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Author: D. T. McNichols Publisher: ISBN: Category : Languages : en Pages : 21
Book Description
Nonparametric estimation of the hazard rate or failure rate is a frequent topic of investigation in the statistical literature because of its practical importance. Until quite recently, hazard rate estimation had been based on complete samples of independent identically distributed lifetimes. However, observations may be censored or truncated in many life testing situations. This occurs often in medical trials when the patients may enter treatment at different times and then either die from the disease under investigation or leave the study before its conclusion. A similar situation may occur in industrial life testing when items are removed from the test at random times for various reasons. It is of interest to be able to estimate nonparametrically the unknown hazard rate of the lifetime random variable from this type of data without ignoring or discarding the right-censored information. The purpose of this paper is to discuss nonparametric estimation of the hazard rate function for right-censored samples. The various types of estimators that have been proposed in the literature will be indicated and briefly discussed in Section 3. These include maximum likelihood estimators, kernel type estimators, Bayesian estimators, and histogram estimators. Due to their computational simplicity and other properties, the kernel-type hazard rate estimators will be emphasized. Results of Tanner (1983) and Tanner and Wong (1983, 1984) will be presented in Section 4 while the estimator considered by McNichols and Padgett (1981) will be discussed in Section 5.
Author: D. T. McNichols Publisher: ISBN: Category : Languages : en Pages : 21
Book Description
Nonparametric estimation of the hazard rate or failure rate is a frequent topic of investigation in the statistical literature because of its practical importance. Until quite recently, hazard rate estimation had been based on complete samples of independent identically distributed lifetimes. However, observations may be censored or truncated in many life testing situations. This occurs often in medical trials when the patients may enter treatment at different times and then either die from the disease under investigation or leave the study before its conclusion. A similar situation may occur in industrial life testing when items are removed from the test at random times for various reasons. It is of interest to be able to estimate nonparametrically the unknown hazard rate of the lifetime random variable from this type of data without ignoring or discarding the right-censored information. The purpose of this paper is to discuss nonparametric estimation of the hazard rate function for right-censored samples. The various types of estimators that have been proposed in the literature will be indicated and briefly discussed in Section 3. These include maximum likelihood estimators, kernel type estimators, Bayesian estimators, and histogram estimators. Due to their computational simplicity and other properties, the kernel-type hazard rate estimators will be emphasized. Results of Tanner (1983) and Tanner and Wong (1983, 1984) will be presented in Section 4 while the estimator considered by McNichols and Padgett (1981) will be discussed in Section 5.
Author: W. J. Padgett Publisher: ISBN: Category : Languages : en Pages : 33
Book Description
The purpose of this article is to present the different types of nonparametric density estimates that have been proposed for the situation that the sample data are censored or incomplete. This type of data arises in many life testing situations and is common in survival analysis problems. Many of the methods of nonparametric density and hazard rate estimation from right-censored observations are discussed. These include histogram and kernel-type procedures, likelihood methods, Fourier series methods, and Bayesian nonparametric approaches. Examples of kernel density estimates are given for mechanical switch life data where data-based choices of the bandwidth values are used. Originator-supplied keywords included: Nonparametric density estimation; Random censorship; Failure rate; Kernel density estimator; Likelihood methods.
Author: Jufen Chu Publisher: ISBN: Category : Censored observations (Statistics) Languages : en Pages : 186
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: Sam Efromovich Publisher: CRC Press ISBN: 135167983X Category : Mathematics Languages : en Pages : 867
Book Description
This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.
Author: John P. Klein Publisher: Springer Science & Business Media ISBN: 1475727283 Category : Medical Languages : en Pages : 508
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: Sam Efromovich Publisher: Springer Science & Business Media ISBN: 0387226389 Category : Mathematics Languages : en Pages : 423
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: Md. Rezaul Karim Publisher: Springer ISBN: 9811397767 Category : Medical Languages : en Pages : 259
Book Description
This book presents and standardizes statistical models and methods that can be directly applied to both reliability and survival analysis. These two types of analysis are widely used in many fields, including engineering, management, medicine, actuarial science, the environmental sciences, and the life sciences. Though there are a number of books on reliability analysis and a handful on survival analysis, there are virtually no books on both topics and their overlapping concepts. Offering an essential textbook, this book will benefit students, researchers, and practitioners in reliability and survival analysis, reliability engineering, biostatistics, and the biomedical sciences.
Author: Jun Ma Publisher: CRC Press ISBN: 1351109707 Category : Mathematics Languages : en Pages : 401
Book Description
Many conventional survival analysis methods, such as the Kaplan-Meier method for survival function estimation and the partial likelihood method for Cox model regression coefficients estimation, were developed under the assumption that survival times are subject to right censoring only. However, in practice, survival time observations may include interval-censored data, especially when the exact time of the event of interest cannot be observed. When interval-censored observations are present in a survival dataset, one generally needs to consider likelihood-based methods for inference. If the survival model under consideration is fully parametric, then likelihood-based methods impose neither theoretical nor computational challenges. However, if the model is semi-parametric, there will be difficulties in both theoretical and computational aspects. Likelihood Methods in Survival Analysis: With R Examples explores these challenges and provides practical solutions. It not only covers conventional Cox models where survival times are subject to interval censoring, but also extends to more complicated models, such as stratified Cox models, extended Cox models where time-varying covariates are present, mixture cure Cox models, and Cox models with dependent right censoring. The book also discusses non-Cox models, particularly the additive hazards model and parametric log-linear models for bivariate survival times where there is dependence among competing outcomes. Features Provides a broad and accessible overview of likelihood methods in survival analysis Covers a wide range of data types and models, from the semi-parametric Cox model with interval censoring through to parametric survival models for competing risks Includes many examples using real data to illustrate the methods Includes integrated R code for implementation of the methods Supplemented by a GitHub repository with datasets and R code The book will make an ideal reference for researchers and graduate students of biostatistics, statistics, and data science, whose interest in survival analysis extend beyond applications. It offers useful and solid training to those who wish to enhance their knowledge in the methodology and computational aspects of biostatistics.
Author: John P. Klein Publisher: CRC Press ISBN: 146655567X Category : Mathematics Languages : en Pages : 635
Book Description
Handbook of Survival Analysis presents modern techniques and research problems in lifetime data analysis. This area of statistics deals with time-to-event data that is complicated by censoring and the dynamic nature of events occurring in time. With chapters written by leading researchers in the field, the handbook focuses on advances in survival analysis techniques, covering classical and Bayesian approaches. It gives a complete overview of the current status of survival analysis and should inspire further research in the field. Accessible to a wide range of readers, the book provides: An introduction to various areas in survival analysis for graduate students and novices A reference to modern investigations into survival analysis for more established researchers A text or supplement for a second or advanced course in survival analysis A useful guide to statistical methods for analyzing survival data experiments for practicing statisticians
Author: D. T. McNichols
Author: D. T. McNichols
Author: W. J. Padgett
Author: Jufen Chu
Author: Sam Efromovich
Author: John P. Klein
Author: Sam Efromovich
Author: Md. Rezaul Karim
Author: Hira L. Koul
Author: Jun Ma
Author: John P. Klein