Estimation from current-status data in continuous time.

The nonparametric maximum likelihood estimator for current-status data has been known for at least 40 years, but only recently have the mathematical-statistical properties been clarified. This note provides a case study in the important and often studied context of estimating age-specific immunization intensities from a seroprevalence survey. Fully parametric and spline-based alternatives (also based on continuous-time models) are given. The basic reproduction number R0 exemplifies estimation of a functional. The limitations implied by the necessarily rather restrictive epidemiological assumptions are briefly discussed.