Survival Analysis with Correlated Endpoints

Takeshi Emura, Chang Gung UniversityShigeyuki Matsui, Department of Biostatistics, Nagoya University Graduate School of Medicine Virginie Rondeau, INSERM U 1219

“This book can be used as a textbook for a course aimed at postgraduate students in biostatistics and medicine.” (Denis Sidorov, zbMATH 1429.62003, 2020)

• Chapter 1: Setting the scene.-1.1 Endpoints.- 1.2 Benefits of investigating correlated endpoints.- 1.3 Copulas and frailty: a brief history.- References.- Chapter 2: Introduction to survival analysis .-2.1 Endpoint and censoring.- 2.2 Kaplan-Meier estimator and survival function.- 2.3 Hazard function.- 2.4 Log-rank test for two-sample comparison.- 2.5 Cox regression.- 2.6 Example of Cox regression.- 2.7 Likelihood inference under non-informative censoring.- 2.8 Theoretical notes.- 2.9 Exercises.- References.- Chapter 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 of the penalized likelihood.- 3.7 Technical note 2: LCV and choice of   and  .- 3.8 Exercises.- References.- Chapter 4: High-dimensional covariates in the joint frailty-copula model.- 4.1 Introduction.- 4.2 Tukey’s compound covariate.- 4.3 Univariate selection.- 4.4 Meta-analytic data with high-dimensional covariates.- 4.5 The joint model with compound covariates .- 4.6 The joint model with ridge or Lasso predictor .- 4.7 Prediction of patient-level survival function .- 4.8 Simulations.- 4.8.1 Simulation design.- 4.8.2 Simulation results.- 4.9 Case study: ovarian cancer data .- 4.9.1 Compound covariate.- 4.9.2 Fitting the joint frailty-copula mode.- 4.9.3 Patient-level survival function.- 4.10 Concluding remarks.- References.- Chapter 5: Dynamic prediction of time-to-death.- 5.1 Accurate prediction of survival.- 5.2 Framework of dynamic prediction.- 5.2.1 Conditional failure function given tumour progression.- 5.2.2 Conditional hazard function given tumour progression.- 5.3 Prediction formulas under the joint frailty-copula model.- 5.4 Estimating prediction formulas.- 5.5 Case study: ovarian cancer data.- 5.6 Discussions.- References.- Chapter 6: Future developments- 6.1 Analysis of recurrent events.- 6.2 Kendall’s tau in meta-analysis.- 6.3 Validation of surrogate endpoints.- 6.4 Left-truncation.- 6.5 Interactions.- 6.6 Parametric failure time models.- 6.7 Compound covariate.- References.- Appendix A: Cubic spline bases.- Appendix B: R codes for the ovarian cancer data analysis.- B1. Using CXCL12 gene as a covariate.- B2. Using compound covariates (CCs) and residual tumour as covariates.- Appendix C: Derivation of prediction formulas.