Counting processes and survival analysis. 2nd ed. (English) Zbl 1079.62093

Fleming, Thomas R.; Harrington, David P.

Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons (ISBN 0-471-76988-6/pbk). xiii, 429 p. (2005).

[For the review of the first edition from 1991 see Zbl 0727.62096).]
This book is intended as a text for graduate students and as theoretical reference for workers in probability and statistics. The prerequisite is honest calculus and one year graduate study in statistics. The text explores, theoretically and practically, the martingale approach to the statistical methods in counting processes, mainly for the case of censored data used in survival analysis. Most practitioners in applied statistics have received some mathematical background, but it will have been fairly brief and largely forgotten by time. For those wishing to discover the theory behind the practice, the book represents a valuable starting point.
Since one of the main purposes of this book is didactic, the theory behind the statistical practice is emphasized in a classical mathematical fashion. By analyzing briefly some concrete examples issued from medical fields, one arrives at an elementary axiomatic setup, followed by a description in a mathematical precise manner and an investigation in a rigorous fashion of the practical techniques. Numerous historical remarks about results, methods and techniques used in each chapter are an intrinsic part of the text. The book ends with an appendix dedicated to exercises for each chapter.
The only ‘minus’ reproachable to the book is the lack of updated references (available references from the first edition, 1991, only), but interested readers could find valuable information throughout libraries.

Reviewer: Florin Gorunescu (Craiova)

MSC:

62Nxx	Survival analysis and censored data
62M99	Inference from stochastic processes
62-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
60G46	Martingales and classical analysis
60H05	Stochastic integrals
62N01	Censored data models
62-02	Research exposition (monographs, survey articles) pertaining to statistics
60G35	Signal detection and filtering (aspects of stochastic processes)

Keywords:

martingale; counting processes; stochastic integrals; survival analysis; censored data; central limit theorem; Kaplan-Meier estimator; proportional hazards regression; log-rank statistics