Survival Analysis with Interval-Censored Data A Practical Approach with R, SAS and WinBUGS

This book describes methods and software implementations for the analysis of interval-censored data. The authors present the theoretical background for all methods and apply the methods to real data sets. They also provide the R, SAS, and WinBUGS code for all the examples, enabling readers to modify the code and use the methods to solve their own practical problems. In addition, most of the data sets used in the text are available online.

Survival Analysis with Interval-Censored Data: A Practical Approach with Examples in R, SAS, and BUGS provides the reader with a practical introduction into the analysis of interval-censored survival times. Although many theoretical developments have appeared in the last fifty years, interval censoring is often ignored in practice. Many are unaware of the impact of inappropriately dealing with interval censoring. In addition, the necessary software is at times difficult to trace. This book fills in the gap between theory and practice. Features: -Provides an overview of frequentist as well as Bayesian methods. -Include a focus on practical aspects and applications. -Extensively illustrates the methods with examples using R, SAS, and BUGS. Full programs are available on a supplementary website. The authors: Kris Bogaerts is project manager at I-BioStat, KU Leuven. He received his PhD in science (statistics) at KU Leuven on the analysis of interval-censored data. He has gained expertise in a great variety of statistical topics with a focus on the design and analysis of clinical trials. Arnošt Komárek is associate professor of statistics at Charles University, Prague. His subject area of expertise covers mainly survival analysis with the emphasis on interval-censored data and classification based on longitudinal data. He is past chair of the Statistical Modelling Society and editor of Statistical Modelling: An International Journal. Emmanuel Lesaffre is professor of biostatistics at I-BioStat, KU Leuven. His research interests include Bayesian methods, longitudinal data analysis, statistical modelling, analysis of dental data, interval-censored data, misclassification issues, and clinical trials. He is the founding chair of the Statistical Modelling Society, past-president of the International Society for Clinical Biostatistics, and fellow of ISI and ASA.

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

Kris Bogaerts, Arnost Komarek and Emmauel Lesaffre