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Statistical Analysis of Counting Processes

M. Jacobsen

Author : M. Jacobsen
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468462753

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Statistical Analysis of Counting Processes by M. Jacobsen Pdf

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 Based on Counting Processes

Per K. Andersen,Ornulf Borgan,Richard D. Gill,Niels Keiding

Author : Per K. Andersen,Ornulf Borgan,Richard D. Gill,Niels Keiding
Publisher : Springer Science & Business Media
Page : 779 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461243489

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Statistical Models Based on Counting Processes by Per K. Andersen,Ornulf Borgan,Richard D. Gill,Niels Keiding Pdf

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.

Counting Processes and Survival Analysis

Thomas R. Fleming,David P. Harrington

Author : Thomas R. Fleming,David P. Harrington
Publisher : John Wiley & Sons
Page : 466 pages
File Size : 47,6 Mb
Release : 2013-08-12
Category : Mathematics
ISBN : 9780471769880

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Counting Processes and Survival Analysis by Thomas R. Fleming,David P. Harrington Pdf

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.

Counting Processes and Survival Analysis

Thomas R. Fleming,David P. Harrington

Author : Thomas R. Fleming,David P. Harrington
Publisher : John Wiley & Sons
Page : 454 pages
File Size : 47,8 Mb
Release : 2011-09-20
Category : Mathematics
ISBN : 9781118150665

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Counting Processes and Survival Analysis by Thomas R. Fleming,David P. Harrington Pdf

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.

Mathematical Statistics and Probability Theory

W. Klonecki,A. Kozek,J. Rosinski

Author : W. Klonecki,A. Kozek,J. Rosinski
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461573975

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Mathematical Statistics and Probability Theory by W. Klonecki,A. Kozek,J. Rosinski Pdf

Since 1972 the Institute of Mathematics and the Committee of Mathematics of the Polish Academy of Sciences organize annually con ferences on mathematical statistics in Wisla. The 1978 conference, supported also by the University of Wroclaw,was held in Wisla from December 7 to December 13 and attended by around 100 participants from 11 countries. K. Urbanik, Rector of the University of Wroclaw, was the honorary chairman of the conference. Traditionally at these conferences there are presented results on mathematical statistics and related fields obtained in Poland during the year of the conference as well as results presented by invited scholars from other countries. In 1978 invitations to present talks were accepted by 20 e~inent statisticians and probabilists. The topics of the invited lectures and contributed papers included theoretical statistics with a broad cover of the theory of linear models, inferences from stochastic processes, probability theory and applications to biology and medicine. In these notes there appear papers submitted by 30 participants of the conference. During the conference, on December 9, there was held a special session of the Polish Mathematical Society on the occasion of elect ing Professor Jerzy Neyman the honorary member of the Polish Mathematical Society. At this session W. Orlicz, president of the Polish Mathematical Society, K.Krickeberg,president of the Bernoulli Society. R. Bartoszynski and K. Doksum gave talks on Neyman IS con tribution to statistics, his organizational achievements in the U.S.

Survival and Event History Analysis

Odd Aalen,Ornulf Borgan,Hakon Gjessing

Author : Odd Aalen,Ornulf Borgan,Hakon Gjessing
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 46,5 Mb
Release : 2008-09-16
Category : Mathematics
ISBN : 9780387685601

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Survival and Event History Analysis by Odd Aalen,Ornulf Borgan,Hakon Gjessing Pdf

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.

The Statistical Analysis of Failure Time Data

John D. Kalbfleisch,Ross L. Prentice

Author : John D. Kalbfleisch,Ross L. Prentice
Publisher : John Wiley & Sons
Page : 462 pages
File Size : 45,8 Mb
Release : 2011-01-25
Category : Mathematics
ISBN : 9781118031230

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The Statistical Analysis of Failure Time Data by John D. Kalbfleisch,Ross L. Prentice Pdf

Contains additional discussion and examples on left truncationas well as material on more general censoring and truncationpatterns. Introduces the martingale and counting process formulation swillbe in a new chapter. Develops multivariate failure time data in a separate chapterand extends the material on Markov and semi Markovformulations. Presents new examples and applications of data analysis.

