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E-raamat: Statistical Analysis of Multivariate Failure Time Data: A Marginal Modeling Approach

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Statistical Analysis of Multivariate Failure Time Data: A Marginal Modeling ApproachSuurem pilt
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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 Womens 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.

Arvustused

"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. 5Summing Up: Recommended. Graduate students, faculty and practitioners.

Preface xi
1 Introduction and Characterization of Multivariate Failure Time Distributions 1(24)
1.1 Failure Time Data and Distributions
1(3)
1.2 Bivariate Failure Time Data and Distributions
4(4)
1.3 Bivariate Failure Time Regression Modeling
8(1)
1.4 Higher Dimensional Failure Time Data and Distributions
9(2)
1.5 Multivariate Response Data: Modeling and Analysis
11(1)
1.6 Recurrent Event Characterization and Modeling
12(1)
1.7 Some Application Settings
13(12)
1.7.1 Aplastic anemia clinical trial
13(1)
1.7.2 Australian twin data
14(1)
1.7.3 Women's Health Initiative hormone therapy trial
15(2)
1.7.4 Bladder tumor recurrence data
17(2)
1.7.5 Women's Health Initiative dietary modification trial
19(6)
2 Univariate Failure Time Data Analysis Methods 25(26)
2.1 Overview
25(1)
2.2 Nonparametric Survivor Function Estimation
25(3)
2.3 Hazard Ratio Regression Estimation Using the Cox Model
28(3)
2.4 Cox Model Properties and Generalizations
31(1)
2.5 Censored Data Rank Tests
32(1)
2.6 Cohort Sampling and Dependent Censoring
33(2)
2.7 Aplastic Anemia Clinical Trial Application
35(1)
2.8 WHI Postmenopausal Hormone Therapy Application
36(4)
2.9 Asymptotic Distribution Theory
40(4)
2.10 Additional Univariate Failure Time Models and Methods
44(1)
2.11 A Cox-Logistic Model for Continuous, Discrete or Mixed Failure Time Data
45(6)
3 Nonparametric Estimation of the Bivariate Survivor Function 51(20)
3.1 Introduction
51(1)
3.2 Plug-In Nonparametric Estimators of F
52(8)
3.2.1 The Volterra estimator
52(3)
3.2.2 The Dabrowska and Prentice-Cai estimators
55(2)
3.2.3 Simulation evaluation
57(2)
3.2.4 Asymptotic distributional results
59(1)
3.3 Maximum Likelihood and Estimating Equation Approaches
60(2)
3.4 Nonparametric Assessment of Dependency
62(3)
3.4.1 Cross ratio and concordance function estimators
62(1)
3.4.2 Australian twin study illustration
63(2)
3.4.3 Simulation evaluation
65(1)
3.5 Additional Estimators and Estimation Perspectives
65(6)
3.5.1 Additional bivariate survivor function estimators
65(2)
3.5.2 Estimation perspectives
67(4)
4 Regression Analysis of Bivariate Failure Time Data 71(28)
4.1 Introduction
71(1)
4.2 Independent Censoring and Likelihood-Based Inference
72(2)
4.3 Copula Models and Estimation Methods
74(4)
4.3.1 Formulation
74(1)
4.3.2 Likelihood-based estimation
75(1)
4.3.3 Unbiased estimating equations
76(2)
4.4 Frailty Models and Estimation Methods
78(1)
4.5 Australian Twin Study Illustration
79(1)
4.6 Regression on Single and Dual Outcome Hazard Rates
79(10)
4.6.1 Semiparametric regression model possibilities
79(1)
4.6.2 Cox models for marginal single and dual outcome hazard rates
80(2)
4.6.3 Dependency measures given covariates
82(1)
4.6.4 Asymptotic distribution theory
82(3)
4.6.5 Simulation evaluation of marginal hazard rate estimators
85(4)
4.7 Breast Cancer Followed by Death in the WHI Low-Fat Diet Intervention Trial
89(2)
4.8 Counting Process Intensity Modeling
91(1)
4.9 Marginal Hazard Rate Regression in Context
92(2)
4.9.1 Likelihood maximization and empirical plug-in estimators
