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Table of Contents
Intro; Preface; About this Book; Use as a Textbook; References; Acknowledgements; Contents; Abbreviations; Notations; 1 Setting the Scene; Abstract; 1.1 Survival Analysis and Censoring; 1.2 Informative Dropout; 1.3 Benefits of Investigating Dependent Censoring; 1.3.1 Examining the Influence of Dependent Censoring; 1.3.2 Improving Prediction by Using Dependent Censoring; 1.4 Copulas and Survival Analysis: A Brief History; References; 2 Introduction to Survival Analysis; Abstract; 2.1 Survival Time; 2.2 Kaplan-Meier Estimator and Survival Function; 2.3 Hazard Function
2.4 Log-Rank Test for Two-Sample Comparison2.5 Cox Regression; 2.6 R Survival Package; 2.7 Likelihood-Based Inference; 2.8 Technical Notes; 2.9 Exercises; References; 3 Copula Models for Dependent Censoring; Abstract; 3.1 Introduction; 3.2 Bivariate Copula; 3.3 Dependence Measures; 3.4 Residual Dependence; 3.5 Biased Estimation of Cox Regression Due to Dependent Censoring; 3.6 Exercises; References; 4 Analysis of Survival Data Under an Assumed Copula; Abstract; 4.1 Introduction; 4.2 The Copula-Graphic (CG) Estimator; 4.3 Model and Likelihood; 4.4 Parametric Models; 4.4.1 The Burr Model
4.4.2 The Weibull Model4.4.3 The Pareto Model; 4.4.4 The Burr III Model; 4.4.5 The Piecewise Exponential Model; 4.5 Semi-parametric Models; 4.5.1 The Transformation Model; 4.5.2 The Spline Model; References; 5 Gene Selection and Survival Prediction Under Dependent Censoring; Abstract; 5.1 Introduction; 5.2 Univariate Selection; 5.3 Copula-Based Univariate Cox Regression; 5.4 Copula-Based Univariate Selection; 5.5 Choosing the Copula Parameter by the C-Index; 5.6 Lung Cancer Data Analysis; 5.6.1 Gene Selection and Prediction; 5.6.2 Assessing Prediction Performance; 5.7 Discussions; References
6 Future DevelopmentsAbstract; 6.1 Log-Rank Test Under Dependent Censoring; 6.2 Dependent Left-Truncation; References; Appendix A: Spline Basis Functions; Appendix B: R Codes for the Lung Cancer Data Analysis; Index
2.4 Log-Rank Test for Two-Sample Comparison2.5 Cox Regression; 2.6 R Survival Package; 2.7 Likelihood-Based Inference; 2.8 Technical Notes; 2.9 Exercises; References; 3 Copula Models for Dependent Censoring; Abstract; 3.1 Introduction; 3.2 Bivariate Copula; 3.3 Dependence Measures; 3.4 Residual Dependence; 3.5 Biased Estimation of Cox Regression Due to Dependent Censoring; 3.6 Exercises; References; 4 Analysis of Survival Data Under an Assumed Copula; Abstract; 4.1 Introduction; 4.2 The Copula-Graphic (CG) Estimator; 4.3 Model and Likelihood; 4.4 Parametric Models; 4.4.1 The Burr Model
4.4.2 The Weibull Model4.4.3 The Pareto Model; 4.4.4 The Burr III Model; 4.4.5 The Piecewise Exponential Model; 4.5 Semi-parametric Models; 4.5.1 The Transformation Model; 4.5.2 The Spline Model; References; 5 Gene Selection and Survival Prediction Under Dependent Censoring; Abstract; 5.1 Introduction; 5.2 Univariate Selection; 5.3 Copula-Based Univariate Cox Regression; 5.4 Copula-Based Univariate Selection; 5.5 Choosing the Copula Parameter by the C-Index; 5.6 Lung Cancer Data Analysis; 5.6.1 Gene Selection and Prediction; 5.6.2 Assessing Prediction Performance; 5.7 Discussions; References
6 Future DevelopmentsAbstract; 6.1 Log-Rank Test Under Dependent Censoring; 6.2 Dependent Left-Truncation; References; Appendix A: Spline Basis Functions; Appendix B: R Codes for the Lung Cancer Data Analysis; Index