A multi-state Markov model using notification data to estimate HIV incidence, number of undiagnosed individuals living with HIV, and delay between infection and diagnosis: Illustration in France, 2008-2018.

Thirty-five years since the discovery of the human immunodeficiency virus (HIV), the epidemic is still ongoing in France. To guide HIV prevention strategies and monitor their impact, it is essential to understand the dynamics of the HIV epidemic. The indicator for reporting the progress of new infections is the HIV incidence. Given that HIV is mainly transmitted by undiagnosed individuals and that earlier treatment leads to less HIV transmission, it is essential to know the number of infected people unaware of their HIV-positive status as well as the time between infection and diagnosis. Our approach is based on a non-homogeneous multi-state Markov model describing the progression of the HIV disease. We propose a penalized likelihood approach to estimate the HIV incidence curve as well as the diagnosis rates. The HIV incidence curve was approximated using cubic M-splines, while an approximation of the cross-validation criterion was used to estimate the smoothing parameter. In a simulation study, we evaluate the performance of the model for reconstructing the HIV incidence curve and diagnosis rates. The method is illustrated in the population of men who have sex with men using HIV surveillance data collected by the French Institute for Public Health Surveillance since 2004.