Bayesian back-calculation using a multi-state model with application to HIV.

Back-calculation is a method of obtaining estimates of the number of infections of a disease over time. Data on an endpoint of the disease, together with knowledge of the time from infection to endpoint, allows reconstruction of the incidence of infection. The technique has had much success when applied to the HIV epidemic, using incidence of AIDS diagnoses to inform past HIV infections. In recent years, the period from infection to AIDS has changed considerably due to new regimes of anti-viral therapies. This has led to attempts to use incidence of first positive HIV test as an alternative basis for back-calculation. Developing on earlier work, this paper explores the feasibility of a multi-state formulation of the back-calculation method that models the disease and diagnosis processes and uses HIV diagnoses as an endpoint. Estimation is carried out in a Bayesian framework, which naturally allows incorporation of external information to inform the diagnosis probabilities. The idea is illustrated on data from the HIV epidemic in homosexuals in England and Wales. Copyright 2005 John Wiley & Sons, Ltd.