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 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.

Table of Contents:
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 I = 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