Estimation of integrated transition hazards and stage occupation probabilities for non-Markov systems under dependent 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 integrated transition hazard matrix has a Nelson-Aalen form where each of the counting processes counting the number of transitions between states and the risk sets for leaving each stage have an 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 integrated 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. Simulation results show satisfactory performance of these estimators. An analysis of data on graft-versus-host disease for bone marrow transplant patients is used as an illustration.