  Case-I interval-censored (current status) data from multistate systems are
often encountered in cancer and other epidemiological studies. In this article,
we focus on the problem of estimating state entry distribution and occupation
probabilities, contingent on a preceding state occupation. This endeavor is
particularly complex owing to the inherent challenge of the unavailability of
directly observed counts of individuals at risk of transitioning from a state,
due to the cross-sectional nature of the data. We propose two nonparametric
approaches, one using the fractional at-risk set approach recently adopted in
the right-censoring framework and the other a new estimator based on the ratio
of marginal state occupation probabilities. Both estimation approaches utilize
innovative applications of concepts from the competing risks paradigm. The
finite-sample behavior of the proposed estimators is studied via extensive
simulation studies where we show that the estimators based on severely censored
current status data have good performance when compared with those based on
complete data. We demonstrate the application of the two methods to analyze
data from patients diagnosed with breast cancer.
