Frailty selection in bivariate survival models: A cautionary note

One problem that researchers face in analyzing the survival times of groups of related individuals is selecting how the distribution of frailty—an unobserved (or not adequately observed) random factor— should be specified. Several distributions have received attention—for instance, the gamma distribution and a nonparametric N‐point, discrete probability distribution. Researchers have selected these distributions more for mathematical convenience than for their ability to represent biological, social, or economic reality, and the implications of choosing one functional representation of frailty over alternative choices have not been studied extensively. In particular, researchers have paid little attention to the type of association that exists among survival times of individuals in a group or between those of a pair under specific frailty distributions. This research paper explores the association among survival times under gamma, inverse Gaussian, nonparametric N‐point, and Poisson distributions. It shows that the pattern and strength of this association depends on how the distribution of frailty is specified.