List of Tables
List of Figures
Notation
Preface
I Introduction
Introduction
Survival concepts
Types of censoring
Right censoring
Interval and left censoring
Some special cases of interval censoring
Doubly interval censoring
Truncation
Ignoring interval censoring
Independent noninformative censoring
Independent noninformative right censoring
Independent noninformative interval censoring
Frequentist inference
Likelihood for interval-censored data
Maximum likelihood theory
Data sets and research questions
Homograft study
Breast cancer study
AIDS clinical trial
Sensory shelf life study
Survey on mobile phone purchases
Mastitis study
Signal Tandmobielr study
Censored data in R and SAS
R
SAS
Inference for right-censored data
Estimation of the survival function
Nonparametric maximum likelihood estimation
R solution
SAS solution
Comparison of two survival distributions
Review of signi_cance tests
R solution
SAS solution
Regression models
The proportional hazards model
Model description and estimation
Model checking
R solution
SAS solution
The accelerated failure time model
Model description and estimation
Model checking
R solution
SAS solution
II Frequentist methods for interval-censored data
Estimating the survival distribution
Nonparametric maximum likelihood
Estimation
Asymptotic results
R solution
SAS solution
Parametric modelling
Estimation
Model selection
Goodness of _t
R solution
SAS solution
Smoothing methods
Logspline density estimation
A smooth approximation to the density
Maximum likelihood estimation
R solution
Classical Gaussian mixture model
Penalized Gaussian mixture model
R solution
Concluding remarks
Comparison of two or more survival distributions
Nonparametric comparison of survival curves
The weighted log-rank test: derivation
The weighted log-rank test: linear form
The weighted log-rank test: derived from the linear
transformation model
The weighted log-rank test: the G family
The weighted log-rank test: significance testing
R solution
SAS solution
Sample size calculation
Concluding remarks
The proportional hazards model
Parametric approaches
Maximum likelihood estimation
R solution
SAS solution
Towards semiparametric approaches
The piecewise exponential baseline survival model
Model description and estimation
R solution
SAS solution
The SemiNonParametric approach
Model description and estimation
SAS solution
Spline-based smoothing approaches
Two spline-based smoothing approaches
R solution
SAS solution
Semiparametric approaches
Finkelstein's approach
Farrington's approach
The iterative convex minorant algorithm
The grouped proportional hazards model
Practical applications
Two examples
R solution
SAS solution
Multiple imputation approach
Data augmentation algorithm
Multiple imputation for interval-censored survival times
R solution
SAS solution
Model checking
Checking the PH model
R solution
SAS solution
Sample size calculation
Concluding remarks
The accelerated failure time model
The parametric model
Maximum likelihood estimation
R solution
SAS solution
The penalized Gaussian mixture model
Penalized maximum likelihood estimation
R solution
The SemiNonParametric approach
SAS solution
Model checking
Sample size calculation
Computational approach
SAS solution
Concluding remarks
Bivariate survival times
Nonparametric estimation of the bivariate survival function
The NPMLE of a bivariate survival function
R solution
SAS solution
Parametric models
Model description and estimation
R solution
SAS solution
Copula models
Background
Estimation procedures
R solution
Flexible survival models
The penalized Gaussian mixture model
SAS solution
Estimation of the association parameter
Measures of association
Estimating measures of association
R solution
SAS solution
Concluding remarks
Additional topics
Doubly interval-censored data
Background
R solution
Regression models for clustered data
Frailty models
R solution
SAS solution
A marginal approach to correlated survival times
Independence working model
SAS solution
A biplot for interval-censored data
The classical biplot
Extension to interval-censored observations
R solution
Concluding remarks
III Bayesian methods for interval-censored data
Bayesian concepts
Bayesian inference
Parametric versus nonparametric Bayesian approaches
Bayesian data augmentation
Markov chain Monte Carlo
Credible regions and contour probabilities
Selecting and checking the model
Sensitivity analysis
Nonparametric Bayesian inference
Bayesian nonparametric modelling of the hazard function
Bayesian nonparametric modelling of the distribution function
Bayesian software
WinBUGS and OpenBUGS
JAGS
R software
SAS procedures
Stan software
Applications for right-censored data
Parametric models
BUGS solution
SAS solution
Nonparametric Bayesian estimation of a survival curve
R solution
Semiparametric Bayesian survival analysis
BUGS solution
Concluding remarks
Bayesian estimation of the survival distribution for interval-censored observations
Bayesian parametric modelling
JAGS solution
SAS solution
Bayesian smoothing methods
Classical Gaussian mixture
R solution
Penalized Gaussian mixture
Nonparametric Bayesian estimation
The Dirichlet Process prior approach
R solution
The Dirichlet Process Mixture approach
R solution
Concluding remarks
The Bayesian proportional hazards model
The parametric PH model
JAGS solution
SAS solution
The PH model with exible baseline hazard
A Bayesian PH model with a smooth baseline hazard
R solution
A PH model with piecewise constant baseline hazard
R solution
The semiparametric PH model
Concluding remarks
The Bayesian accelerated failure time model
The Bayesian parametric AFT model
JAGS solution
SAS solution
AFT model with a classical Gaussian mixture as an error distribution
R solution
AFT model with a penalized Gaussian mixture as an error distribution
R solution
A Bayesian semiparametric AFT model
R solution
Concluding remarks
Additional topics
Hierarchical models
Parametric shared frailty models
JAGS solution
SAS solution
Flexible shared frailty models
R solution
Semiparametric shared frailty models
Multivariate models
Parametric bivariate models
JAGS solution
SAS solution
Bivariate copula models
Flexible bivariate models
R solution
Semiparametric bivariate models
R solution
The multivariate case
Doubly interval censoring
Parametric modelling of univariate DI-censored data
JAGS solution
Flexible modelling of univariate DI-censored data
R solution
Semiparametric modelling of univariate DI-censored data
R solution
Modelling of multivariate DI-censored data
Concluding remarks
IV Concluding part
Omitted topics and outlook
Omitted topics
Competing risks and multi-state models
Survival models with a cured subgroup
Multilevel models
Informative censoring
Interval-censored covariates
Joint longitudinal and survival models
Spatial-temporal models
Time points measured with error
Quantile regression
Outlook
V Appendices
A Data sets
A Homograft study
A AIDS clinical trial
A Survey on mobile phone purchases
A Mastitis study
A Signal Tandmobiel R study
B Distributions
B Log-normal LN(; _)
B Log-logistic LL(; _)
B Weibull W(; _)
B Exponential E(_)
B Rayleigh R(_)
B Gamma(; _)
B R solution
B SAS solution
B BUGS solution
B R and BUGS parametrizations
C Prior distributions
C Beta prior: Beta(_; _)
C Dirichlet prior: Dir (_)
C Gamma prior: G(_; _)
C Inverse gamma prior: IG(_; _)
C Wishart prior: Wishart(R; k)
C Inverse Wishart prior: Wishart(R; k)
C Link between Beta, Dirichlet and Dirichlet Process prior
D Description of selected R packages
D The icensBKL package
D The Icens package
D The interval package
D The survival package
D The logspline package
D The smoothSurv package
D The mixAK package
D The bayesSurv package
D The DPpackage package
D Other packages
E Description of selected SAS procedures
E PROC LIFEREG
E PROC RELIABILITY
E PROC ICLIFETEST
E PROC ICPHREG
F Technical details
F The Iterative Convex Minorant (ICM) algorithm
F Regions of possible support for bivariate interval-censored data
F The algorithm of Gentleman and Vandal ()
F The algorithm of Bogaerts and Lesa_re ()
F The height map algorithm of Maathuis ()
F Splines
F Polynomial _tting
F Polynomial splines
F Natural cubic splines
F Truncated power series
F B-splines
F M-splines and I-splines
F Penalized splines (P-splines)
References
Author Index
Subject Index