The Statistical Analysis of Multivariate Failure Time Data: A Marginal Modeling Approach
by Ross L. Prentice (Author), Shanshan Zhao (Author)

About the Author
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.

About this book
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.

Brief contents
1 Introduction and Characterization of Multivariate Failure Time Distributions 1
    1.1 Failure Time Data and Distributions 1
    1.2 Bivariate Failure Time Data and Distributions 4
    1.3 Bivariate Failure Time Regression Modeling 8
    1.4 Higher Dimensional Failure Time Data and Distributions 9
    1.5 Multivariate Response Data: Modeling and Analysis 11
    1.6 Recurrent Event Characterization and Modeling 12
    1.7 Some Application Settings 13
        1.7.1 Aplastic anemia clinical trial 13
        1.7.2 Australian twin data 14
        1.7.3 Women’s Health Initiative hormone therapy trial 15
        1.7.4 Bladder tumor recurrence data 17
        1.7.5 Women’s Health Initiative dietary modification trial 19
2 Univariate Failure Time Data Analysis Methods 25
    2.1 Overview 25
    2.2 Nonparametric Survivor Function Estimation 25
    2.3 Hazard Ratio Regression Estimation Using the Cox Model 28
    2.4 Cox Model Properties and Generalizations 31
    2.5 Censored Data Rank Tests 32
    2.6 Cohort Sampling and Dependent Censoring 33
    2.7 Aplastic Anemia Clinical Trial Application 35
    2.8 WHI Postmenopausal Hormone Therapy Application 36
    2.9 Asymptotic Distribution Theory 40
    2.10 Additional Univariate Failure Time Models and Methods 44
    2.11 A Cox-Logistic Model for Continuous, Discrete or Mixed Failure Time Data 45
3 Nonparametric Estimation of the Bivariate Survivor Function 51
    3.1 Introduction 51
    3.2 Plug-In Nonparametric Estimators of F 52
        3.2.1 The Volterra estimator 52
        3.2.2 The Dabrowska and Prentice–Cai estimators 55
        3.2.3 Simulation evaluation 57
        3.2.4 Asymptotic distributional results 59
    3.3 Maximum Likelihood and Estimating Equation Approaches 60
    3.4 Nonparametric Assessment of Dependency 62
        3.4.1 Cross ratio and concordance function estimators 62
        3.4.2 Australian twin study illustration 63
        3.4.3 Simulation evaluation 65
    3.5 Additional Estimators and Estimation Perspectives 65
        3.5.1 Additional bivariate survivor function estimators 65
        3.5.2 Estimation perspectives 67
4 Regression Analysis of Bivariate Failure Time Data 71
    4.1 Introduction 71
    4.2 Independent Censoring and Likelihood-Based Inference 72
    4.3 Copula Models and Estimation Methods 74
        4.3.1 Formulation 74
        4.3.2 Likelihood-based estimation 75
        4.3.3 Unbiased estimating equations 76
    4.4 Frailty Models and Estimation Methods 78
    4.5 Australian Twin Study Illustration 79
    4.6 Regression on Single and Dual Outcome Hazard Rates 79
        4.6.1 Semiparametric regression model possibilities 79
        4.6.2 Cox models for marginal single and dual outcome hazard rates 80
        4.6.3 Dependency measures given covariates 82
        4.6.4 Asymptotic distribution theory 82
        4.6.5 Simulation evaluation of marginal hazard rate estimators 85
    4.7 Breast Cancer Followed by Death in the WHI Low-Fat Diet Intervention Trial 89
    4.8 Counting Process Intensity Modeling 91
    4.9 Marginal Hazard Rate Regression in Context 92
        4.9.1 Likelihood maximization and empirical plug-in estimators 92
        4.9.2 Independent censoring and death outcomes 92
        4.9.3 Marginal hazard rates for competing risk data 93
    4.10 Summary 94
5 Trivariate Failure Time Data Modeling and Analysis 99
