Using mark-recapture methodology to estimate the size of a population at risk for sexually transmitted diseases

To study the spread of sexually transmitted diseases (STDs) using social/sexual mixing models, one must have quantitative information about sexual mixing. An unavoidable complication in gathering such information by survey is that members of the surveyed population will almost certainly have sexual contacts outside that population. The number of these outsiders may be substantial and, hence, important for the modelling process. In this paper, we develop a mark-recapture model for estimating the size of the population at risk for contracting a STD due to direct sexual contact with a specified population targeted by a survey. This mark-recapture methodology provides a reliable method of estimating the number of outsiders. Because not everyone in the targeted population may be sexually active, the size of the sexually active subset, used as the number marked in our tag-recapture formulation, must be estimated, which introduces extra variability. We derive an estimator of the variance of the estimated total number at risk that accounts for this extra variability and an expression for the bias of that estimator. We extend the methodology to stratified surveys and illustrate its use with data collected from a population of university undergraduates to estimate sexual mixing parameters of a deterministic model of the spread of STDs.