ESTIMATION OF TIME SINCE INFECTION USING LONGITUDINAL DISEASE-MARKER DATA

We propose a method to estimate the usually unknown time since infecti on for individuals infected with human immunodeficiency virus type 1 ( HIV-1). If we assume the time since infection has an exponential prior distribution, then under the model the conditional distribution of ti me since infection, given the CD4 level at the time of the first posit ive HIV-1 antibody test, is a truncated normal density. We applied the method to prevalent cohort data both from intravenous drug users and from homosexual/bisexual men. For the intravenous drug users the estim ated mean time since infection was 15.0 months from infection at a pre sumed mean CD4 level of 1060 cells/ml to first positive antibody test at a CD4 level of 597 cells/ml, which was the average CD4 at enrolment for infected subjects. For the homosexual/bisexual men the estimated mean time since infection was 16.7 months from infection at a presumed mean CD4 level of 699 cells/ml to first positive antibody test at an average CD4 level of 577 cells/ml. We performed a validation study usi ng initially seronegative subjects in these cohorts who seroconverted to HIV-1-positive antibody status during the follow-up period. For the intravenous drug users, data were too few to provide definitive verif ication of the method. In the cohort of homosexual/bisexual men, howev er, there was a total of 70 seroconverters with relevant data. Among t hem, the median absolute difference between the midpoint of the known seroconversion interval and the estimated mean infection date was 4.6 months, conditional on CD4-lymphocyte measurements taken approximately 18 months subsequent to infection. Conditional on CD4 approximately 3 0 months after infection, this median difference increased modestly to 8.2 months. Our analysis suggested that the underlying mathematical m odel tends to overestimate short times since infection and underestima te long times since infection. We consider potential corrective modifi cations to the model.