Modeling Survival Data Using Frailty Models

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 Lévy 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.

David D. Hanagal is a professor of statistics at the University of Pune in India.