Statistical Models Based on Counting Processes

Statistical Models Based on Counting Processes
Author: PER KRAGH ANDERSEN
Publisher: Springer Science & Business Media
Total Pages: 785
Release: 1996-12-20
Genre: Mathematics
ISBN: 0387945199

Modern survival analysis and more general event history analysis may be effectively handled within the mathematical framework of counting processes. This book presents this theory, which has been the subject of intense research activity over the past 15 years. The exposition of the theory is integrated with careful presentation of many practical examples, drawn almost exclusively from the authors'own experience, with detailed numerical and graphical illustrations. Although Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, almost all the methods are given in concrete detail for use in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliability 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.

Statistical Models Based on Counting Processes

Statistical Models Based on Counting Processes
Author: Per K. Andersen
Publisher: Springer Science & Business Media
Total Pages: 779
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461243483

Modern survival analysis and more general event history analysis may be effectively handled within the mathematical framework of counting processes. This book presents this theory, which has been the subject of intense research activity over the past 15 years. The exposition of the theory is integrated with careful presentation of many practical examples, drawn almost exclusively from the authors'own experience, with detailed numerical and graphical illustrations. Although Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, almost all the methods are given in concrete detail for use in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliability 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.

Statistical Analysis of Counting Processes

Statistical Analysis of Counting Processes
Author: M. Jacobsen
Publisher: Springer Science & Business Media
Total Pages: 235
Release: 2012-12-06
Genre: Mathematics
ISBN: 146846275X

A first version of these lecture notes was prepared for a course given in 1980 at the University of Copenhagen to a class of graduate students in mathematical statistics. A thorough revision has led to the result presented here. The main topic of the notes is the theory of multiplicative intens ity models for counting processes, first introduced by Odd Aalen in his Ph.D. thesis from Berkeley 1975, and in a subsequent fundamental paper in the Annals of Statistics 1978. In Copenhagen the interest in statistics on counting processes was sparked by a visit by Odd Aalen in 1976. At present the activities here are centered around Niels Keiding and his group at the Statistical Re search Unit. The Aalen theory is a fine example of how advanced probability theory may be used to develop a povlerful, and for applications very re levant, statistical technique. Aalen's work relies quite heavily on the 'theorie generale des processus' developed primarily by the French school of probability the ory. But the general theory aims at much more general and profound re sults, than what is required to deal with objects of such a relatively simple structure as counting processes on the line. Since also this process theory is virtually inaccessible to non-probabilists, it would appear useful to have an account of what Aalen has done, that includes exactly the amount of probability required to deal satisfactorily and rigorously with statistical models for counting processes.

Statistical Models and Methods for Lifetime Data

Statistical Models and Methods for Lifetime Data
Author: Jerald F. Lawless
Publisher: John Wiley & Sons
Total Pages: 662
Release: 2011-01-25
Genre: Mathematics
ISBN: 1118031253

Praise for the First Edition "An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . ." -Choice "This is an important book, which will appeal to statisticians working on survival analysis problems." -Biometrics "A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook." -Statistics in Medicine The statistical analysis of lifetime or response time data is a key tool in engineering, medicine, and many other scientific and technological areas. This book provides a unified treatment of the models and statistical methods used to analyze lifetime data. Equally useful as a reference for individuals interested in the analysis of lifetime data and as a text for advanced students, Statistical Models and Methods for Lifetime Data, Second Edition provides broad coverage of the area without concentrating on any single field of application. Extensive illustrations and examples drawn from engineering and the biomedical sciences provide readers with a clear understanding of key concepts. New and expanded coverage in this edition includes: * Observation schemes for lifetime data * Multiple failure modes * Counting process-martingale tools * Both special lifetime data and general optimization software * Mixture models * Treatment of interval-censored and truncated data * Multivariate lifetimes and event history models * Resampling and simulation methodology

