On the Addams family of discrete frailty distributions for modelling multivariate case I interval-censored data

TL;DR

This paper introduces the Addams family of discrete frailty distributions for modeling heterogeneity in multivariate interval-censored survival data, offering new estimation methods and interpretational benefits over traditional continuous models.

Contribution

It develops estimation techniques for the Addams family of discrete frailty distributions within shared frailty models, allowing covariate stratification and improved interpretability.

Findings

Effective modeling of heterogeneity in multivariate interval-censored data.

Advantages of discrete frailty distributions in interpretability and covariate effects.

Application to infection data demonstrates practical utility.

Abstract

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.