The statistical analysis of multivariate failure time data: a marginal modeling approach

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

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

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.

https://www.crcpress.com/The-Statistical-Analysis-of-Multivariate-Failure-Time-Data-A-Marginal-Modeling/Prentice-Zhao/p/book/9781482256574