and Estimation Perspectives
Additional bivariate survivor function estimators
Estimation perspectives
4. Regression Analysis of Bivariate Failure Time Data
Introduction
Independent Censoring and Likelihood-Based Inference
Copula Models and Estimation Methods
Formulation
Likelihood-based estimation
Unbiased estimating equations
Frailty Models and Estimation Methods
Australian Twin Study Illustration
Hazard Rate Regression
Semiparametric regression model possibilities
Cox models for marginal single and dual outcome hazard rates
Dependency measures given covariates
Asymptotic distribution theory
Simulation evaluation of marginal hazard rate estimators
Composite Outcomes in a Low-Fat Diet Trial
Counting Process Intensity Modeling
Marginal Hazard Rate Regression in Context
Likelihood maximization and empirical plug-in estimators
Independent censoring and death outcomes
Marginal hazard rates for competing risk data
Summary
5. Trivariate Failure Time Data Modeling and Analysis
Introduction
Trivariate Survivor Function Estimation
Dabrowska-type Estimator Development
Volterra Estimator
Trivariate Dependency Assessment
Simulation Evaluation and Comparison
Trivariate Regression Analysis via Copulas
Marginal Hazard Rate Regression
Simulation Evaluation of Hazard Ratio Estimators
Hormone Therapy and Disease Occurrence
6. Higher Dimensional Failure Time Data Modeling and Estimation
Introduction
M-dimensional Survivor Function Estimation
Dabrowska-type estimator development
Volterra nonparametric survivor function estimator
Multivariate dependency assessment
Single Failure Hazard Rate Regression
Regression on Marginal Hazard Rates and Dependencies
Likelihood specification
Estimation using copula models
Marginal Single and Double Failure Hazard Rate Modeling
Counting Process Intensity Modeling and Estimation
Women’s Health Initiative Hormone Therapy Illustration
More on Estimating Equations and Likelihood
7. Recurrent Event Data Analysis Methods
Introduction
Intensity Process Modeling on a Single Failure Time Axis
Counting process intensity modeling and estimation
Bladder tumor recurrence illustration
Intensity modeling with multiple failure types
Marginal Failure Rate Estimation with Recurrent Events
Single and Double Failure Rate Models for Recurrent Events
WHI Dietary Modification Trial Illustration
Absolute Failure Rates and Mean Models for Recurrent Events
Intensity Versus Marginal Hazard Rate Modeling
8. Additional Important Multivariate Failure Time Topics
Introduction
Dependent Censorship, Confounding and Mediation
Dependent censorship
Confounding control and mediation analysis
Cohort Sampling and Missing Covariates
Introduction
Case-cohort and two-phase sampling
Nested case–control sampling
Missing covariate data methods
Mismeasured Covariate Data
Background
Hazard rate estimation with a validation subsample
Hazard rate estimation without a validation subsample
Energy intake and physical activity in relation to chronic disease risk
Joint Covariate and Failure Rate Modeling
Model Checking
Marked Point Processes and Multistate Models
Imprecisely Measured Failure Times
Appendix : Technical Materials
A Product Integrals and Steiltjes Integration
A Generalized Estimating Equations for Mean Parameters
A Some Basic Empirical Process Results
Appendix Software and Data
A Software for Multivariate Failure Time Analysis
A Data Access
Biography
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.
"Here, Prentice (Univ. of Washington) and Zhao (National Inst. of Environmental Health Sciences) provide a systematic introduction to novel statistical methodology, using a “marginal modeling approach” relevant to a number of fields where interpretation of survival outcomes and failure over time data is required.The authors explore the entirety of each method covered, progressing from background mathematics to assumptions and caveats, and finally to interpretation. Intended for biostatistical researchers engaged in analysis of complex population data sets as encountered, for example, in randomized clinical trials, this volume may also serve as a reference for quantitative epidemiologists. Readers will need a solid understanding of statistical estimation methods and a reasonable command of calculus and probability theory. Appropriate exercises accompany each chapter, and links to software and sample data are provided (appendix B)."
~K. J. Whitehair, independent scholar, CHOICE, January 2020 Vol. 57 No. 5
Summing Up: Recommended. Graduate students, faculty and practitioners."This book gives thorough coverage and rigorous discussion of statistical methods for the analysis of multivariate failure time data. The structure of the book has been thoughtfully planned and it is carefully and clearly written - it does a nice job of clearly introducing concepts and models, as well as describing nonparametric methods of estimation. For the core theme on the analysis of multiple failure times, it explores different approaches to estimation and inference, and critiques competing methods in terms of robustness and efficiency. Authoritative coverage of additional topics including recurrent event analysis, multistate modeling, dependent censoring, and others, ensures it will serve as an excellent reference for those with interest in life history analysis. Illustrative examples given in the chapters help make the issues and approaches for dealing with them tangible, while the exercises at the end of each chapter give readers an opportunity to gauge their understanding of the material. It will therefore also serve very nicely as a basis for a second graduate course on specialized topics of life history analysis."
~Richard Cook, University of Waterloo"Let me congratulate the authors with this impressive work…This book could be a textbook for an advanced masters or Ph.D level course for a degree in biostatistics and statistics…This book focusses on the case that we want to understand the association between covariate process and a multivariate survival outcome. It includes targeting the univariate conditional hazards as well as the multivariate hazards functions. Instead of targeting intensities that condition on the full observed history, it focusses on histories that exclude the failure time history, so that a change in the Z process represents a change in future multivariate survival experience. The book also reviews copula models, frailty models, and models of intensities of counting processes, beyond their marginal hazard modeling approach…An important strength is the illustrations with real world interesting data from the Women's Health Study. Another important strength is its overview of various competing approaches, making it comprehensive, beyond the presentation of the unique marginal modeling approach developed by the authors. ~Mark van der Laan, University of California, Berkeley
"I expect this book to be highly useful to: (i) researches dealing with developing statistical multivariate survival methods; (ii) teachers of advanced survival methods for graduate classes; and (iii) Biostatistics/statistics PhD students focusing in the area of multivariate survival analysis. I believe that the book would be very useful as a reference and as a textbook. I, personally, would definitely use it for both purposes.. There is a need for a well-organized book focusing mainly on the recent developments in this research area, that are not included in older books...The manuscript is technically correct, very clearly written, and it is a pleasure reading it." (
~Malka Gorfine, Tel Aviv University"This well-written book offers the basics of innovative approach to analyse and interpret correlated failure times data . . . I enjoyed reading this book. I highly recommend this book to statistics researchers, graduate students, engineers, and computing professionals."
~ Ramalingam Shanmugam, Texas State University