Statistical Models and Control Charts for High-Quality Processes

Statistical Models and Control Charts for High-Quality Processes
Author: Min Xie
Publisher: Springer Science & Business Media
Total Pages: 282
Release: 2012-12-06
Genre: Business & Economics
ISBN: 1461510155

Control charts are widely used in industry to monitor processes that are far from Zero-Defect (ZD), and their use in a near Zero-Defect manufacturing environment poses many problems. This book presents techniques of using control charts for high-quality processes, and some recent findings and applications of statistical control chart techniques for ZD processes are presented. A powerful technique based on counting of the cumulative conforming (CCC) items between two nonconforming ones is discussed in detail. Extensions of the CCC chart are described, as well as applications of cumulative sum and exponentially weighted moving average techniques to CCC-related data, multivariate methods, economic design of control chart procedures, and modeling and analysis of trended but regularly adjusted processes. Many examples, charts, and procedures, are presented throughout the book, and references are provided for those interested in exploring the details. A number of questions and issues are posed for further investigations. Researchers and students may find many ideas in this book useful in their academic work, as a foundation is laid for the exploration of many further theoretical and practical issues.

Survival and Event History Analysis

Survival and Event History Analysis
Author: Odd Aalen
Publisher: Springer Science & Business Media
Total Pages: 550
Release: 2008-09-16
Genre: Mathematics
ISBN: 038768560X

The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.

Counting Processes and Survival Analysis

Counting Processes and Survival Analysis
Author: Thomas R. Fleming
Publisher: John Wiley & Sons
Total Pages: 454
Release: 2011-09-20
Genre: Mathematics
ISBN: 111815066X

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "The book is a valuable completion of the literature in this field. It is written in an ambitious mathematical style and can be recommended to statisticians as well as biostatisticians." -Biometrische Zeitschrift "Not many books manage to combine convincingly topics from probability theory over mathematical statistics to applied statistics. This is one of them. The book has other strong points to recommend it: it is written with meticulous care, in a lucid style, general results being illustrated by examples from statistical theory and practice, and a bunch of exercises serve to further elucidate and elaborate on the text." -Mathematical Reviews "This book gives a thorough introduction to martingale and counting process methods in survival analysis thereby filling a gap in the literature." -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts "The authors have performed a valuable service to researchers in providing this material in [a] self-contained and accessible form. . . This text [is] essential reading for the probabilist or mathematical statistician working in the area of survival analysis." -Short Book Reviews, International Statistical Institute Counting Processes and Survival Analysis explores the martingale approach to the statistical analysis of counting processes, with an emphasis on the application of those methods to censored failure time data. This approach has proven remarkably successful in yielding results about statistical methods for many problems arising in censored data. A thorough treatment of the calculus of martingales as well as the most important applications of these methods to censored data is offered. Additionally, the book examines classical problems in asymptotic distribution theory for counting process methods and newer methods for graphical analysis and diagnostics of censored data. Exercises are included to provide practice in applying martingale methods and insight into the calculus itself.

基于计数过程的统计模型

基于计数过程的统计模型
Author:
Publisher:
Total Pages: 767
Release: 1998
Genre: Point processes
ISBN: 9787506238175

The aim of the book is to present a theory for handling such statistical problems, when observation is assumed to happen in continuous time. In most of the book, a minimum of assumptions are made(non- and semiparametric theory), although one chapter considers parametric models.

Modeling Survival Data: Extending the Cox Model

Modeling Survival Data: Extending the Cox Model
Author: Terry M. Therneau
Publisher: Springer Science & Business Media
Total Pages: 356
Release: 2013-11-11
Genre: Mathematics
ISBN: 1475732945

This book is for statistical practitioners, particularly those who design and analyze studies for survival and event history data. Building on recent developments motivated by counting process and martingale theory, it shows the reader how to extend the Cox model to analyze multiple/correlated event data using marginal and random effects. The focus is on actual data examples, the analysis and interpretation of results, and computation. The book shows how these new methods can be implemented in SAS and S-Plus, including computer code, worked examples, and data sets.