Back-projection of German AIDS data using information on dates of tests

The paper presents an application of back-projection methods to the reported AIDS data which are collected by the AIDS Center in the Federal Office of Health, Berlin. The analysis is based on all data reported up to 31 December 1992. The data are broken down by major risk groups. Correction for reporting delays takes into account temporal changes in their distribution. The paper applies the EMS algorithm for the estimation of HIV incidence. The incubation period is modelled according to a convolution of several exponential distributions which describe time dependent phenomena like change of case definition and therapy effects. For each case it is reported whether an antibody test has been performed before diagnosis, and if yes, at what time this test was performed. The modelling of the incubation distribution takes into account the transition from a state 'not yet tested' into a state 'tested'. Only tested individuals in three pre-AIDS states are eligible for treatment. The model allows us to estimate not only the current total HIV prevalence but also a breakdown into those that are not yet tested, those that are tested but not yet treated and those that are under treatment. The results depend on the assumptions about the effect of treatment and on the degree of smoothing applied in the EMS algorithm.