Modelling time varying heterogeneity in recurrent infection processes: an application to serological data
Frailty models are often used in survival analysis to model multivariate time-to-event data. In infectious disease epidemiology, frailty models have been proposed to model heterogeneity in the acquisition of infection and to accommodate association in the occurrence of multiple types of infection. Although traditional frailty models rely on the assumption of lifelong immunity after recovery, refinements have been made to account for reinfections with the same pathogen. Recently, Abrams and Hens quantified the effect of misspecifying the underlying infection process on the basic and effective reproduction number in the context of bivariate current status data on parvovirus B19 and varicella zoster virus. Furthermore, Farrington, Unkel and their co-workers introduced and applied time varying shared frailty models to paired bivariate serological data. In this paper, we consider an extension of the proposed frailty methodology by Abrams and Hens to account for age-dependence in individual heterogeneity through the use of age-dependent shared and correlated gamma frailty models. The methodology is illustrated by using two data applications. ; The authors gratefully acknowledge support by the Research Fund of Hasselt University (grantBOF11NI31) and support of the University of Antwerp Scientific Chair in Evidence-based Vaccinology sponsored in 2009–2016 by a gift from Pfizer and GlaxoSmithKline. The work of AW was supported by the German Research Council, project WI 3288/1-2. This research is part of a project that has received funding from the European Research Council under the European Union's 'Horizon 2020' research and innovation program (grant agreement 682540—TransMID). The computational resources and services used in this work were provided by the Flemish Supercomputer Center, funded by the Research Foundation—Flanders and the Flemish Government—Department Economy, Science and Innovation.
