Statistical Models Based on Counting Processes

TLDR

Modern survival and event history analysis can be effectively handled using counting processes, stochastic integration, martingale CLT, and product integration. The book aims to present this theory, developed over the past decade and a half, as a comprehensive monograph for mathematical statisticians and related researchers. It integrates theory with numerous practical examples, detailed numerical and graphical illustrations, and extensive applications drawn from the authors' experience. The book compiles material previously scattered in journal literature into a single, invaluable survey for researchers across multiple disciplines.

Abstract

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 the careful presentation of many practical examples, based almost exlusively on the authors' 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 sufficient detail to be used in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuariala mathematicians, reliability engineers, biologists). Much of the material has so far only been available in the journal literature (if at all), and a wide variety of researchers will find this an invlauable survey of the subject.