Multi-State Survival Models for Interval-Censored Data

Ardo van den Hout

• PrefaceIntroductionMulti-state survival modelsBasic conceptsExamplesOverview of methods and literatureData used in this bookModelling Survival DataFeatures of survival data and basic terminologyHazard, density and survivor functionParametric distributions for time to event dataRegression models for the hazardPiecewise-constant hazardMaximum likelihood estimationExample: survival in the CAV studyProgressive Three-State Survival ModelFeatures of multi-state data and basic terminologyParametric modelsRegression models for the hazardsPiecewise-constant hazardsMaximum likelihood estimationA simulation studyExampleGeneral Multi-State Survival ModelDiscrete-time Markov processContinuous-time Markov processesHazard regression models for transition intensitiesPiecewise-constant hazardsMaximum likelihood estimationScoring algorithmModel comparisonExampleModel validationExampleFrailty ModelsMixed-effects models and frailty termsParametric frailty distributionsMarginal likelihood estimationMonte-Carlo Expectation-Maximisation algorithmExample: frailty in ELSANon-parametric frailty distributionExample: frailty in ELSA (continued)Bayesian Inference for Multi-State Survival ModelsIntroductionGibbs samplerDeviance Information Criterion (DIC)Example: frailty in ELSA (continued)Inference using the BUGS softwareRedifual State-Specific Life ExpectancyIntroductionDefinitions and data considerationsComputation: integrationExample: a three-state survival processComputation: micro-simulationExample: life expectancies in CFASFurther TopicsDiscrete-time models for continuous-time processesUsing cross-sectional dataMissing state dataModelling the first observed stateMisclassification of statesSmoothing splines and scoringSemi-Markov modelsMatrix P(t) When Matrix Q is ConstantTwo-state modelsThree-state modelsModels with more than three statesScoring for the Progressive Three-State ModelSome Code for the R and BUGS SoftwareGeneral-purpose optimiserCode for Chapter 2Code for Chapter 3Code for Chapter 4Code for numerical integrationCode for Chapter 6BibliographyIndex

"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