Statistical Models Based on Counting Processes

Klappentext

Modern survival analysis and more general event history analysis may be effectively handled in the mathematical framework of counting processes, stochastic integration, martingale central limit theory and product integration. This book presents this theory, which has been the subject of an intense research activity during the past one-and-a- half decades. The exposition of the theory is integrated with careful presentation of many practical examples, almost exclusively from the authors' own experience, with detailed numerical and graphical illustrations. Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, although almost all methods are given in concrete detail to be used in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliabilty engineers and biologists). Much of the material has so far only been available in the journal literature (if at all), and so a wide variety of researchers will find this an invaluable survey of the subject."This book is a masterful account of the counting process approach...is certain to be the standard reference for the area, and should be on the bookshelf of anyone interested in event-history analysis." International Statistical Institute Short Book Reviews "...this impressive reference, which contains a a wealth of powerful mathematics, practical examples, and analytic insights, as well as a complete integration of historical developments and recent advances in event history analysis." Journal of the American Statistical Association

Inhalt

Contents: Introduction.- The mathematical background.- Model specification and censoring.- Nonparametric estimation.- Nonparametric hypothesis testing.- Parametric models.- Regression models.- Asymptotic efficiency.- Frailty models.- Multivariate time scales.- Appendix: The melanoma survival data and standard mortality tables for the Danish population 1971-75.