Modeling Survival Data Using Frailty Models - Rilegato

Hanagal, David D.

Rilegato

ISBN 10: 1439836671 ISBN 13: 9781439836675

Casa editrice: Chapman & Hall, 2011

Riassunto

When designing and analyzing a medical study, researchers focusing on survival data must take into account the heterogeneity of the study population: due to uncontrollable variation, some members change states more rapidly than others. Survival data measures the time to a certain event or change of state. For example, the event may be death, occurrence of disease, time to an epileptic seizure, or time from response until disease relapse. Frailty is a convenient method to introduce unobserved proportionality factors that modify the hazard functions of an individual. In spite of several new research developments on the topic, there are very few books devoted to frailty models. Modeling Survival Data Using Frailty Models covers recent advances in methodology and applications of frailty models, and presents survival analysis and frailty models ranging from fundamental to advanced. Eight data on survival times with covariates sets are discussed, and analysis is carried out using the R statistical package. This book covers: Basic concepts in survival analysis, shared frailty models and bivariate frailty models Parametric distributions and their corresponding regression models Nonparametric Kaplan--Meier estimation and Cox's proportional hazard model The concept of frailty and important frailty models Different estimation procedures such as EM and modified EM algorithms Logrank tests and CUSUM of chi-square tests for testing frailty Shared frailty models in different bivariate exponential and bivariate Weibull distributions Frailty models based on Levy processes Different estimation procedures in bivariate frailty models Correlated gamma frailty, lognormal and power variance function frailty models Additive frailty models Identifiability of bivariate frailty and correlated frailty models The problem of analyzing time to event data arises in a number of applied fields, such as medicine, biology, public health, epidemiology, engineering, economics, and demography. Although the statistical tools presented in this book are applicable to all these disciplines, this book focuses on frailty in biological and medical statistics, and is designed to prepare students and professionals for experimental design and analysis.

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Recensione

A statistician seeking guidance on the use of frailty models in genetic applications, two component systems, and/or Levy processes would benefit more from Hanagal’s book. If someone wanted to find references on the use of frailty models, both books [Hanagal; Weinke’s Frailty Models in Survival Analysis] should be consulted because both books have extensive references (>300) and the references are largely non-overlapping.
—William Mietlowski, Journal of Biopharmaceutical Statistics, January 2012

Contenuti

Contents
List of Tables
List of Figures
Preface
About the Author

Basic Concepts in Survival Analysis
Introduction to Survival Analysis
Introduction
Bone Marrow Transplantation (BMT) for Leukemia
Remission Duration from a Clinical Trial for Acute Leukemia
Times of Infection of Kidney Dialysis Patients
Kidney Infection Data
Litters of Rats Data
Kidney Dialysis (HLA) Patients Data
Diabetic Retinopathy Data
Myeloma Data
Definitions and Notations
.Survival Function
.Failure (or Hazard) Rate
Censoring
Some Parametric Methods
Introduction
Exponential Distribution
Weibull Distribution
Extreme Value Distributions
Lognormal
Gamma
Loglogistic
Maximum Likelihood Estimation
Parametric Regression Models
Nonparametric and Semiparametric Models
Empirical Survival Function
Graphical Plotting
Graphical Estimation
Empirical Model Fitting: Distribution Free (Kaplan-Meier) Approach
Comparison between Two Survival Functions
Cox's Proportional Hazards Model

Univariate and Shared Frailty Models for Survival Data
The Frailty Concept
Introduction
The Definition of Shared Frailty
The Implications of Frailty
The Conditional Parametrization
The Marginal Parametrization
Frailty as a Model for Omitted Covariates
Frailty as a Model of Stochastic Hazard
Identifiability of Frailty Models
Various Frailty Models
Introduction
Gamma Frailty
Positive Stable Frailty
Power Variance Function Frailty
Compound Poisson Frailty
Compound Poisson Distribution with Random Scale
Frailty Models in Hierarchical Likelihood
Frailty Models in Mixture Distributions
Estimation Methods for Shared Frailty Models
Introduction
Inference for the Shared Frailty Model
The EM Algorithm
The Gamma Frailty Model
The Positive Stable Frailty Model
The Lognormal Frailty Model
Application to Seizure Data
Modified EM (MEM) Algorithm for Gamma Frailty Models
Application
Discussion
Analysis of Survival Data in Shared Frailty Models
Introduction
Analysis for Bone Marrow Transplantation (BMT) Data
Analysis for Acute Leukemia Data
Analysis for HLA Data
Analysis for Kidney Infection Data
Analysis of Litters of Rats
Analysis for Diabetic Retinopathy Data
Tests of Hypotheses in Frailty Models
Introduction
Tests for Gamma Frailty Based on Likelihood Ratio and Score Tests
Logrank Tests for Testing β = 0
Test for Heterogeneity in Kidney Infection Data
Shared Frailty in Bivariate Exponential and Weibull Models
Introduction
Bivariate Exponential Distributions
Gamma Frailty in BVW Models
Positive Stable Frailty in BVW Models
Power Variance Function Frailty in BVW Models
Weibull Extension of BVE Models
Lognormal and Weibull Frailties in BVW Models
Compound Poisson Frailty in BVW Models
Compound Poisson (with Random Scale) Frailty in BVW Models
Estimation and Tests for Frailty under BVW Baseline
Frailty Models Based on Levy Processes
Introduction
Levy Processes and Subordinators
Proportional Hazards Derived from Levy Processes
Other Frailty Process Constructions
Hierarchical Levy Frailty Models

Bivariate Frailty Models for Survival Data
Bivariate Frailty Models and Estimation Methods
Introduction
Bivariate Frailty Models and Laplace Transforms
Proportional Hazard Model for Covariate Effects
The Problem of Confounding
A General Model of Covariate Dependence
Pseudo-Frailty Model
Likelihood Construction
Semiparametric Representations
Estimation Methods in Bivariate Frailty Models
Correlated Frailty Models
Introduction
Correlated Gamma Frailty Model
Correlated Power Variance Function Frailty Model
Genetic Analysis of Duration
General Bivariate Frailty Model
Correlated Compound Poisson Frailty for the Bivariate Survival
Applications
Additive Frailty Models
Introduction
Modeling Multivariate Survival Data Using the Frailty Model
Correlated Frailty Model
Relations to Other Frailty Models
Additive Genetic Gamma Frailty
Additive Genetic Gamma Frailty for Linkage Analysis of Diseases
Identifiability of Bivariate Frailty Models
Introduction
Identifiability of Bivariate Frailty Models
Identifiability of Correlated Frailty Models
Non-Identifiability of Frailty Models without Observed Covariates
Discussion
Appendix
Bibliography
Index

Dettagli dell'edizione

• Editore: Chapman & Hall
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 1439836671
• ISBN 13: 9781439836675
• Rilegatura: Copertina rigida
• Numero di pagine: 314
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile