Analysis of multivariate survival data.

*(English)*Zbl 0962.62096
Statistics for Biology and Health. New York, NY: Springer. xiv, 542 p. DM 179.00; öS 1307.00; sFr 162.00; £61.50; $ 84.95 (2000).

Standard methods for analysis of survival data or more general time-to-event data require that all time variables are univariate and independent. This book extends the field by considering methods for analysis of multivariate survival data which occur when independence between survival times cannot be assumed. The author distinguishes six types of dependence in multivariate survival data: individuals which are related in some way (e.g. twins), similar organs (e.g. eyes, kidneys, teeth), recurrent events (e.g. infections, insurance claims), repeated measurements (e.g. cross-over experiments with survival time outcome), different events (e.g. disability model with three states, healthy, disabled and dead), and competing risks (e.g. dead of hearth disease, cancer or other causes). Four approaches to handle multivariate survival data are presented in this book: multi-state models, frailty models, marginal modeling and nonparametric methods.

The intended readership are persons, who already have some experience with survival data. Throughout the book theoretical developments are extensively exemplified by real-life examples and computational aspects are dealt with as well. The book consists of 15 chapters and 2 appendices. A commendable feature is that each of the chapters starts with an intuitional introduction and ends with a brief summary section, bibliographic comments and exercises. However, there are no solutions for the latter.

Chapter 1 is a key chapter where the concepts both for simple survival data and multivariate survival data are clarified and a classification is developed that helps in finding the most appropriate model for a specific kind of data set. Chapter 2 is an introduction to standard methods for univariate survival data. Chapter 3 is another key chapter where the various mechanisms that create dependence in multivariate survival data are discussed. Chapter 4 covers bivariate dependence measures.

Multi-state models are described in Chapters 5 and 6. A multi-state model is defined as a model for a stochastic process, which at any time point occupies one of a set of discrete states. In the book the main focus is on Markov processes.

Shared frailty models are described in Chapters 7 and 8. A shared frailty model can be considered as a random effects model with two sources of variation, that is the group variation described by the frailty and the individual random variation described by the hazard function. The special case of shared frailty models for recurrent events is considered separately in Chapter 9. More general models for varying degrees of dependence are multivariate frailty models, which are considered in Chapter 10. Markov multi-state models and shared frailty models lead to a long-term dependence structure, that is, the whole history is important. On the other hand there can be short-term dependence (risk of an event is particularly high shortly after a previous event and fades away thereafter) and even instantaneous dependence (multiple events happen at exactly the same time). These cases are considered in Chapter 11. Approaches to handle competing risks are discussed in Chapter 12. Marginal modeling and its sensible combination with copula models is the topic of Chapter 13.

Multivariate nonparametric estimates are introduced in Chapter 14. Obviously these approaches seem to need more consideration and further experience before their routine practical use can be recommended. Chapter 15 summarizes the theory, the course of analysis and the applications.

Appendix A describes key mathematical and statistical results, which are needed for the study of the properties of frailty models: Laplace transforms, exponential families, distribution theory and some mathematical functions. Appendix B is about the Newton-Raphson iteration, its extensions and modifications, and standard error evaluation.

The intended readership are persons, who already have some experience with survival data. Throughout the book theoretical developments are extensively exemplified by real-life examples and computational aspects are dealt with as well. The book consists of 15 chapters and 2 appendices. A commendable feature is that each of the chapters starts with an intuitional introduction and ends with a brief summary section, bibliographic comments and exercises. However, there are no solutions for the latter.

Chapter 1 is a key chapter where the concepts both for simple survival data and multivariate survival data are clarified and a classification is developed that helps in finding the most appropriate model for a specific kind of data set. Chapter 2 is an introduction to standard methods for univariate survival data. Chapter 3 is another key chapter where the various mechanisms that create dependence in multivariate survival data are discussed. Chapter 4 covers bivariate dependence measures.

Multi-state models are described in Chapters 5 and 6. A multi-state model is defined as a model for a stochastic process, which at any time point occupies one of a set of discrete states. In the book the main focus is on Markov processes.

Shared frailty models are described in Chapters 7 and 8. A shared frailty model can be considered as a random effects model with two sources of variation, that is the group variation described by the frailty and the individual random variation described by the hazard function. The special case of shared frailty models for recurrent events is considered separately in Chapter 9. More general models for varying degrees of dependence are multivariate frailty models, which are considered in Chapter 10. Markov multi-state models and shared frailty models lead to a long-term dependence structure, that is, the whole history is important. On the other hand there can be short-term dependence (risk of an event is particularly high shortly after a previous event and fades away thereafter) and even instantaneous dependence (multiple events happen at exactly the same time). These cases are considered in Chapter 11. Approaches to handle competing risks are discussed in Chapter 12. Marginal modeling and its sensible combination with copula models is the topic of Chapter 13.

Multivariate nonparametric estimates are introduced in Chapter 14. Obviously these approaches seem to need more consideration and further experience before their routine practical use can be recommended. Chapter 15 summarizes the theory, the course of analysis and the applications.

Appendix A describes key mathematical and statistical results, which are needed for the study of the properties of frailty models: Laplace transforms, exponential families, distribution theory and some mathematical functions. Appendix B is about the Newton-Raphson iteration, its extensions and modifications, and standard error evaluation.

Reviewer: Harald Heinzl (Wien)

##### MSC:

62Nxx | Survival analysis and censored data |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62N01 | Censored data models |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62H99 | Multivariate analysis |