    5.1 Introduction 99
    5.2 Nonparametric Estimation of the Trivariate Survivor Function 100
        5.2.1 Dabrowska-type estimator development 100
        5.2.2 Volterra estimator 104
        5.2.3 Trivariate dependency assessment 105
        5.2.4 Simulation evaluation and comparison 106
    5.3 Trivariate Regression Analysis via Copulas 109
    5.4 Regression on Marginal Single, Double and Triple Failure Hazard Rates 110
    5.5 Simulation Evaluation of Hazard Ratio Estimators 113
    5.6 Postmenopausal Hormone Therapy in Relation to CVD and Mortality 115
6 Higher Dimensional Failure Time Data Modeling and Estimation 119
    6.1 Introduction 119
    6.2 Nonparametric Estimation of the m-Dimensional Survivor Function 120
        6.2.1 Dabrowska-type estimator development 120
        6.2.2 Volterra nonparametric survivor function estimator 123
        6.2.3 Multivariate dependency assessment 124
    6.3 Regression Analysis on Marginal Single Failure Hazard Rates 125
    6.4 Regression on Marginal Hazard Rates and Dependencies 129
        6.4.1 Likelihood specification 129
        6.4.2 Estimation using copula models 130
    6.5 Marginal Single and Double Failure Hazard Rate Modeling 133
    6.6 Counting Process Intensity Modeling and Estimation 136
    6.7 Women’s Health Initiative Hormone Therapy Illustration 137
    6.8 More on Estimating Equations and Likelihood 140
7 Recurrent Event Data Analysis Methods 143
    7.1 Introduction 143
    7.2 Intensity Process Modeling on a Single Failure Time Axis 144
        7.2.1 Counting process intensity modeling and estimation 144
        7.2.2 Bladder tumor recurrence illustration 146
        7.2.3 Intensity modeling with multiple failure types 148
    7.3 Marginal Failure Rate Estimation with Recurrent Events 149
    7.4 Single and Double Failure Rate Models for Recurrent Events 151
    7.5 WHI Dietary Modification Trial Illustration 151
    7.6 Absolute Failure Rates and Mean Models for Recurrent Events 152
    7.7 Perspective on Regression Modeling via Intensities and Marginal Models 153
8 Additional Important Multivariate Failure Time Topics 157
    8.1 Introduction 157
    8.2 Dependent Censorship, Confounding and Mediation 158
        8.2.1 Dependent censorship 158
        8.2.2 Confounding control and mediation analysis 164
    8.3 Cohort Sampling and Missing Covariates 166
        8.3.1 Introduction 166
        8.3.2 Case-cohort and two-phase sampling 166
        8.3.3 Nested case–control sampling 169
        8.3.4 Missing covariate data methods 170
    8.4 Mismeasured Covariate Data 171
        8.4.1 Background 171
        8.4.2 Hazard rate estimation with a validation subsample 171
        8.4.3 Hazard rate estimation without a validation subsample 172
        8.4.4 Energy intake and physical activity in relation to chronic disease risk 174
    8.5 Joint Modeling of Longitudinal Covariates and Failure Rates 177
    8.6 Model Checking 180
    8.7 Marked Point Processes and Multistate Models 181
    8.8 Imprecisely Measured Failure Times 182
Glossary of Notation 187
Appendix A: Technical Materials 191
    A.1 Product Integrals and Stieltjes Integration 191
    A.2 Generalized Estimating Equations for Mean Parameters 193
    A.3 Some Basic Empirical Process Results 194
Appendix B: Software and Data 197
    B.1 Software for Multivariate Failure Time Analysis 197
    B.2 Data Access 199
Bibliography 201
Author Index 213
Subject Index 219

Series: Chapman & Hall/CRC Monographs on Statistics and Applied Probability (Book 1)
Pages: 240 pages
Publisher: Chapman and Hall/CRC; 1 edition (May 16, 2019)
Language: English
ISBN-10: 1482256576
ISBN-13: 978-1482256574