Current status observation of a three-state counting process with application to simultaneous accurate and diluted HIV test data

Karen McKeown and Nicholas Jewell have a new paper in Canadian Journal of Statistics as part of the Kalbfleisch and Lawless special issue. The paper considers non-parametric inference for three-state progressive models subject to current status data observation. The authors note previous work by van der Laan and Jewell (Annals of Statistics, 2003) that shows that a naive estimator using only information on the first event cannot be improved upon in a fully non-parametric setting. The authors consider situations where additional assumptions are made about the waiting time (between the first and second events). In the motivating example, there is a fairly extreme case of current status data where all subjects are observed at the same time point (i.e. a cross-sectional sample). In this case, if an assumption that the distribution for the first event time is assumed to be locally linear, then only the mean waiting time is relevant. The authors then consider a couple of different scenarios with a view to choosing an optimal assumed mean waiting time that minimizes the mean squared error of some quantity of interest relating to the first event time distribution (e.g. the mean cumulative hazard in some time interval).