The Statistical Analysis of Interval-censored Failure Time Data

Jianguo Sun

Author : Jianguo Sun
Publisher : Springer
Page : 304 pages
File Size : 48,6 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9780387371191

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The Statistical Analysis of Interval-censored Failure Time Data by Jianguo Sun Pdf

This book collects and unifies statistical models and methods that have been proposed for analyzing interval-censored failure time data. It provides the first comprehensive coverage of the topic of interval-censored data and complements the books on right-censored data. The focus of the book is on nonparametric and semiparametric inferences, but it also describes parametric and imputation approaches. This book provides an up-to-date reference for people who are conducting research on the analysis of interval-censored failure time data as well as for those who need to analyze interval-censored data to answer substantive questions.

Statistical Analysis of Panel Count Data

Jianguo Sun,Xingqiu Zhao

Author : Jianguo Sun,Xingqiu Zhao
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 51,5 Mb
Release : 2013-10-09
Category : Medical
ISBN : 9781461487159

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Statistical Analysis of Panel Count Data by Jianguo Sun,Xingqiu Zhao Pdf

Panel count data occur in studies that concern recurrent events, or event history studies, when study subjects are observed only at discrete time points. By recurrent events, we mean the event that can occur or happen multiple times or repeatedly. Examples of recurrent events include disease infections, hospitalizations in medical studies, warranty claims of automobiles or system break-downs in reliability studies. In fact, many other fields yield event history data too such as demographic studies, economic studies and social sciences. For the cases where the study subjects are observed continuously, the resulting data are usually referred to as recurrent event data. This book collects and unifies statistical models and methods that have been developed for analyzing panel count data. It provides the first comprehensive coverage of the topic. The main focus is on methodology, but for the benefit of the reader, the applications of the methods to real data are also discussed along with numerical calculations. There exists a great deal of literature on the analysis of recurrent event data. This book fills the void in the literature on the analysis of panel count data. This book provides an up-to-date reference for scientists who are conducting research on the analysis of panel count data. It will also be instructional for those who need to analyze panel count data to answer substantive research questions. In addition, it can be used as a text for a graduate course in statistics or biostatistics that assumes a basic knowledge of probability and statistics.

Modeling Survival Data: Extending the Cox Model

Terry M. Therneau,Patricia M. Grambsch

Author : Terry M. Therneau,Patricia M. Grambsch
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 54,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475732948

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Modeling Survival Data: Extending the Cox Model by Terry M. Therneau,Patricia M. Grambsch Pdf

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.

The Statistical Analysis of Failure Time Data

John D. Kalbfleisch,Ross L. Prentice

Author : John D. Kalbfleisch,Ross L. Prentice
Publisher : Wiley-Interscience
Page : 344 pages
File Size : 48,5 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015012442854

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The Statistical Analysis of Failure Time Data by John D. Kalbfleisch,Ross L. Prentice Pdf

Failure time models; Inference in parametric models and related topics; The proportional hazards model; Likelihood construction and further results on the proportional hazards model; Inference based on ranks in the accelerated failure time model; Multivariate failure time data and competing risks; Miscellaneous topics.

Random Point Processes in Time and Space

Donald L. Snyder,Michael I. Miller

Author : Donald L. Snyder,Michael I. Miller
Publisher : Springer Science & Business Media
Page : 489 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461231660

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Random Point Processes in Time and Space by Donald L. Snyder,Michael I. Miller Pdf

This book is a revision of Random Point Processes written by D. L. Snyder and published by John Wiley and Sons in 1975. More emphasis is given to point processes on multidimensional spaces, especially to pro cesses in two dimensions. This reflects the tremendous increase that has taken place in the use of point-process models for the description of data from which images of objects of interest are formed in a wide variety of scientific and engineering disciplines. A new chapter, Translated Poisson Processes, has been added, and several of the chapters of the fIrst edition have been modifIed to accommodate this new material. Some parts of the fIrst edition have been deleted to make room. Chapter 7 of the fIrst edition, which was about general marked point-processes, has been eliminated, but much of the material appears elsewhere in the new text. With some re luctance, we concluded it necessary to eliminate the topic of hypothesis testing for point-process models. Much of the material of the fIrst edition was motivated by the use of point-process models in applications at the Biomedical Computer Labo ratory of Washington University, as is evident from the following excerpt from the Preface to the first edition. "It was Jerome R. Cox, Jr. , founder and [1974] director of Washington University's Biomedical Computer Laboratory, who ftrst interested me [D. L. S.

