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 "true recent infections" using the BED CEIA. This enables us to write down expressions for the sensitivity, short term specificity and long term specificity of a test for recent infection defined by a BED ODn below a threshold. We then derive an identity which shows the relationship between these parameters, allowing the elimination of sensitivity and short term specificity from an expression relating the proportion of "true recent infections" to the proportion of seropositive individuals testing below threshold. This has two important consequences. Firstly, the simplified formula is substantially more amenable to calibration. Secondly, naively treating the parameters as independent would lead to an incorrect estimate of uncertainty due to imperfect calibration.