Estimation of incidence of HIV infection using cross-sectional marker surveys

Methods of estimating the probability density function of infection times for a population, using serial cross-sectional measurements of a marker of disease progression, are presented. The infection time distribution may be calculated back to the beginning of the epidemic, if it is possible to sample individuals who were infected at the beginning of the epidemic; otherwise, under a Markov assumption, the infection time distribution may be calculated conditional on infection after sampling has begun. In either case, the proportion of prevalent cases infected in an arbitrary time interval between the onset and termination of sampling may be measured. Data from the San Francisco Men's Health Study are analyzed; the infection time distribution compares well with that estimated by Bacchetti (1990, Journal of the American Statistical Association 85, 1002-1008) using stored sera from several San Francisco cohort studies.