Bayesian Forecasting of the Human Immunodeficiency Virus Epidemic in Scotland

The most commonly used method for acquired immune deficiency syndrome (AIDS) forecasting (backprojection) assumes that the incubation distribution of the time from infection with human immunodeficiency virus (HIV) to AIDS is known, and makes no explicit use of information on the number of individuals who have been infected with HIV. Now that we are further into the epidemic our predictions are more sensitive to assumptions about the incubation distribution which may now be influenced by pre‐AIDS treatment. At the same time we have gained more knowledge about the HIV infection curve in Scotland as a result of retrospective testing of stored samples. In addition to AIDS case reports data are collected in Scotland on CD4 counts for HIV positive patients under medical care, which give incidence data on CD200 cases (two consecutive CD4 counts below 200 or an AIDS diagnosis). We have developed Bayesian methodology to make use of our partial knowledge of both the incubation distribution and the infection curve to make short‐term forecasts of AIDS and CD200 cases. The range of forecasts from this approach includes the uncertainty in our specification of both the incubation distribution and the infection curve.