A time-varying shared frailty model with application to infectious diseases

TL;DR

This paper introduces a new parametric time-varying shared frailty model for infectious disease data, capturing changes in population heterogeneity over time, with applications to modeling age-related susceptibility and contact rates.

Contribution

It develops a novel frailty model using a power transformation of a generalized gamma variable, improving upon previous models by avoiding time-dependent support issues.

Findings

Model effectively captures time-varying heterogeneity.

Applications demonstrate improved fit to infectious disease data.

Provides insights into age-dependent contact and susceptibility patterns.

Abstract

We propose a new parametric time-varying shared frailty model to represent changes over time in population heterogeneity, for use with bivariate current status data. The model uses a power transformation of a time-invariant frailty $U$, and is particularly convenient when $U$ is a member of the generalized gamma family. This model avoids some shortcomings of a previously suggested time-varying frailty model, notably time-dependent support. We describe some key properties of the model, including its relative frailty variance function in different settings and how the model can be fitted to data. We describe several applications to shared frailty modeling of bivariate current status data on infectious diseases, in which the frailty represents age-dependent heterogeneity in contact rates or susceptibility to infection.