Overview

Multi-State Survival Models for Interval-Censored Data introduces methods to describe stochastic processes that consist of transitions between states over time. It is targeted at researchers in medical statistics, epidemiology, demography, and social statistics. One of the applications in the book is a three-state process for dementia and survival in the older population. This process is described by an illness-death model with a dementia-free state, a dementia state, and a dead state. Statistical modelling of a multi-state process can investigate potential associations between the risk of moving to the next state and variables such as age, gender, or education. A model can also be used to predict the multi-state process. The methods are for longitudinal data subject to interval censoring. Depending on the definition of a state, it is possible that the time of the transition into a state is not observed exactly. However, when longitudinal data are available the transition time may be known to lie in the time interval defined by two successive observations. Such an interval-censored observation scheme can be taken into account in the statistical inference. Multi-state modelling is an elegant combination of statistical inference and the theory of stochastic processes. Multi-State Survival Models for Interval-Censored Data shows that the statistical modelling is versatile and allows for a wide range of applications.

Full Product Details

Author:   Ardo van den Hout
Publisher:   Taylor & Francis Inc
Imprint:   CRC Press Inc
Volume:   152
Dimensions:   Width: 15.60cm , Height: 2.00cm , Length: 23.40cm
Weight:   0.476kg
ISBN:  

9781466568402

ISBN 10:   1466568402
Pages:   256
Publication Date:   02 December 2016
Audience:   Professional and scholarly ,  College/higher education ,  Professional & Vocational ,  Tertiary & Higher Education
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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

Reviews

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</p>

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

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Ardo van den Hout

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