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Multi-State Survival Models for Interval-Censored Data
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Table of Contents

Preface

Introduction
Multi-state survival models
Basic concepts
Examples
Overview of methods and literature
Data used in this book

Modelling Survival Data
Features of survival data and basic terminology
Hazard, density and survivor function
Parametric distributions for time to event data
Regression models for the hazard
Piecewise-constant hazard
Maximum likelihood estimation
Example: survival in the CAV study

Progressive Three-State Survival Model
Features of multi-state data and basic terminology
Parametric models
Regression models for the hazards
Piecewise-constant hazards
Maximum likelihood estimation
A simulation study
Example

General Multi-State Survival Model
Discrete-time Markov process
Continuous-time Markov processes
Hazard regression models for transition intensities
Piecewise-constant hazards
Maximum likelihood estimation
Scoring algorithm
Model comparison
Example
Model validation
Example

Frailty Models
Mixed-effects models and frailty terms
Parametric frailty distributions
Marginal likelihood estimation
Monte-Carlo Expectation-Maximisation algorithm
Example: frailty in ELSA
Non-parametric frailty distribution
Example: frailty in ELSA (continued)

Bayesian Inference for Multi-State Survival Models
Introduction
Gibbs sampler
Deviance Information Criterion (DIC)
Example: frailty in ELSA (continued)
Inference using the BUGS software

Redifual State-Specific Life Expectancy
Introduction
Definitions and data considerations
Computation: integration
Example: a three-state survival process
Computation: micro-simulation
Example: life expectancies in CFAS

Further TopicsDiscrete-time models for continuous-time processes
Using cross-sectional data
Missing state data
Modelling the first observed state
Misclassification of states
Smoothing splines and scoring
Semi-Markov models

Matrix P(t) When Matrix Q is Constant
Two-state models
Three-state models
Models with more than three states

Scoring for the Progressive Three-State Model

Some Code for the R and BUGS Software
General-purpose optimiser
Code for Chapter 2
Code for Chapter 3
Code for Chapter 4
Code for numerical integration
Code for Chapter 6

Bibliography

Index

About the Author

Ardo van den Hout

Reviews

"This book introduces Markov models for studying transitions between states over time, when the exact times of transitions are not always observed. Such data are common in medicine, epidemiology, demography, and social sciences research. The multi-state survival modeling framework can be useful for investigating potential associations between covariates and the risk of moving between states and for prediction of multi-state survival processes. The book is appropriate for researchers with a bachelor’s or master’s degree knowledge of mathematical statistics. No prior knowledge of survival analysis or stochastic processes is assumed. …
Multi-State Survival Models for Interval-Censored Data serves as a useful starting point for learning about multi-state survival models."
—Li C. Cheung, National Cancer Institute, in the Journal of the American Statistical Association, January 2018"This book aims to provide an overview of the key issues in multistate models, conduct and analysis of models with interval censoring. Applications of the book concern on longitudinal data and most of them are subject to interval censoring. The book contains theoretical and applicable examples of different multistate models. … In summary, this book contains an excellent theoretical coverage of multistate models concepts and different methods with practical examples and codes, and deals with other topics relevant this kind of modelling in a comprehensive but summarised way."
— Morteza Hajihosseini, ISCB News, May 2017"This is the first book that I know of devoted to multi-state models for intermittently-observed data. Even though this is a common situation in medical and social statistics, these methods have only previously been covered in scattered papers, software manuals and book chapters. The level is approximately suitable for a postgraduate statistics student or applied statistician. The structure is clear, gradually building up complexity from standard survival models through to more general state patterns. An important later chapter covers estimation of expected time spent in states such as healthy life, and a range of advanced topics such as frailty models and Bayesian inference are introduced. The models advocated are flexible enough to cover all typical applications. Dependence of transition rates on age or time is emphasised throughout, and made straightforward through a novel piecewise-constant approximation method. The writing style strikes a good balance between readability and mathematical rigour. Each new topic is generally introduced with an approachable explanation, with formal definitions following later. The applied motivation is stressed throughout. Each new model is illustrated through one of several running examples related to long-term illness or ageing. A helpful appendix gives some useful algebraic results, and example R implementations of the non-standard methods. I'll be recommending this book to the users of my "msm" software and my students, especially anyone modelling chronic diseases or age-dependent conditions."
—Christopher Jackson, MRC Biostatistics Unit, Cambridge"...To my knowledge, this book comprises the first devoted to multi-state models for intermittently-observed data …The book is motivated by applications in demography, disease, and survival, as shown by its title and structure, which starts with standard survival analysis for times to death. This focus on one area is probably a sensible choice to keep the book clear and concise, though inexperienced practitioners in other areas may face an extra hurdle...The models advocated are flexible enough to cover all typical applications. Dependence of transition rates on age or time is emphasized, and modelling this dependence is made straightforward through a novel piecewise-constant approximation method. This is an advance over methods available in current software. Sensible modelling choices, such as parsimony constraints on model parameters, are illustrated through the examples. The writing style strikes a good balance between readability and mathematical rigor. Each new topic is generally begun with an approachable explanation, with formal definitions following later. A helpful appendix gives some useful algebraic results and example R implementations of the non-standard methods...I will be recommending this book to users of the "msm" package and my students, especially anyone modelling chronic diseases or age-dependent conditions."
-Christopher Jackson, University of Cambridge

