Mixture models for calibrating the BED for HIV incidence testing.

A number of antibody biomarkers have been developed to distinguish between recent and established Human Immunodeficiency Virus (HIV) infection and used for HIV incidence estimation from cross-sectional specimens. In general, a cut-off value is specified, and estimates of the following parameters are needed: (i) the mean time interval .w/ between seroconversion and reaching that cut-off; (ii) the probability of correctly identifying individuals who became infected in the last w years (sensitivity); and (iii) the probability of correctly identifying individuals who have been infected for more than w years (specificity). We develop two statistical methods to study the distribution of a biomarker and derive a formula for estimating HIV incidence from a cross-sectional survey. Both methods allow handling interval censored data and basically consist of using a generalized mixture model to model the growth of the biomarker as a function of time since infection. The first uses data from all followed-up individuals and allows incidence estimation in the cohort, whereas the second only uses data from seroconverters. We illustrate our methods using repeated measures of the IgG capture BED enzyme immunoassay. Estimates of calibration parameters, that is, mean window period, mean recency period, sensitivity, and specificities obtained from both models are comparable. The formula derived for incidence estimation gives the maximum likelihood estimate of incidence which, for a given window period, depends only on sensitivity and specificity. The optimal choice of the window period is discussed. Numerical simulations suggest that data from seroconverters can provide reasonable estimates of the calibration parameters.