Hidden Frailty: Myths and Reality

Hidden differences in the survival chances of individuals in a population influence the shape of the mortality rate observed in demographic and epidemiological studies. To evaluate the contribution of such hidden variations to observed hazards, frailty models have been suggested. The application of these models to the analysis of survival data in demography, epidemiology, and biostatistics has opened up new avenues for survival studies. However, along with many useful insights and ideas, several unjustified beliefs (myths) have also been generated. In this paper we critically discuss these beliefs. In particular, we discuss the notion of individual frailty and show that the interpretation thereof depends on the identifiability conditions specified for the respective frailty model. We discuss strengths and weaknesses of shared frailty models with and without observed covariates. We explain why bivariate correlated frailty models are the most appropriate for the analysis of survival data on related individuals. We discuss new bivariate survival models with non-gamma frailty distribution and potential directions for further research.