Nonparametric Hazard Rate Estimation with Left Truncated and Right Censored Data PDF Download
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Author: Jufen Chu
Publisher:
ISBN:
Category : Censored observations (Statistics)
Languages : en
Pages : 186
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Book Description
Nonparametric estimation of the hazard rate function, based on data modified by left truncation and/or right censoring, is considered. The hazard rate is not integrable over its support and hence it is traditionally estimated over a fixed interval under the mean integrated squared error (MISE) criterion. It is well known in the literature that neither left truncation nor right censoring affect the rate of the MISE convergence, but so far no results on how the modified data and the interval of estimation affect the MISE convergence have been known. To understand the affect, asymptotic theory of sharp minimax estimation is developed which indicates how the modified data and the interval of estimation affect the MISE convergence. The theory is complemented by presenting a data-driven estimator for small samples which is tested on numerical simulations and real data.
Author: Jufen Chu
Publisher:
ISBN:
Category : Censored observations (Statistics)
Languages : en
Pages : 186
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Book Description
Nonparametric estimation of the hazard rate function, based on data modified by left truncation and/or right censoring, is considered. The hazard rate is not integrable over its support and hence it is traditionally estimated over a fixed interval under the mean integrated squared error (MISE) criterion. It is well known in the literature that neither left truncation nor right censoring affect the rate of the MISE convergence, but so far no results on how the modified data and the interval of estimation affect the MISE convergence have been known. To understand the affect, asymptotic theory of sharp minimax estimation is developed which indicates how the modified data and the interval of estimation affect the MISE convergence. The theory is complemented by presenting a data-driven estimator for small samples which is tested on numerical simulations and real data.
Author: Wei Pan
Publisher:
ISBN:
Category :
Languages : en
Pages : 224
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Book Description
Author: John P. Klein
Publisher: Springer Science & Business Media
ISBN: 1475727283
Category : Medical
Languages : en
Pages : 508
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Book Description
Making complex methods more accessible to applied researchers without an advanced mathematical background, the authors present the essence of new techniques available, as well as classical techniques, and apply them to data. Practical suggestions for implementing the various methods are set off in a series of practical notes at the end of each section, while technical details of the derivation of the techniques are sketched in the technical notes. This book will thus be useful for investigators who need to analyse censored or truncated life time data, and as a textbook for a graduate course in survival analysis, the only prerequisite being a standard course in statistical methodology.
Author: Mara Tableman
Publisher: CRC Press
ISBN: 0203501411
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Survival Analysis Using S: Analysis of Time-to-Event Data is designed as a text for a one-semester or one-quarter course in survival analysis for upper-level or graduate students in statistics, biostatistics, and epidemiology. Prerequisites are a standard pre-calculus first course in probability and statistics, and a course in applied linear regression models. No prior knowledge of S or R is assumed. A wide choice of exercises is included, some intended for more advanced students with a first course in mathematical statistics. The authors emphasize parametric log-linear models, while also detailing nonparametric procedures along with model building and data diagnostics. Medical and public health researchers will find the discussion of cut point analysis with bootstrap validation, competing risks and the cumulative incidence estimator, and the analysis of left-truncated and right-censored data invaluable. The bootstrap procedure checks robustness of cut point analysis and determines cut point(s). In a chapter written by Stephen Portnoy, censored regression quantiles - a new nonparametric regression methodology (2003) - is developed to identify important forms of population heterogeneity and to detect departures from traditional Cox models. By generalizing the Kaplan-Meier estimator to regression models for conditional quantiles, this methods provides a valuable complement to traditional Cox proportional hazards approaches.
Author: Hongsheng Dai
Publisher: Academic Press
ISBN: 0081010087
Category : Mathematics
Languages : en
Pages : 104
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Book Description
Survival Analysis for Bivariate Truncated Data provides readers with a comprehensive review on the existing works on survival analysis for truncated data, mainly focusing on the estimation of univariate and bivariate survival function. The most distinguishing feature of survival data is known as censoring, which occurs when the survival time can only be exactly observed within certain time intervals. A second feature is truncation, which is often deliberate and usually due to selection bias in the study design. Truncation presents itself in different ways. For example, left truncation, which is often due to a so-called late entry bias, occurs when individuals enter a study at a certain age and are followed from this delayed entry time. Right truncation arises when only individuals who experienced the event of interest before a certain time point can be observed. Analyzing truncated survival data without considering the potential selection bias may lead to seriously biased estimates of the time to event of interest and the impact of risk factors. - Assists statisticians, epidemiologists, medical researchers, and actuaries who need to understand the mechanism of selection bias - Reviews existing works on survival analysis for truncated data, mainly focusing on the estimation of univariate and bivariate survival function - Offers a guideline for analyzing truncated survival data
Author: Sam Efromovich
Publisher: Springer Science & Business Media
ISBN: 0387226389
Category : Mathematics
Languages : en
Pages : 423
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Book Description
This book gives a systematic, comprehensive, and unified account of modern nonparametric statistics of density estimation, nonparametric regression, filtering signals, and time series analysis. The companion software package, available over the Internet, brings all of the discussed topics into the realm of interactive research. Virtually every claim and development mentioned in the book is illustrated with graphs which are available for the reader to reproduce and modify, making the material fully transparent and allowing for complete interactivity.
