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In this short note, we analyze the assumptions made by McDougal et al (2006),both explicit and implicit, in their estimation of the proportion of "truerecent infections" using the BED CEIA. This enables us to write downexpressions for the sensitivity, short term specificity and long termspecificity of a test for recent infection defined by a BED ODn below athreshold. We then derive an identity which shows the relationship betweenthese parameters, allowing the elimination of sensitivity and short termspecificity from an expression relating the proportion of "true recentinfections" to the proportion of seropositive individuals testing belowthreshold. This has two important consequences. Firstly, the simplified formulais substantially more amenable to calibration. Secondly, naively treating theparameters as independent would lead to an incorrect estimate of uncertaintydue to imperfect calibration.

On the Estimation of the Proportion of True Recent Infections Using the BED Capture Enzyme Immunoassay