Estimating future stage entry and occupation probabilities in a multistage model based on randomly right-censored data

A general multistage model is considered where all individuals start at a given initial stage at time zero. Based on randomly right-censored data, we provide both individual-specific and overall estimates of the probabilities of entry to a future stage. We also provide normalized estimators of the probability of occupying each stage as a function of time. These estimators are constructed using competing risks techniques but with risk sets consisting of fractional observations. The fractional observations correspond to estimates of the numbers of persons who ultimately enter each stage, based on the censored data.