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

The authors examine multistate current status data defined by two survival times of interest where one only observes whether or not each of the individual survival times exceed a common observed monitoring time. An individual can therefore belong to one of three states. The authors are interested in whether current status information on the second event can be used to improve estimation of the distribution function of time to the first event. For both single and multiple monitoring time scenarios, in the fully nonparametric setting, one cannot improve the naive estimator, using information on the first event only, when estimating "smooth" functionals of the distribution of time to the first event (van der Laan & Jewell, 2003). Therefore, improving the naive estimator is examined when parametric assumptions about the waiting time between the two events are made. For situations where this waiting time is modifiable by design, the issue of determining the optimal length of the waiting time for estimation of the cumulative hazard of the distribution of time to the first event in the recent past is also addressed. The ideas are motivated by and applied to an example on simultaneous accurate and diluted assay HIV test data.