Nonparametric estimation of a future entry time distribution given the knowledge of a past state occupation in a progressive multistate model with current status data

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.