Advanced Survival Models (Chapman & Hall/CRC Biostatistics Series)

Description

Survival data analysis is a very broad field of statistics, encompassing a large variety of methods used in a wide range of applications, and in particular in medical research. During the last twenty years, several extensions of "classical" survival models have been developed to address particular situations often encountered in practice. This book aims to gather in a single reference the most commonly used extensions, such as frailty models (in case of unobserved heterogeneity or clustered data), cure models (when a fraction of the population will not experience the event of interest), competing risk models (in case of different types of event), and joint survival models for a time-to-event endpoint and a longitudinal outcome. Features Presents state-of-the art approaches for different advanced survival models including frailty models, cure models, competing risk models and joint models for a longitudinal and a survival outcome Uses consistent notation throughout the book for the different techniques presented Explains in which situation each of these models should be used, and how they are linked to specific research questions Focuses on the understanding of the models, their implementation, and their interpretation, with an appropriate level of methodological development for masters students and applied statisticians Provides references to existing R packages and SAS procedure or macros, and illustrates the use of the main ones on real datasets This book is primarily aimed at applied statisticians and graduate students of statistics and biostatistics. It can also serve as an introductory reference for methodological researchers interested in the main extensions of classical survival analysis. Cover Half Title Series Page Title Page Copyright Page Dedication Contents Preface Acknowledgment for use of data List of Figures List of Tables Author Symbols 1. Introduction 1.1. Survival data analysis 1.2. Basic concepts 1.2.1. Censoring and truncation 1.2.2. Basic functions 1.3. Examples 1.3.1. Colon cancer data 1.3.2. Rectal cancer data 1.3.3. Diabetic retinopathy data 1.3.4. Children ALL data 1.3.5. Melanoma data 1.3.6. Advanced ovarian cancer data 1.4. Scope of this book 2. Classical Survival Analysis 2.1. Introduction 2.2. Likelihood function 2.3. Estimation of the survival and hazard function 2.3.1. Parametric estimation 2.3.2. Non-parametric estimation 2.4. Hypothesis testing 2.5. Modeling survival data 2.5.1. Proportional hazards models 2.5.2. Accelerated failure time models 2.5.3. Proportional odds models 2.6. Software and examples revisited 2.6.1. Available softwares for classical survival analysis 2.6.2. Colon cancer data 2.6.3. Rectal cancer data 2.7. Further reading 3. Frailty Models 3.1. Introduction 3.2. Univariate frailty models 3.3. Multivariate frailty models 3.4. Frailty distributions 3.4.1. Discrete frailty distribution 3.4.2. Continuous frailty distribution 3.5. Estimation 3.5.1. Parametric frailty models 3.5.2. Semi-parametric frailty models 3.6. Extensions of the shared frailty model 3.7. Software and examples revisited 3.7.1. Diabetic retinopathy data 3.7.2. Rectal cancer data 3.8. Further reading 4. Cure Models 4.1. Introduction 4.2. Mixture cure models 4.2.1. The incidence and the latency submodels 4.2.2. Estimation 4.2.3. Interpretation 4.3. Promotion time cure models 4.3.1. Estimation 4.3.2. Interpretation 4.3.3. Extended promotion time cure model 4.4. When to use a cure model 4.5. Software and examples revisited 4.5.1. Children ALL data 4.5.2. Melanoma data 4.6. Further reading 5. Competing Risks 5.1. Introduction 5.2. Basic concepts, notations, and definitions 5.2.1. Combined analysis or time to the first event analysis 5.2.2. Marginal analysis 5.2.3. Competing risk analysis 5.2.4. A note on censoring 5.3. Estimation 5.4. Hypotheses testing 5.5. Modeling 5.5.1. Proportional cause-specific hazards model 5.5.2. Fine and Gray model 5.5.3. Choice of model 5.6. Software and examples revisited 5.6.1. Advanced ovarian cancer data 5.7. Further reading 6. Joint Modeling 6.1. Introduction 6.2. Time-dependent covariates in survival models 6.2.1. Exogenous time-dependent covariates and extended Cox model 6.2.2. Endogenous time-dependent covariates and joint models 6.3. The shared random effect approach 6.3.1. Model for the marker trajectory 6.3.2. Model for the time-to-event outcome 6.3.3. Estimation 6.3.4. Association structure 6.4. The joint latent class approach 6.4.1. Model for the latent class membership probability 6.4.2. Model for the class-specific marker trajectory 6.4.3. Model for the class-specific risk of event 6.4.4. Estimation 6.5. JCLM versus SREM 6.6. Software 6.7. Further reading Bibliography Index