Multi-State Survival Models for Interval-Censored Data

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**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**

Ardo van den Hout

"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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