In survival analysis there has long been a need for models that goes beyond the Cox model as the proportional hazards assumption often fails in practice. This book studies and applies modern flexible regression models for survival data with a special focus on extensions of the Cox model and alternative models with the specific aim of describing time-varying effects of explanatory variables. One model that receives special attention is Aalen's additive hazards model that is particularly well suited for dealing with time-varying effects. The book covers the use of residuals and resampling techniques to assess the fit of the models and also points out how the suggested models can be utilised for clustered survival data. The authors demonstrate the practically important aspect of how to do hypothesis testing of time-varying effects making backwards model selection strategies possible for the flexible models considered.
The use of the suggested models and methods is illustrated on real data examples. The methods are available in the R-package timereg developed by the authors, which is applied throughout the book with worked examples for the data sets. This gives the reader a unique chance of obtaining hands-on experience.
This book is well suited for statistical consultants as well as for those who would like to see more about the theoretical justification of the suggested procedures. It can be used as a textbook for a graduate/master course in survival analysis, and students will appreciate the exercises included after each chapter. The applied side of the book with many worked examples accompanied with R-code shows in detail how one can analyse real data and at the same time gives a deeper understanding of the underlying theory.
1 Introduction 1
2 Probabilistic background 17
3 Estimation for filtered counting process data 49
4 Nonparametric procedures for survival data 81
5 Additive Hazards Models 103
6 Multiplicative hazards models 175
7 Multiplicative-Additive hazards models 249
8 Accelerated failure time and transformation models 293
9 Clustered failure time data 313
10 Competing Risks Model 347
11 Marked point process models 375
A Khmaladze's transformation 411
B Matrix derivative s 415
C The Timereg survival package for R 417
From the reviews: "This book is a welcome addition to the literature on survival analysis for several reasons. The coverage of both multiplicative and, especially, additive models with time-varying covariates is well beyond that found in other books. There is also more emphasis on model checking than in most books. ! the book is enjoyable to read. ! This book is an important resource for anyone with an interest in survival or event history analysis." (J. F. Lawless, Short Book Reviews, Vol. 26 (2), 2006) "'Dynamic regression models' ! are able to capture time-varying dynamics of covariate effects. ! this book provides a timely summary of the results for topics which are important to practical applications. The readers who are interested in further research in these areas will find the detailed derivations of mathematical results helpful. ! The rich exercises at the end of each chapter make this book an excellent choice as a textbook for an advanced survival analysis course." (Dongsheng Tu, Zentrablatt MATH, Vol. 1096 (22), 2006) "Survival data analysis has been a very active research field for several decades. An important contribution that stimulated the entire field was the counting process formulation ! . that is also used in this monograph. ! There are exercises at the end of each chapter ! . The practical aspects of survival analysis are illustrated with a set of worked out examples using R. ! The book is primarily aimed at the biostatistical community ! . It is well written ! ." (Rainer Schlittgen, Statistical Papers, Vol. 48 (3), 2007) "The book under review is a welcome addition to existing excellent books on survival analysis ! . It should be a useful reference to both applied as well as theoretical bio-statisticians. Perhaps it could also be used as a text for a graduate level course in survival analysis." (Subhash C. Kochar, Mathematical Reviews, Issue 2007 b) "This book is aimed at advanced graduate students and statistical researchers in statistics/biostatistics departments. ! The inspiration and influence of Andersen et al. (1993) on the presentation style, terminology, and approach to the subject are very visible in many parts of the book. ! In summary, this book definitely deserves a place in the collection of any serious survival analyst. It is also recommended to theoretically sound data analysts interested in dynamic and semiparametric survival models beyond the class of multiplicative models." (Debajyoti Sinha, Journal of the American Statistical Association, Vol. 102 (480), 2007)