Andersen P.K., Borgan Ø., Gill R.D., Keiding N. Statistical Models Based on Counting Processes

N.-Y.: Springer, 1993. - 784p.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.The Mathematical Background
Model Specification and Censoring
Nonparametric Estimation
Nonparametric Hypothesis Testing
Parametric Models
Regression Models
Asymptotic Efficiency
Frailty Models
Multivariate Time Scales