Multi-State Survival Models for Interval-Censored Data: 1st Edition (Hardback) book cover

Multi-State Survival Models for Interval-Censored Data

1st Edition

By Ardo van den Hout

Chapman and Hall/CRC

238 pages | 42 B/W Illus.

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Description

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.

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

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 Topics

Discrete-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 Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General