Estimating biomarker-based HIV incidence using prevalence data in high risk groups with missing outcomes

The novel two-step serologic sensitive/less sensitive testing algorithm for detecting recent HIV seroconversion (STARHS) provides a simple and practical method to estimate HTV-1 incidence using crosssectional HIV seroprevalence data. STARHS has been used increasingly in epidemiologic studies. However, the uncertainty of incidence estimates using this algorithm has not been well described, especially for high risk groups or when missing data is present because a fraction of sensitive enzyme immunoassay (EIA) positive specimens are not tested by the less sensitive EIA. Ad hoc methods used in practice provide incorrect confidence limits and thus may jeopardize statistical inference. In this report, we propose maximum likelihood and Bayesian methods for correctly estimating the uncertainty in incidence estimates obtained using prevalence data with a fraction missing, and extend the methods to regression settings. Using a study of injection drug users participating in a drug detoxification program in New York city as an example, we demonstrated the impact of underestimating the uncertainty in incidence estimates using ad hoc methods. Our methods can be applied to estimate the incidence of other diseases from prevalence data using similar testing algorithms when missing data is present.