Time varying frailty models and the estimation of heterogeneities in transmission of infectious diseases

A frailty modelling framework is presented for representing and making inference on individual heterogeneities that are relevant to the transmission of infectious diseases, including heterogeneities that evolve over time. Central to this framework is the use of multivariate data on several infections. We explore new simple but flexible families of time-dependent frailty models, in which the frailty is modulated over time in a deterministic fashion. Methods of estimation, issues of identifiability and model choice are discussed. Results from such models are interpreted in the light of concomitant information on routes of transmission. Applications to paired serological survey data on a range of infections with the same or different routes of transmission are presented.