"This book introduces Markov models for studying transitions between states over time, when the exact times of transitions are not always observed. Such data are common in medicine, epidemiology, demography, and social sciences research. The multi-state survival modeling framework can be useful for investigating potential associations between covariates and the risk of moving between states and for prediction of multi-state survival processes. The book is appropriate for researchers with a bachelor’s or master’s degree knowledge of mathematical statistics. No prior knowledge of survival analysis or stochastic processes is assumed. …
Multi-State Survival Models for Interval-Censored Data serves as a useful starting point for learning about multi-state survival models."
—Li C. Cheung, National Cancer Institute, in the Journal of the American Statistical Association, January 2018"This book aims to provide an overview of the key issues in multistate models, conduct and analysis of models with interval censoring. Applications of the book concern on longitudinal data and most of them are subject to interval censoring. The book contains theoretical and applicable examples of different multistate models. … In summary, this book contains an excellent theoretical coverage of multistate models concepts and different methods with practical examples and codes, and deals with other topics relevant this kind of modelling in a comprehensive but summarised way."
— Morteza Hajihosseini, ISCB News, May 2017"This is the first book that I know of devoted to multi-state models for intermittently-observed data. Even though this is a common situation in medical and social statistics, these methods have only previously been covered in scattered papers, software manuals and book chapters. The level is approximately suitable for a postgraduate statistics student or applied statistician. The structure is clear, gradually building up complexity from standard survival models through to more general state patterns. An important later chapter covers estimation of expected time spent in states such as healthy life, and a range of advanced topics such as frailty models and Bayesian inference are introduced. The models advocated are flexible enough to cover all typical applications. Dependence of transition rates on age or time is emphasised throughout, and made straightforward through a novel piecewise-constant approximation method. The writing style strikes a good balance between readability and mathematical rigour. Each new topic is generally introduced with an approachable explanation, with formal definitions following later. The applied motivation is stressed throughout. Each new model is illustrated through one of several running examples related to long-term illness or ageing. A helpful appendix gives some useful algebraic results, and example R implementations of the non-standard methods. I'll be recommending this book to the users of my "msm" software and my students, especially anyone modelling chronic diseases or age-dependent conditions."
—Christopher Jackson, MRC Biostatistics Unit, Cambridge"...To my knowledge, this book comprises the first devoted to multi-state models for intermittently-observed data …The book is motivated by applications in demography, disease, and survival, as shown by its title and structure, which starts with standard survival analysis for times to death. This focus on one area is probably a sensible choice to keep the book clear and concise, though inexperienced practitioners in other areas may face an extra hurdle...The models advocated are flexible enough to cover all typical applications. Dependence of transition rates on age or time is emphasized, and modelling this dependence is made straightforward through a novel piecewise-constant approximation method. This is an advance over methods available in current software. Sensible modelling choices, such as parsimony constraints on model parameters, are illustrated through the examples. The writing style strikes a good balance between readability and mathematical rigor. Each new topic is generally begun with an approachable explanation, with formal definitions following later. A helpful appendix gives some useful algebraic results and example R implementations of the non-standard methods...I will be recommending this book to users of the "msm" package and my students, especially anyone modelling chronic diseases or age-dependent conditions."
-Christopher Jackson, University of Cambridge

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