Author: John P. Klein
Publisher: Springer Science & Business Media
ISBN: 0387216456
Category : Medical
Languages : en
Pages : 538
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Book Description
Applied statisticians in many fields must frequently analyze time to event data. While the statistical tools presented in this book are applicable to data from medicine, biology, public health, epidemiology, engineering, economics, and demography, the focus here is on applications of the techniques to biology and medicine. The analysis of survival experiments is complicated by issues of censoring, where an individual's life length is known to occur only in a certain period of time, and by truncation, where individuals enter the study only if they survive a sufficient length of time or individuals are included in the study only if the event has occurred by a given date. The use of counting process methodology has allowed for substantial advances in the statistical theory to account for censoring and truncation in survival experiments. This book makes these complex methods more accessible to applied researchers without an advanced mathematical background. The authors present the essence of these techniques, as well as classical techniques not based on counting processes, and apply them to data. Practical suggestions for implementing the various methods are set off in a series of Practical Notes at the end of each section. Technical details of the derivation of the techniques are sketched in a series of Technical Notes. This book will be useful for investigators who need to analyze censored or truncated life time data, and as a textbook for a graduate course in survival analysis. The prerequisite is a standard course in statistical methodology.
Author: Hira L. Koul
Publisher: IMS
ISBN: 9780940600393
Category : Censored observations (Statistics)
Languages : en
Pages : 310
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Book Description
Author: Will Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
Motivated from lung cancer study data, we consider a model is an observable variable and Z is a hidden variable contaminated in X = Z + E, where X X with a measurement error E. Such a model can also apply to studies in microfluorimetry, electrophoresis, biostatistics, and some other fields, where the measurements Z cannot be observed directly. The objective of this project is to estimate the hazard rate of the unobservable survival time Z in a lung cancer study. Assuming the additive measurement error E has a known distribution, we combine deconvolution kernel density estimation and inverse-probability of-censoring weighting methods to formulate a nonparametric hazard rate estimator based on random right-censored observations of X, when the distribution of X is unknown. Simulation studies show that the estimator performs well when sample sizes are relatively large.
Author: Stuart A. Klugman
Publisher: John Wiley & Sons
ISBN: 0470391332
Category : Business & Economics
Languages : en
Pages : 758
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Book Description
An update of one of the most trusted books on constructing and analyzing actuarial models Written by three renowned authorities in the actuarial field, Loss Models, Third Edition upholds the reputation for excellence that has made this book required reading for the Society of Actuaries (SOA) and Casualty Actuarial Society (CAS) qualification examinations. This update serves as a complete presentation of statistical methods for measuring risk and building models to measure loss in real-world events. This book maintains an approach to modeling and forecasting that utilizes tools related to risk theory, loss distributions, and survival models. Random variables, basic distributional quantities, the recursive method, and techniques for classifying and creating distributions are also discussed. Both parametric and non-parametric estimation methods are thoroughly covered along with advice for choosing an appropriate model. Features of the Third Edition include: Extended discussion of risk management and risk measures, including Tail-Value-at-Risk (TVaR) New sections on extreme value distributions and their estimation Inclusion of homogeneous, nonhomogeneous, and mixed Poisson processes Expanded coverage of copula models and their estimation Additional treatment of methods for constructing confidence regions when there is more than one parameter The book continues to distinguish itself by providing over 400 exercises that have appeared on previous SOA and CAS examinations. Intriguing examples from the fields of insurance and business are discussed throughout, and all data sets are available on the book's FTP site, along with programs that assist with conducting loss model analysis. Loss Models, Third Edition is an essential resource for students and aspiring actuaries who are preparing to take the SOA and CAS preliminary examinations. It is also a must-have reference for professional actuaries, graduate students in the actuarial field, and anyone who works with loss and risk models in their everyday work. To explore our additional offerings in actuarial exam preparation visit www.wiley.com/go/actuarialexamprep.