基于计数过程的统计模型

Anonim

Author : Anonim
Publisher : Unknown
Page : 767 pages
File Size : 42,6 Mb
Release : 1998
Category : Point processes
ISBN : 7506238179

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基于计数过程的统计模型 by Anonim Pdf

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.

Stochastic Epidemic Models and Their Statistical Analysis

Hakan Andersson,Tom Britton

Author : Hakan Andersson,Tom Britton
Publisher : Springer Science & Business Media
Page : 140 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211587

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Stochastic Epidemic Models and Their Statistical Analysis by Hakan Andersson,Tom Britton Pdf

The present lecture notes describe stochastic epidemic models and methods for their statistical analysis. Our aim is to present ideas for such models, and methods for their analysis; along the way we make practical use of several probabilistic and statistical techniques. This will be done without focusing on any specific disease, and instead rigorously analyzing rather simple models. The reader of these lecture notes could thus have a two-fold purpose in mind: to learn about epidemic models and their statistical analysis, and/or to learn and apply techniques in probability and statistics. The lecture notes require an early graduate level knowledge of probability and They introduce several techniques which might be new to students, but our statistics. intention is to present these keeping the technical level at a minlmum. Techniques that are explained and applied in the lecture notes are, for example: coupling, diffusion approximation, random graphs, likelihood theory for counting processes, martingales, the EM-algorithm and MCMC methods. The aim is to introduce and apply these techniques, thus hopefully motivating their further theoretical treatment. A few sections, mainly in Chapter 5, assume some knowledge of weak convergence; we hope that readers not familiar with this theory can understand the these parts at a heuristic level. The text is divided into two distinct but related parts: modelling and estimation.

Statistical Inference in Stochastic Processes

N.U. Prabhu

Author : N.U. Prabhu
Publisher : CRC Press
Page : 289 pages
File Size : 55,9 Mb
Release : 2020-08-13
Category : Mathematics
ISBN : 9781000104530

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Statistical Inference in Stochastic Processes by N.U. Prabhu Pdf

Covering both theory and applications, this collection of eleven contributed papers surveys the role of probabilistic models and statistical techniques in image analysis and processing, develops likelihood methods for inference about parameters that determine the drift and the jump mechanism of a di

Statistical Analysis Of Counting Processes

Statistical Analysis of Counting Processes by M. Jacobsen Pdf

Statistical Models Based on Counting Processes by Per K. Andersen,Ornulf Borgan,Richard D. Gill,Niels Keiding Pdf

Counting Processes and Survival Analysis by Thomas R. Fleming,David P. Harrington Pdf

Counting Processes and Survival Analysis by Thomas R. Fleming,David P. Harrington Pdf

Mathematical Statistics and Probability Theory by W. Klonecki,A. Kozek,J. Rosinski Pdf

Survival and Event History Analysis by Odd Aalen,Ornulf Borgan,Hakon Gjessing Pdf

The Statistical Analysis of Failure Time Data by John D. Kalbfleisch,Ross L. Prentice Pdf

The Statistical Analysis of Interval-censored Failure Time Data by Jianguo Sun Pdf

Statistical Analysis of Panel Count Data by Jianguo Sun,Xingqiu Zhao Pdf

Modeling Survival Data: Extending the Cox Model by Terry M. Therneau,Patricia M. Grambsch Pdf

The Statistical Analysis of Failure Time Data by John D. Kalbfleisch,Ross L. Prentice Pdf

Random Point Processes in Time and Space by Donald L. Snyder,Michael I. Miller Pdf

基于计数过程的统计模型 by Anonim Pdf

Stochastic Epidemic Models and Their Statistical Analysis by Hakan Andersson,Tom Britton Pdf

Statistical Inference in Stochastic Processes by N.U. Prabhu Pdf

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