Nonparametric Tests for Censored Data

Preface xi

Terms and Notation xv

Chapter 1. Censored and Truncated Data 1

1.1. Right-censored data 2

1.2. Left truncation 12

1.3. Left truncation and right censoring 14

1.4. Nelson–Aalen and Kaplan–Meier estimators 15

1.5 Bibliographic notes 17

Chapter 2. Chi-squared Tests 19

2.1. Chi-squared test for composite hypothesis  19

2.2. Chi-squared test for exponential distributions 31

2.3. Chi-squared tests for shape-scale distribution families 36

2.4. Chi-squared tests for other families 51

2.5. Exercises 59

2.6. Answers 60

Chapter 3. Homogeneity Tests for Independent Populations 63

3.1 Data 64

3.2 Weighted logrank statistics 64

3.3. Logrank test statistics as weighted sums of differences between observed and expected number of failures 66

3.4 Examples of weights 67

3.5. Weighted logrank statistics as modified score statistics 69

3.6. The first two moments of weighted logrank statistics 71

3.7. Asymptotic properties of weighted logrank statistics 73

3.8. Weighted logrank tests 80

3.9. Homogeneity testing when alternatives are crossings of survival functions 85

3.10. Exercises 98

3.11. Answers 102

Chapter 4. Homogeneity Tests for Related Populations 105

4.1. Paired samples 106

4.2. Logrank-type tests for homogeneity of related k > 2 samples 119

4.3. Homogeneity tests for related samples against crossing marginal survival functions alternatives 122

4.4. Exercises 125

4.5 Answers 126

Chapter 5. Goodness-of-fit for Regression Models 127

5.1. Goodness-of-fit for the semi-parametric Cox model 127

5.2. Chi-squared goodness-of-fit tests for parametric AFT models 142

5.3. Chi-squared test for the exponential AFT model 153

5.4. Chi-squared tests for scale-shape AFT models 159

Bibliographic notes 172

5.6. Exercises 173

Answers 174

APPENDICES 177

Appendix A. 179

Appendix B. 191

Appendix C. 211

Bibliography 225

Index 231