Estimation of Integrated Transition Hazards and Stage Occupation Probabilities for NonâMarkov Systems Under Dependent Censoring
2002
Datta, Somnath | Satten, Glen A.
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 timeâdependent covariate process as opposed to assuming a fixed censoring hazard (independent censoring). The estimator of the integrated transition hazard matrix has a NelsonâAalen 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 nonâMarkov models is established and asymptotic variance formulas are provided. Simulation results show satisfactory performance of these estimators. An analysis of data on graftâversusâhost disease for bone marrow transplant patients is used as an illustration.
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