Survival analysis with correlated endpoints : joint frailty-copula models / Takeshi Emura, Shigeyuki Matsui, Virginie Rondeau.

Intro; Preface; Use as a Textbook; Use as a Reference Book; Acknowledgements; Contents; Abbreviations; Notations; 1 Setting the Scene; 1.1 Endpoints and Censoring; 1.2 Motivations for Investigating Correlated Endpoints; 1.2.1 Understanding Disease Progression Mechanisms; 1.2.2 Dynamic Prediction of Death; 1.2.3 Validating Surrogate Endpoints; 1.3 Copulas and Bivariate Survival Models: A Brief History; References; 2 Introduction to Multivariate Survival Analysis; 2.1 Endpoints and Censoring; 2.2 Basic Terminologies; 2.3 Cox Regression; 2.3.1 R Survival Package; 2.4 Likelihood-Based Method

2.4.1 Spline and Penalized Likelihood2.5 Clustered Survival Data; 2.5.1 Shared Frailty Model; 2.5.2 Likelihood Function; 2.5.3 Penalized Likelihood and Spline; 2.6 Copulas for Bivariate Event Times; 2.6.1 Measures of Dependence; 2.6.2 Residual Dependence; 2.6.3 Likelihood Function; 2.7 Exercises; References; 3 The Joint Frailty-Copula Model for Correlated Endpoints; 3.1 Introduction; 3.2 Semi-competing Risks Data; 3.3 Joint Frailty-Copula Model; 3.4 Penalized Likelihood with Splines; 3.5 Case Study: Ovarian Cancer Data; 3.6 Technical Note 1: Numerical Maximization

6.4 Left Truncation6.5 Interactions; 6.5.1 (Gene × Gene) Interaction; 6.5.2 (Gene × Time) Interaction; 6.6 Parametric Failure Time Models; 6.7 Compound Covariate; References; Appendix A: Spline Basis Functions; Appendix B: R Codes for the Ovarian Cancer Data Analysis; B1. Using the CXCL12 Gene as a Covariate; B2. Using the Compound Covariates (CCs) and Residual Tumour as Covariates; Appendix C: Derivation of Prediction Formulas; Index