Datta: Nonparametric estimation of stage occupation probabilities in multistage
       models under censoring
       
We propose nonparametric estimators of the stage occupation probabilities
and transition hazards for a multistage system that is not necessarily
Markovian, using data that are subject to dependent right censoring.  We
assume that the hazard of being censored at a given instant depends on a
possibly time dependent covariate process as opposed to assuming a fixed
censoring hazard (independent censoring).  The estimator of the transition
hazard matrix has a Nelson-Aalen form where the each of the counting
processes counting the number of transitions between states and the risk
sets of leaving the states have the IPCW (inverse probability of censoring
weighted) form.  We estimate these weights using Aalen's linear hazard
model. Finally, the stage occupation probabilities are obtained from the
estimated transition hazard matrix via product integration.  Consistency of
these estimators under the general paradigm of non-Markov models is
established and asymptotic variance formulas are provided.

In the second part of the talk, the same problem will be addressed in the
context of a different censoring scheme, namely the current status data. We
show that a kernel smoothing technique combined with weighted estimation can
be used to obtain valid estimators of stage occupation probabilities.