Analysis of Multivariate Survival Data

Survival data or more general time-to-event data occur in many areas, including medicine, biology, engineering, economics, and demography, but previously standard methods have requested that all time variables are univariate and independent. This book extends the field by allowing for multivariate times. Applications where such data appear are survival of twins, survival of married couples and families, time to failure of right and left kidney for diabetic patients, life history data with time to outbreak of disease, complications and death, recurrent episodes of diseases and cross-over studies with time responses. As the field is rather new, the concepts and the possible types of data are described in detail and basic aspects of how dependence can appear in such data is discussed. Four different approaches to the analysis of such data are presented. The multi-state models where a life history is described as the subject moving from state to state is the most classical approach. The Markov models make up an important special case, but it is also described how easily more general models are set up and analyzed. Frailty models, which are random effects models for survival data, made a second approach, extending from the most simple shared frailty models, which are considered in detail, to models with more complicated dependence structures over individuals or over time. Marginal modelling has become a popular approach to evaluate the effect of explanatory factors in the presence of dependence, but without having specified a statistical model for the dependence. Finally, the completely non-parametric approach to bivariate censored survival data is described. This book is aimed at investigators who need to analyze multivariate survival data, but due to its focus on the concepts and the modelling aspects, it is also useful for persons interested in such data, but Front Matter....Pages i-xvii Introduction....Pages 1-35 Univariate Survival Data....Pages 36-111 Dependence structures....Pages 112-127 Bivariate dependence measures....Pages 128-138 Probability aspects of multi-state models....Pages 139-176 Statistical inference for multi-state models....Pages 177-214 Shared frailty models....Pages 215-262 Statistical inference for shared frailty models....Pages 263-311 Shared frailty models for recurrent events....Pages 312-344 Multivariate frailty models....Pages 345-384 Instantaneous and short-term frailty models....Pages 385-405 Competing risks models....Pages 406-418 Marginal and copula modeling....Pages 419-441 Multivariate non-parametric estimates....Pages 442-482 Summary....Pages 483-496 Back Matter....Pages 497-542 "This book is aimed at investigators who need to analyze multivariate survival data. It can be used as a textbook for a graduate course in multivariate survival data. It is written from an applied point of view and covers all the essential aspects of applying multivariate survival models. More theoretical evaluations, like asymptotic theory, are also described, but only to the extent useful in applications and for understanding the models. To read the book, it is useful, but not necessary, to have an understanding of univariate survival data."--BOOK JACKET.