Frailty Models in Survival Analysis

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.

Andreas Wienke is a docent in the Institute of Medical Epidemiology, Biostatistics, and Informatics at Martin-Luther-University Halle-Wittenberg in Germany. In addition to statistical consulting and teaching courses on biostatistics and epidemiology, Dr. Wienke plans, designs, and supervises clinical trials in the University’s Coordination Centre of Clinical Trials.

Introduction Goals and outline Examples

Survival Analysis Basic concepts in survival analysis Censoring and truncation Parametric modelsEstimation of survival and hazard functionsRegression models Identifiability problems

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

Shared Frailty ModelsMarginal versus frailty model The concept of shared frailty Shared gamma frailty modelShared 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 covariatesCox 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 modelsApplications of frailty models Software for frailty models
Appendix
References
Index