We present a new analysis of relationships between disease incidence and the prevalence of an experimentally defined state of `recent infection'. This leads to a clean separation between biological parameters (properties of disease progression as reflected in a test for recent infection), which need to be calibrated, and epidemiological state variables, which are estimated in a cross-sectional survey. The framework takes into account the possibility that details of the assay and host/pathogen chemistry leave a (knowable) fraction of the population in the recent category for all times. This systematically addresses an issue which is the source of some controversy about the appropriate use of the BED assay for defining recent HIV infection. Analysis of relative contributions of error arising variously from statistical considerations and simplifications of general expressions indicate that statistical error dominates heavily over all sources of bias for realistic epidemiological and biological scenarios. Numerical calculations validate the approximations made in analytical relations.