Using time of first positive HIV test and other auxiliary data in back-projection of AIDS incidence

Estimation of HIV incidence by the method of back-projection typically uses data on the time of diagnosis of AIDS cases, together with known information about the incubation distribution of AIDS. This paper discusses back-projection using auxiliary data on AIDS cases, particularly the time of first positive HIV test. We discuss the possibility that certain types of auxiliary data, including time of first positive test, can be useful in back-projection because they provide extra information about the incubation period of AIDS cases. Under a back-projection model, theoretical efficiency calculations are given comparing back-projection with and without the time of first positive HIV test of AIDS cases. These calculations suggest that such data have the potential to significantly improve HIV incidence estimates, particularly in the recent past. Smoothed non-parametric estimates of both HIV incidence and time-dependent testing rates are described. These can be obtained using the EM algorithm, in conjunction with a smoothing step or a penalized likelihood. The benefit of these methods in practice needs to be assessed as such data become available.