Individuals who are infected with the HIV virus, may or may not have had a positive HIV antibody test. From a public health point of view it is important to know the rate at which infected individuals have their infection diagnosed, that is, when they have their first positive antibody test. We will call this the rate of HIV diagnosis. Only HIV diagnosis prior to one year before AIDS diagnosis will be considered, since HIV tests close to AIDS diagnosis may possibly be closely linked to disease development.
One approach to estimating the rate of HIV diagnosis, is through information on the time of first HIV-diagnosis among individuals who develop AIDS. Such information has been made available for England and Wales by the Public Health Laboratory Service (PHLS) AIDS Centre at the Communicable Disease Surveillance Centre. For the period 1981–91, data are available on the number of AIDS cases diagnosed in each quarter, and reported by mid 1992, and, furthermore, on the number who had an earlier HIV-diagnosis, and on the quarter of this diagnosis.
We have defined an extended backcalculation method to incorporate the HIV diagnosis information. Three exposure groups are considered: homo/ bisexuals, injecting drug users, heterosexuals. For the first two groups the infection curve is assumed to have a quadratic exponential form up to a specified time (the knot) and constant thereafter; the knot has been taken at the beginning of 1987 and 1988 respectively. For the heterosexuals a quadratic exponential infection curve has been used.
A Weibull incubation period is assumed for the homo/bisexuals and heterosexuals, and a gamma incubation period for the injecting drug users.