The concept of frailty offers a convenient way to introduce unobserved heterogeneity and associations into models for survival data. In its simplest form, frailty is an unobserved random proportionality factor that modifies the hazard function of an individual or a group of related individuals. Frailty Models in Survival Analysis presents a comprehensive overview of the fundamental approaches in the area of frailty models.

The book extensively explores how univariate frailty models can represent unobserved heterogeneity. It also emphasizes correlated frailty models as extensions of univariate and shared frailty models. The author analyzes similarities and differences between frailty and copula models; discusses problems related to frailty models, such as tests for homogeneity; and describes parametric and semiparametric models using both frequentist and Bayesian approaches. He also shows how to apply the models to real data using the statistical packages of R, SAS, and Stata. The appendix provides the technical mathematical results used throughout.

Written in nontechnical terms accessible to nonspecialists, this book explains the basic ideas in frailty modeling and statistical techniques, with a focus on real-world data application and interpretation of the results. By applying several models to the same data, it allows for the comparison of their advantages and limitations under varying model assumptions. The book also employs simulations to analyze the finite sample size performance of the models.

Accessible to nonspecialists, this book explains the basic ideas in frailty modeling and statistical techniques, with a focus on real data application and interpretation of the results. It extensively explores how univariate frailty models can represent unobserved heterogeneity. It also emphasizes correlated frailty models as extensions of univariate and shared frailty models. The author analyzes similarities and differences between frailty and copula models, discusses problems related to frailty models, and describes parametric and semiparametric models using both frequentist and Bayesian approaches. He also shows how to apply the models to real data using R, SAS, and Stata.

Introduction
Goals and outline
Examples

Survival Analysis
Basic concepts in survival analysis
Censoring and truncation
Parametric models
Estimation of survival and hazard functions
Regression models
Identifiability problems

Univariate Frailty Models
The concept of univariate frailty
Discrete frailty model
Gamma frailty model
Log-normal frailty model
Inverse Gaussian frailty model
Positive stable frailty model
PVF frailty model
Compound Poisson frailty model
Quadratic hazard frailty model
Levy-type frailty models
Log-t frailty model
Univariate frailty cure models
Missing covariates in proportional hazard models

Shared Frailty Models
Marginal versus frailty model
The concept of shared frailty
Shared gamma frailty model
Shared log-normal frailty model
Shared positive stable frailty model
Shared compound Poisson/PVF frailty model
Shared frailty models more general
Dependence measures
Limitations of the shared frailty model

Correlated Frailty Models
The concept of correlated frailty
Correlated gamma frailty model
Correlated log-normal frailty model
MCMC methods for the correlated log-normal frailty model
Correlated compound Poisson frailty model
Correlated quadratic hazard frailty model
Other correlated frailty models
Bivariate frailty cure models
Comparison of different estimation strategies
Dependent competing risks in frailty models

Copula Models
Shared gamma frailty copula
Correlated gamma frailty copula
General correlated frailty copula
Cross-ratio function

Different Aspects of Frailty Modeling
Dependence and interaction between frailty and observed covariates
Cox model with general Gaussian random effects
Nested frailty models
Recurrent event time data
Tests for heterogeneity
Log-rank test in frailty models
Time-dependent frailty models
Identifiability of frailty models
Applications of frailty models
Software for frailty models

Appendix

References

Index