Application of the promotion time cure model with time-changing exposure to the study of HIV/AIDS and other infectious diseases.

Infectious diseases are caused by single or successive contacts with pathogens. Nevertheless, contacts with pathogens do not implicate infection. In 1993, Yakovlev et al. proposed a model to study a population of cancer patients with a cured fraction, a well adapted model to describe an infectious disease with a unique infection occasion. Extensions of this model have been proposed in the recent years. We present a mechanistic formulation in the context of infectious diseases with multiple infection occasions. It is a mixture model that enables to study risk factors associated with infection intensity at each infection occasion and factors shortening the delay from exposure to clinical event. Simulations are performed to evaluate the model fitting and two examples are presented for illustration: an analysis of an HIV-1 mother-to-child transmission data set and an analysis of nosocomial urinary tract infections data set.