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E-raamat: Multi-State Survival Models for Interval-Censored Data

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Multi-State Survival Models for Interval-Censored DataSuurem pilt
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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.

Arvustused

"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 bachelors or masters 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

Preface xv
Acknowledgments xvii
1 Introduction
1(16)
1.1 Multi-state survival models
1(2)
1.2 Basic concepts
3(2)
1.3 Example
5(7)
1.3.1 Cardiac allograft vasculopathy (CAV) study
5(3)
1.3.2 A four-state progressive model
8(4)
1.4 Overview of methods and literature
12(2)
1.5 Data used in this book
14(3)
2 Modelling Survival Data
17(16)
2.1 Features of survival data and basic terminology
17(1)
2.2 Hazard, density, and survivor function
18(2)
2.3 Parametric distributions for time to event
20(4)
2.3.1 Exponential distribution
20(1)
2.3.2 Weibull distribution
21(1)
2.3.3 Gompertz distribution
21(1)
2.3.4 Comparing exponential, Weibull and Gompertz
22(2)
2.4 Regression models for the hazard
24(1)
2.5 Piecewise-constant hazard
24(1)
2.6 Maximum likelihood estimation
25(1)
2.7 Example: survival in the CAV study
26(7)
3 Progressive Three-State Survival Model
33(22)
3.1 Features of multi-state data and basic terminology
33(2)
3.2 Parametric models
35(3)
3.2.1 Exponential model
35(1)
3.2.2 Weibull model
36(1)
3.2.3 Gompertz model
37(1)
3.2.4 Hybrid models
37(1)
3.3 Regression models for the hazards
38(1)
3.4 Piecewise-Constant hazards
38(1)
3.5 Maximum likelihood estimation
39(2)
3.6 Simulation study
41(3)
3.7 Example
44(11)
3.7.1 Parkinson's disease study
44(2)
3.7.2 Baseline hazard models
46(5)
3.7.3 Regression models
51(4)
4 General Multi-State Survival Model
55(40)
4.1 Discrete-time Markov process
55(1)
4.2 Continuous-time Markov processes
56(4)
4.3 Hazard regression models for transition intensities
60(1)
4.4 Piecewise-constant hazards
61(2)
4.5 Maximum likelihood estimation
63(3)
4.6 Scoring algorithm
66(3)
4.7 Model comparison
69(1)
4.8 Example
70(11)
4.8.1 English Longitudinal Study of Ageing (ELSA)
70(2)
4.8.2 A five-state model for remembering words
72(9)
4.9 Model validation
81(3)
4.10 Example
84(11)
4.10.1 Cognitive Function and Ageing Study (CFAS)
84(2)
4.10.2 A five-state model for cognitive impairment
86(9)
5 Frailty Models
95(24)
5.1 Mixed-effects models and frailty terms
95(2)
5.2 Parametric frailty distributions
97(1)
5.3 Marginal likelihood estimation
98(3)
5.4 Monte-Carlo Expectation-Maximisation algorithm
101(3)
5.5 Example: frailty in ELSA
104(4)
5.6 Non-parametric frailty distribution
108(3)
5.7 Example: frailty in ELSA (continued)
111(8)
6 Bayesian Inference for Multi-State Survival Models
119(22)
6.1 Introduction
119(2)
6.2 Gibbs sampler
121(5)
6.3 Deviance information criterion (DIC)
126(2)
6.4 Example: frailty in ELSA (continued)
128(1)
6.5 Inference using the BUGS software
129(12)
6.5.1 Adapted likelihood function
132(1)
6.5.2 Multinomial distribution
133(1)
6.5.3 Right censoring
134(1)
6.5.4 Example: frailty in the Parkinson's disease study
135(6)
7 Residual State-Specific Life Expectancy
141(18)
7.1 Introduction
141(1)
7.2 Definitions and data considerations
142(4)
7.3 Computation: integration
146(1)
7.4 Example: a three-state survival process
147(3)
7.5 Computation: Micro-simulation
150(3)
7.6 Example: life expectancies in CFAS
153(6)
8 Further Topics
159(40)
8.1 Discrete-time model for continuous-time process
159(6)
8.1.1 A simulation study
162(1)
8.1.2 Example: Parkinson's disease study revisited
163(2)
8.2 Using cross-sectional data
165(11)
8.2.1 Three-state model, no death
166(5)
8.2.2 Three-state survival model
171(5)
8.3 Missing state data
176(4)
8.4 Modelling the first observed state
180(2)
8.5 Misclassification of states
182(6)
8.5.1 Example: CAV study revisited
185(3)
8.5.2 Extending the misclassification model
188(1)
8.6 Smoothing splines and scoring
188(4)
8.6.1 Example: ELSA study revisited
191(1)
8.6.2 More on the use of splines
192(1)
8.7 Semi-Markov models
192(7)
A Matrix P(t) When Matrix Q Is Constant
199(8)
A.1 Two-state models
201(1)
A.2 Three-state models
202(3)
A.3 Models with more than three states
205(2)
B Scoring for the Progressive Three-State Model
207(4)
C Some Code for the R and BUGS Software
211(11)
C.1 General-purpose optimiser
211(1)
C.2 Code for
Chapter 2
212(2)
C.3 Code for
Chapter 3
214(2)
C.4 Code for
Chapter 4
216(1)
C.5 Code for numerical integration
217(1)
C.6 Code for
Chapter 6
218(4)
Bibliography 222(13)
Index 235
Ardo van den Hout
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