92(1)
4.9.2 Independent censoring and death outcomes
92(1)
4.9.3 Marginal hazard rates for competing risk data
93(1)
4.10 Summary
94(5)
5 Trivariate Failure Time Data Modeling and Analysis 99(20)
5.1 Introduction
99(1)
5.2 Nonparametric Estimation of the Trivariate Survivor Function
100(9)
5.2.1 Dabrowska-type estimator development
100(4)
5.2.2 Volterra estimator
104(1)
5.2.3 Trivariate dependency assessment
105(1)
5.2.4 Simulation evaluation and comparison
106(3)
5.3 Trivariate Regression Analysis via Copulas
109(1)
5.4 Regression on Marginal Single, Double and Triple Failure Hazard Rates
110(3)
5.5 Simulation Evaluation of Hazard Ratio Estimators
113(2)
5.6 Postmenopausal Hormone Therapy in Relation to CVD and Mortality
115(4)
6 Higher Dimensional Failure Time Data Modeling and Estimation 119(24)
6.1 Introduction
119(1)
6.2 Nonparametric Estimation of the m-Dimensional Survivor Function
120(5)
6.2.1 Dabrowska-type estimator development
120(3)
6.2.2 Volterra nonparametric survivor function estimator
123(1)
6.2.3 Multivariate dependency assessment
124(1)
6.3 Regression Analysis on Marginal Single Failure Hazard Rates
125(4)
6.4 Regression on Marginal Hazard Rates and Dependencies
129(4)
6.4.1 Likelihood specification
129(1)
6.4.2 Estimation using copula models
130(3)
6.5 Marginal Single and Double Failure Hazard Rate Modeling
133(3)
6.6 Counting Process Intensity Modeling and Estimation
136(1)
6.7 Women's Health Initiative Hormone Therapy Illustration
137(3)
6.8 More on Estimating Equations and Likelihood
140(3)
7 Recurrent Event Data Analysis Methods 143(14)
7.1 Introduction
143(1)
7.2 Intensity Process Modeling on a Single Failure Time Axis
144(5)
7.2.1 Counting process intensity modeling and estimation
144(2)
7.2.2 Bladder tumor recurrence illustration
146(2)
7.2.3 Intensity modeling with multiple failure types
148(1)
7.3 Marginal Failure Rate Estimation with Recurrent Events
149(2)
7.4 Single and Double Failure Rate Models for Recurrent Events
151(1)
7.5 WHI Dietary Modification Trial Illustration
151(1)
7.6 Absolute Failure Rates and Mean Models for Recurrent Events
152(1)
7.7 Perspective on Regression Modeling via Intensities and Marginal Models
153(4)
8 Additional Important Multivariate Failure Time Topics 157(30)
8.1 Introduction
157(1)
8.2 Dependent Censorship, Confounding and Mediation
158(8)
8.2.1 Dependent censorship
158(6)
8.2.2 Confounding control and mediation analysis
164(2)
8.3 Cohort Sampling and Missing Covariates
166(5)
8.3.1 Introduction
166(1)
8.3.2 Case-cohort and two-phase sampling
166(3)
8.3.3 Nested case-control sampling
169(1)
8.3.4 Missing covariate data methods
170(1)
8.4 Mismeasured Covariate Data
171(6)
8.4.1 Background
171(1)
8.4.2 Hazard rate estimation with a validation subsample
171(1)
8.4.3 Hazard rate estimation without a validation subsample
172(2)
8.4.4 Energy intake and physical activity in relation to chronic disease risk
174(3)
8.5 Joint Modeling of Longitudinal Covariates and Failure Rates
177(3)
8.6 Model Checking
180(1)
8.7 Marked Point Processes and Multistate Models
181(1)
8.8 Imprecisely Measured Failure Times
182(5)
Glossary of Notation 187(4)
Appendix A: Technical Materials 191(6)
A.1 Product Integrals and Stieltjes Integration
191(2)
A.2 Generalized Estimating Equations for Mean Parameters
193(1)
A.3 Some Basic Empirical Process Results
194(3)
Appendix B: Software and Data 197(4)
B.1 Software for Multivariate Failure Time Analysis
197(2)
B.2 Data Access
199(2)
Bibliography 201(12)
Author Index 213(6)
Subject Index 219
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.
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