Pairwise Survival Analysis of Infectious Disease Transmission Data

Abstract

Frailty models are frequently used in survival analysis to model multivariate time-to-event data. In recent years, frailty models have been applied in infectious disease modeling to describe individual heterogeneity in the acquisition of infections and to accommodate association in the occurrence of multiple infection types. Such models are used in the context of bivariate serological survey data on infections in the same individuals. This chapter provides an overview of time-independent and time-varying shared and correlated frailty models. More specifically, it is shown how these frailty models impose a different association structure among the infection times for the pathogens under study and how these assumptions translate into a specific choice regarding sources of heterogeneity, such as susceptibility to infection, infectiousness upon infection, and social contact behavior. Although traditional frailty models rely on the assumption of lifelong humoral immunity upon recovery, refinements in the case of reinfection dynamics have been proposed based on mathematical transmission models describing these underlying infection processes. The frailty methodology is illustrated based on bivariate serological survey data on (1) parvovirus B19 and varicella zoster virus from Belgium, and (2) hepatitis A and B serology from Flanders, Belgium.