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.
Author(s): Ross L. Prentice, Shanshan Zhao
Series: Chapman & Hall/CRC Monographs On Statistics And Applied Probability (Book 1)
Publisher: Chapman & Hall/CRC
Year: 2019
Language: English
Pages: 241
Tags: Multivariate Failure
Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
Table of Contents......Page 8
Preface......Page 12
1.1 Failure Time Data and Distributions......Page 18
1.2 Bivariate Failure Time Data and Distributions......Page 21
1.3 Bivariate Failure Time Regression Modeling......Page 25
1.4 Higher Dimensional Failure Time Data and Distributions......Page 26
1.5 Multivariate Response Data: Modeling and Analysis......Page 28
1.6 Recurrent Event Characterization and Modeling......Page 29
1.7.1 Aplastic anemia clinical trial......Page 30
1.7.2 Australian twin data......Page 31
1.7.3 Women’s Health Initiative hormone therapy trial......Page 32
1.7.4 Bladder tumor recurrence data......Page 34
1.7.5 Women’s Health Initiative dietary modification trial......Page 36
2.2 Nonparametric Survivor Function Estimation......Page 42
2.3 Hazard Ratio Regression Estimation Using the Cox Model......Page 45
2.4 Cox Model Properties and Generalizations......Page 48
2.5 Censored Data Rank Tests......Page 49
2.6 Cohort Sampling and Dependent Censoring......Page 50
2.7 Aplastic Anemia Clinical Trial Application......Page 52
2.8 WHI Postmenopausal Hormone Therapy Application......Page 53
2.9 Asymptotic Distribution Theory......Page 57
2.10 Additional Univariate Failure Time Models and Methods......Page 61
2.11 A Cox-Logistic Model for Continuous, Discrete or Mixed Failure Time Data......Page 62
3.1 Introduction......Page 68
3.2.1 The Volterra estimator......Page 69
3.2.2 The Dabrowska and Prentice–Cai estimators......Page 72
3.2.3 Simulation evaluation......Page 74
3.2.4 Asymptotic distributional results......Page 76
3.3 Maximum Likelihood and Estimating Equation Approaches......Page 77
3.4.1 Cross ratio and concordance function estimators......Page 79
3.4.2 Australian twin study illustration......Page 80
3.5.1 Additional bivariate survivor function estimators......Page 82
3.5.2 Estimation perspectives......Page 84
4.1 Introduction......Page 88
4.2 Independent Censoring and Likelihood-Based Inference......Page 89
4.3.1 Formulation......Page 91
4.3.2 Likelihood-based estimation......Page 92
4.3.3 Unbiased estimating equations......Page 93
4.4 Frailty Models and Estimation Methods......Page 95
4.6.1 Semiparametric regression model possibilities......Page 96
4.6.2 Cox models for marginal single and dual outcome hazard rates......Page 97
4.6.4 Asymptotic distribution theory......Page 99
4.6.5 Simulation evaluation of marginal hazard rate estimators......Page 102
4.7 Breast Cancer Followed by Death in the WHI Low-Fat Diet Intervention Trial......Page 106
4.8 Counting Process Intensity Modeling......Page 108
4.9.2 Independent censoring and death outcomes......Page 109
4.9.3 Marginal hazard rates for competing risk data......Page 110
4.10 Summary......Page 111
5.1 Introduction......Page 116
5.2.1 Dabrowska-type estimator development......Page 117
5.2.2 Volterra estimator......Page 121
5.2.3 Trivariate dependency assessment......Page 122
5.2.4 Simulation evaluation and comparison......Page 123
5.3 Trivariate Regression Analysis via Copulas......Page 126
5.4 Regression on Marginal Single, Double and Triple Failure Hazard Rates......Page 127
5.5 Simulation Evaluation of Hazard Ratio Estimators......Page 130
5.6 Postmenopausal Hormone Therapy in Relation to CVD and Mortality......Page 132
6.1 Introduction......Page 136
6.2.1 Dabrowska-type estimator development......Page 137
6.2.2 Volterra nonparametric survivor function estimator......Page 140
6.2.3 Multivariate dependency assessment......Page 141
6.3 Regression Analysis on Marginal Single Failure Hazard Rates......Page 142
6.4.1 Likelihood specification......Page 146
6.4.2 Estimation using copula models......Page 147
6.5 Marginal Single and Double Failure Hazard Rate Modeling......Page 150
6.6 Counting Process Intensity Modeling and Estimation......Page 153
6.7 Women’s Health Initiative Hormone Therapy Illustration......Page 154
6.8 More on Estimating Equations and Likelihood......Page 157
7.1 Introduction......Page 160
7.2.1 Counting process intensity modeling and estimation......Page 161
7.2.2 Bladder tumor recurrence illustration......Page 163
7.2.3 Intensity modeling with multiple failure types......Page 165
7.3 Marginal Failure Rate Estimation with Recurrent Events......Page 166
7.5 WHI Dietary Modification Trial Illustration......Page 168
7.6 Absolute Failure Rates and Mean Models for Recurrent Events......Page 169
7.7 Perspective on Regression Modeling via Intensities and Marginal Models......Page 170
8.1 Introduction......Page 174
8.2.1 Dependent censorship......Page 175
8.2.2 Confounding control and mediation analysis......Page 181
8.3.2 Case-cohort and two-phase sampling......Page 183
8.3.3 Nested case–control sampling......Page 186
8.3.4 Missing covariate data methods......Page 187
8.4.2 Hazard rate estimation with a validation subsample......Page 188
8.4.3 Hazard rate estimation without a validation subsample......Page 189
8.4.4 Energy intake and physical activity in relation to chronic disease risk......Page 191
8.5 Joint Modeling of Longitudinal Covariates and Failure Rates......Page 194
8.6 Model Checking......Page 197
8.7 Marked Point Processes and Multistate Models......Page 198
8.8 Imprecisely Measured Failure Times......Page 199
Glossary of Notation......Page 204
A.1 Product Integrals and Stieltjes Integration......Page 208
A.2 Generalized Estimating Equations for Mean Parameters......Page 210
A.3 Some Basic Empirical Process Results......Page 211
B.1 Software for Multivariate Failure Time Analysis......Page 214
B.2 Data Access......Page 216
Bibliography......Page 218
Author Index......Page 230
Subject Index......Page 236
