The Statistical Analysis of Multivariate Failure Time Data : A Marginal Modeling Approach book cover
1st Edition

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

ISBN 9781482256574
Published May 16, 2019 by Chapman and Hall/CRC
240 Pages

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Book Description

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.

Table of Contents

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


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


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


Independent Censoring and Likelihood-Based Inference

Copula Models and Estimation Methods


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


5. Trivariate Failure Time Data Modeling and Analysis


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


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


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


Dependent Censorship, Confounding and Mediation

Dependent censorship

Confounding control and mediation analysis

Cohort Sampling and Missing Covariates


Case-cohort and two-phase sampling

Nested case–control sampling

Missing covariate data methods

Mismeasured Covariate Data


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

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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