  Random effect models for time-to-event data, also known as frailty models,
provide a conceptually appealing way of quantifying association between
survival times and of representing heterogeneities resulting from factors which
may be difficult or impossible to measure. In the literature, the random effect
is usually assumed to have a continuous distribution. However, in some areas of
application, discrete frailty distributions may be more appropriate. The
present paper is about the implementation and interpretation of the Addams
family of discrete frailty distributions. We propose methods of estimation for
this family of densities in the context of shared frailty models for the hazard
rates for case I interval-censored data. Our optimization framework allows for
stratification of random effect distributions by covariates. We highlight
interpretational advantages of the Addams family of discrete frailty
distributions and the K-point distribution as compared to other frailty
distributions. A unique feature of the Addams family and the K-point
distribution is that the support of the frailty distribution depends on its
parameters. This feature is best exploited by imposing a model on the
distributional parameters, resulting in a model with non-homogeneous covariate
effects that can be analysed using standard measures such as the hazard ratio.
Our methods are illustrated with applications to multivariate case I
interval-censored infection data.
