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| Author | : Wei Wang |
| Publisher | : |
| Total Pages | : 266 |
| Release | : 2001 |
| Genre | : |
| ISBN | : |
| Author | : Dimitris Rizopoulos |
| Publisher | : CRC Press |
| Total Pages | : 279 |
| Release | : 2012-06-22 |
| Genre | : Mathematics |
| ISBN | : 1439872864 |
In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest, e.g., prostate cancer studies where longitudinal PSA level measurements are collected in conjunction with the time-to-recurrence. Joint Models for Longitudinal and Time-to-Event Data: With Applications in R provides a full treatment of random effects joint models for longitudinal and time-to-event outcomes that can be utilized to analyze such data. The content is primarily explanatory, focusing on applications of joint modeling, but sufficient mathematical details are provided to facilitate understanding of the key features of these models. All illustrations put forward can be implemented in the R programming language via the freely available package JM written by the author. All the R code used in the book is available at: http://jmr.r-forge.r-project.org/
| Author | : Roger Alan Erich |
| Publisher | : |
| Total Pages | : |
| Release | : 2012 |
| Genre | : |
| ISBN | : |
Abstract: In this research, we develop innovative regression models for survival analysis that model time to event data using a latent health process which stabilizes around an equilibrium point; a characteristic often observed in biological systems. Regression modeling in survival analysis is typically accomplished using Cox regression, which requires the assumption of proportional hazards. An alternative model, which does not require proportional hazards, is the First Hitting Time (FHT) model where a subject's health is modeled using a latent stochastic process. In this modeling framework, an event occurs once the process hits a predetermined boundary. The parameters of the process are related to covariates through generalized link functions thereby providing regression coefficients with clinically meaningful interpretations. In this dissertation, we present an FHT model based on the Ornstein-Uhlenbeck (OU) process; a modified Wiener process which drifts from the starting value of the process toward a state of equilibrium or homeostasis present in many biological applications. We extend previous OU process models to allow the process to change according to covariate values. We also discuss extensions of our methodology to include random effects accounting for unmeasured covariates. In addition, we present a mixture model with a cure rate using the OU process to model the latent health status of those subjects susceptible to experiencing the event under study. We apply these methods to survival data collected on melanoma patients and to another survival data set pertaining to carcinoma of the oropharynx.
| Author | : Mikhail Nikulin |
| Publisher | : Springer |
| Total Pages | : 131 |
| Release | : 2016-04-11 |
| Genre | : Mathematics |
| ISBN | : 3662493322 |
This book will be of interest to readers active in the fields of survival analysis, genetics, ecology, biology, demography, reliability and quality control. Since Sir David Cox’s pioneering work in 1972, the proportional hazards model has become the most important model in survival analysis. The success of the Cox model stimulated further studies in semiparametric and nonparametric theories, counting process models, study designs in epidemiology, and the development of many other regression models that could offer more flexible or more suitable approaches in data analysis. Flexible semiparametric regression models are increasingly being used to relate lifetime distributions to time-dependent explanatory variables. Throughout the book, various recent statistical models are developed in close connection with specific data from experimental studies in clinical trials or from observational studies.
| Author | : Lang Wu |
| Publisher | : CRC Press |
| Total Pages | : 431 |
| Release | : 2009-11-11 |
| Genre | : Mathematics |
| ISBN | : 9781420074086 |
Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.
| Author | : Jimin Ding |
| Publisher | : |
| Total Pages | : 246 |
| Release | : 2006 |
| Genre | : |
| ISBN | : |
| Author | : John O'Quigley |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 549 |
| Release | : 2008-01-25 |
| Genre | : Medical |
| ISBN | : 0387686398 |
The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models – proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter – which underlie modern survival analysis. Researchers and students alike will find that this text differs from most recent works in that it is mostly concerned with methodological issues rather than the analysis itself.
| Author | : |
| Publisher | : |
| Total Pages | : 776 |
| Release | : 2001 |
| Genre | : Dissertation abstracts |
| ISBN | : |
| 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.
| Author | : Gerhard Tutz |
| Publisher | : Springer |
| Total Pages | : 252 |
| Release | : 2016-06-14 |
| Genre | : Mathematics |
| ISBN | : 3319281585 |
This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are explained. Each section includes a set of exercises on the respective topics. Various functions and tools for the analysis of discrete survival data are collected in the R package discSurv that accompanies the book.
