Estimating HIV incidence based on combined prevalence testing

Knowledge of incidence rates of HIV and other infectious diseases is important in evaluating the state of an epidemic as well as for designing interventional studies. Estimation of disease incidence from longitudinal studies can be expensive and time consuming. Alternatively, Janssen et al. (1998, Journal of the American Medical Association 280, 42-48) proposed the estimation of HIV incidence at a single point in time based on the combined use of a standard and "detuned" antibody assay. This article frames the problem from a longitudinal perspective, from which the maximum likelihood estimator of incidence is determined and compared with the Janssen estimator. The formulation also allows estimation for general situations, including different batteries of tests among subjects, inclusion of covariates, and a comparative evaluation of different test batteries to help guide study design. The methods are illustrated with data from an HIV interventional trial and a seroprevalence survey recently conducted in Botswana.