First Hitting Time Regression Models
Title | First Hitting Time Regression Models PDF eBook |
Author | Chrysseis Caroni |
Publisher | John Wiley & Sons |
Pages | 206 |
Release | 2017-07-19 |
Genre | Mathematics |
ISBN | 1119437253 |
This book aims to promote regression methods for analyzing lifetime (or time-to-event) data that are based on a representation of the underlying process, and are therefore likely to offer greater scientific insight compared to purely empirical methods. In contrast to the rich statistical literature, the regression methods actually employed in lifetime data analysis are limited, particularly in the biomedical field where D. R. Cox’s famous semi-parametric proportional hazards model predominates. Practitioners should become familiar with more flexible models. The first hitting time regression models (or threshold regression) presented here represent observed events as the outcome of an underlying stochastic process. One example is death occurring when the patient’s health status falls to zero, but the idea has wide applicability – in biology, engineering, banking and finance, and elsewhere. The central topic is the model based on an underlying Wiener process, leading to lifetimes following the inverse Gaussian distribution. Introducing time-varying covariates and many other extensions are considered. Various applications are presented in detail.
Theory and Practice of Risk Assessment
Title | Theory and Practice of Risk Assessment PDF eBook |
Author | Christos P. Kitsos |
Publisher | Springer |
Pages | 414 |
Release | 2015-05-18 |
Genre | Medical |
ISBN | 3319180290 |
This book covers the latest results in the field of risk analysis. Presented topics include probabilistic models in cancer research, models and methods in longevity, epidemiology of cancer risk, engineering reliability and economical risk problems. The contributions of this volume originate from the 5th International Conference on Risk Analysis (ICRA 5). The conference brought together researchers and practitioners working in the field of risk analysis in order to present new theoretical and computational methods with applications in biology, environmental sciences, public health, economics and finance.
Demography of Population Health, Aging and Health Expenditures
Title | Demography of Population Health, Aging and Health Expenditures PDF eBook |
Author | Christos H. Skiadas |
Publisher | Springer Nature |
Pages | 448 |
Release | 2020-08-24 |
Genre | Social Science |
ISBN | 3030446956 |
This book provides theoretical and applied material for estimating vital parts of demography and health issues including the healthy aging process along with calculating the healthy life years lost to disability. It further includes the appropriate methodology for the optimum health expenditure allocation. Through providing data analysis, statistical and stochastic methodology, probability approach and important applications, the book explores topics such as aging and mortality, birth-death processes, self-perceived age, life-time and survival as well as pension and labor-force. By providing a methodological approach to health problems in demography and society including and quantifying important parameters, this book is a valuable guide for researchers, theoreticians and practitioners from various disciplines.
Mathematical and Statistical Models and Methods in Reliability
Title | Mathematical and Statistical Models and Methods in Reliability PDF eBook |
Author | V.V. Rykov |
Publisher | Springer Science & Business Media |
Pages | 465 |
Release | 2010-11-02 |
Genre | Technology & Engineering |
ISBN | 0817649719 |
The book is a selection of invited chapters, all of which deal with various aspects of mathematical and statistical models and methods in reliability. Written by renowned experts in the field of reliability, the contributions cover a wide range of applications, reflecting recent developments in areas such as survival analysis, aging, lifetime data analysis, artificial intelligence, medicine, carcinogenesis studies, nuclear power, financial modeling, aircraft engineering, quality control, and transportation. Mathematical and Statistical Models and Methods in Reliability is an excellent reference text for researchers and practitioners in applied probability and statistics, industrial statistics, engineering, medicine, finance, transportation, the oil and gas industry, and artificial intelligence.
Regression Modeling of Time to Event Data Using the Ornstein-Uhlenbeck Process
Title | Regression Modeling of Time to Event Data Using the Ornstein-Uhlenbeck Process PDF eBook |
Author | Roger Alan Erich |
Publisher | |
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.
Semi-parametric Survival Analysis Via Dirichlet Process Mixtures of the First Hitting Time Model
Title | Semi-parametric Survival Analysis Via Dirichlet Process Mixtures of the First Hitting Time Model PDF eBook |
Author | Jonathan A. Race |
Publisher | |
Pages | 149 |
Release | 2019 |
Genre | Survival analysis (Biometry) |
ISBN |
Time-to-event data often violate the proportional hazards assumption inherent in the popular Cox regression model. Such violations are especially common in the sphere of biological and medical data where latent heterogeneity due to unmeasured covariates or time varying effects are common. A variety of parametric survival models have been proposed which make more appropriate assumptions on the hazard function, at least for certain applications. One such model is derived from the First Hitting Time (FHT) paradigm which assumes that a subject's event time is determined by a latent stochastic process reaching a threshold value. Several random effects specifications of the FHT model have also been proposed which allow for better modeling of data with unmeasured covariates. While often appropriate, these methods often display limited flexibility due to their inability to model a wide range of heterogeneities. To address this issue, we propose two Bayesian models which loosen assumptions on the mixing distribution inherent in the random effects FHT models currently in use. The first proposed model is ideally suited for standard regression analyses. The second model is designed for use in clinical trials where survival is the outcome of interest. We demonstrate via simulation study that the proposed models greatly improve both survival and parameter estimation in the presence of latent heterogeneity. We also apply the proposed methodologies to data from a toxicology/carcinogenicity study which exhibits nonproportional hazards and contrast the results with competing methods.
Predictions in Time Series Using Regression Models
Title | Predictions in Time Series Using Regression Models PDF eBook |
Author | Cory Terrell |
Publisher | Scientific e-Resources |
Pages | 300 |
Release | 2019-09-02 |
Genre | |
ISBN | 1839473290 |
Regression methods have been a necessary piece of time arrangement investigation for over a century. As of late, new advancements have made real walks in such territories as non-constant information where a direct model isn't fitting. This book acquaints the peruser with fresher improvements and more assorted regression models and methods for time arrangement examination. Open to any individual who knows about the fundamental present day ideas of factual deduction, Regression Models for Time Series Analysis gives a truly necessary examination of late measurable advancements. Essential among them is the imperative class of models known as summed up straight models (GLM) which gives, under a few conditions, a bound together regression hypothesis reasonable for constant, all out, and check information. The creators stretch out GLM methodology deliberately to time arrangement where the essential and covariate information are both arbitrary and stochastically reliant. They acquaint readers with different regression models created amid the most recent thirty years or somewhere in the vicinity and condense traditional and later outcomes concerning state space models.