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Ⅰ．Introduction 1

Ⅰ.1 General Introduction to the Book 1

Ⅰ.2 Brief Survey of the Development of the Subject 6

Ⅰ.3 Presentation of Practical Examples 10

Ⅱ．The Mathematical Background 45

Ⅱ.1 An Informal Introduction to the Basic Concepts 48

Ⅱ.2 Preliminaries:Processes,Filtrations,and Stopping Times 59

Ⅱ.3 Martingale Theory 64

Ⅱ.4 Counting Processes 72

Ⅱ.5 Limit Theory 82

Ⅱ.6 Product-Integration and Markov Processes 88

Ⅱ.7 Likelihoods and Partial Likelihoods for Counting Processes 95

Ⅱ.8 The Functional Delta-Method 109

Ⅱ.9 Bibliographic Remarks 115

Ⅲ．Model Specification and Censoring 121

Ⅲ.1 Examples of Counting Process models for Complete Life History Data.The Multiplicative Intensity Model 122

Ⅲ.2 Right-Censoring 135

Ⅲ.3 Left-Truncation 152

Ⅲ.4 General Censorship,Filtering,and Truncation 161

Ⅲ.5 Partial Model Specification.Time-Dependent Covariates 168

Ⅲ.6 Bibliographic Remarks 172

Ⅳ．Nonparametric Estimation 176

Ⅳ.1 The Nelson-Aalen estimator 177

Ⅳ.2 Smoothing the Nelson-Aalen Estimator 229

Ⅳ.3 The Kaplan-Meier Estimator 255

Ⅳ.4 The Product-Limit Estimator for the Transition Matrix of a Nonhomogeneous Markov Process 287

Ⅳ.5 Bibliographic Remarks 321

Ⅴ．Nonparametric Hypothesis Testing 332

Ⅴ.1 One-Sample Tests 333

Ⅴ.2 k-Sample Tests 345

Ⅴ.3 Other Linear Nonparametric Tests 379

Ⅴ.4 Using the Complete Test Statistic Process 390

Ⅴ.5 Bibliographic Remarks 397

Ⅵ．Parametric Models 401

Ⅵ.1 Maximum Likelihood Estimation 402

Ⅵ.2 M-Estimators 433

Ⅵ.3 Model Checking 444

Ⅵ.4 Bibliographic Remarks 471

Ⅶ．Regression Models 476

Ⅶ.1 Introduction.Regression Model Formulation 476

Ⅶ.2 Semiparametric Multiplicative Hazard Models 481

Ⅶ.3 Goodness-of-Fit Methods for the Semiparametric Multiplicative Hazard Model 539

Ⅶ.4 Nonparametric Additive Hazard Models 562

Ⅶ.5 Other Non-and Semi-parametric Regression Models 578

Ⅶ.6 Parametric Regression Models 583

Ⅶ.7 Bibliographic Remarks 588

Ⅷ．Asymptotic Efficiency 592

Ⅷ.1 Contiguity andLocal Asymptotic Normality 594

Ⅷ.2 Local Asymptotic Normality in Counting Process Models 607

Ⅷ.3 Infinite-dimensional Parameter Spaces:the General Theory 627

Ⅷ.4 Semiparametric Counting Process Models 635

Ⅷ.5 Bibliographic Remarks 656

Ⅸ．Frailty Models 660

Ⅸ.1 Introduction 660

Ⅸ.2 Model Construction 662

Ⅸ.3 Likelihoods and Intensities 664

Ⅸ.4 Parametric and Nonparametric Maximum Likelihood Estimation with the EM-Algorithm 667

Ⅸ.5 Bibliographic Remarks 673

Ⅹ．Multivariate Time Scales 675

Ⅹ.1 Examples of Several Time Scales 676

Ⅹ.2 Sequential Analysis of Censored Survival Data with Staggered Entry 683

Ⅹ.3 Nonparametric Estimation of the Multivariate Survival Function 688

Ⅹ.4 Bibliographic Remarks 706

Appendix The Melanoma Survival Data and Standard Mortality Tables for the Danish Population 1971-75 709

References 715

Author Index 747

Subject Index 755