Smoothed nonparametric back-projection of AIDS incidence data with adjustment for therapy.

Back-projection is a major tool for assessing the extent of the HIV epidemic. Its application relies on a model for the incubation period of AIDS into which the administration and effect of therapy has been incorporated. We propose a compartmental model with proportional transition rates to describe variation and changes in the duration of the incubation period. The model is easily related to available data and offers fast computation. Its detailed and direct reflection of the administration and effect of therapy makes it relatively easy to ensure that therapy has been accommodated to an appropriate extent. The effect of therapy on back-projection estimates of the HIV epidemic curve is demonstrated with an application to Australian AIDS incidence data.