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The Statistical Analysis of Recurrent Events

The Statistical Analysis of Recurrent Events
Author: Richard J. Cook
Publisher: Springer Science & Business Media
Total Pages: 415
Release: 2007-08-02
Genre: Medical
ISBN: 0387698094
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This book presents models and statistical methods for the analysis of recurrent event data. The authors provide broad, detailed coverage of the major approaches to analysis, while emphasizing the modeling assumptions that they are based on. More general intensity-based models are also considered, as well as simpler models that focus on rate or mean functions. Parametric, nonparametric and semiparametric methodologies are all covered, with procedures for estimation, testing and model checking.

Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications

Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications
Author: Wayne B. Nelson
Publisher: SIAM
Total Pages: 157
Release: 2003-01-01
Genre: Technology & Engineering
ISBN: 0898715229
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Survival data consist of a single event for each population unit, namely, end of life, which is modeled with a life distribution. However, many applications involve repeated-events data, where a unit may accumulate numerous events over time. This applied book provides practitioners with basic nonparametric methods for such data.

Statistical Analysis of Panel Count Data

Statistical Analysis of Panel Count Data
Author: Jianguo Sun
Publisher: Springer Science & Business Media
Total Pages: 283
Release: 2013-10-09
Genre: Medical
ISBN: 1461487153
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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.

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
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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.

Functional and High-Dimensional Statistics and Related Fields

Functional and High-Dimensional Statistics and Related Fields
Author: Germán Aneiros
Publisher: Springer Nature
Total Pages: 254
Release: 2020-06-19
Genre: Mathematics
ISBN: 3030477568
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This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.

The Frailty Model

The Frailty Model
Author: Luc Duchateau
Publisher: Springer Science & Business Media
Total Pages: 329
Release: 2007-10-23
Genre: Mathematics
ISBN: 038772835X
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Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.

Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications

Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications
Author: Wayne B. Nelson
Publisher: SIAM
Total Pages: 151
Release: 2003-01-01
Genre: Technology & Engineering
ISBN: 0898718457
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Survival data consist of a single event for each population unit, namely, end of life, which is modeled with a life distribution. In contrast, many applications involve repeated-events data, where a unit may accumulate any number of events over time. Examples include the number and cost of repairs of products, the number and treatment costs of recurrent disease episodes in patients, and the number of childbirths to statisticians. This applied book provides practitioners with basic nonparametric methods for such data, particularly the plot of the estimate of the population mean cumulative function (MCF), which yields most of the information sought. Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications is the first book to present a simple, unified theory that includes data on costs or other "values" of discrete events, not just the number of events. It surveys computer programs that calculate and plot the MCF estimate with confidence limits, shows their output, and explains how to interpret such plots. Many such calculations can be easily done with a pocket calculator or spreadsheet program. Also, the book introduces basic Poisson and Cox regression models and parametric models, including homogeneous and nonhomogeneous Poisson processes and renewal processes.

Survival Analysis: State of the Art

Survival Analysis: State of the Art
Author: John P. Klein
Publisher: Springer Science & Business Media
Total Pages: 446
Release: 2013-03-09
Genre: Mathematics
ISBN: 9401579830
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Survival analysis is a highly active area of research with applications spanning the physical, engineering, biological, and social sciences. In addition to statisticians and biostatisticians, researchers in this area include epidemiologists, reliability engineers, demographers and economists. The economists survival analysis by the name of duration analysis and the analysis of transition data. We attempted to bring together leading researchers, with a common interest in developing methodology in survival analysis, at the NATO Advanced Research Workshop. The research works collected in this volume are based on the presentations at the Workshop. Analysis of survival experiments is complicated by issues of censoring, where only partial observation of an individual's life length is available and left truncation, where individuals enter the study group if their life lengths exceed a given threshold time. Application of the theory of counting processes to survival analysis, as developed by the Scandinavian School, has allowed for substantial advances in the procedures for analyzing such experiments. The increased use of computer intensive solutions to inference problems in survival analysis~ in both the classical and Bayesian settings, is also evident throughout the volume. Several areas of research have received special attention in the volume.

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
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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.