Estimating Stage Occupation Probabilities in Non-Markov Models

We study non-Markov multistage models under dependent censoring regarding estimation of stage occupation probabilities. The individual transition and censoring mechanisms are linked together through covariate processes that affect both the transition intensities and the censoring hazard for the corresponding subjects. In order to adjust for the dependent censoring, an additive hazard regression model is applied to the censoring times, and all observed counting and "at risk" processes are subsequently given an inverse probability of censoring weighted form. We examine the bias of the Datta-Satten and Aalen-Johansen estimators of stage occupation probability, and also consider the variability of these estimators by studying their estimated standard errors and mean squared errors. Results from different simulation studies of frailty models indicate that the Datta-Satten estimator is approximately unbiased, whereas the Aalen-Johansen estimator either under- or overestimates the stage occupation probability due to the dependent nature of the censoring process. However, in our simulations, the mean squared error of the latter estimator tends to be slightly smaller than that of the former estimator. Studies on development of nephropathy among diabetics and on blood platelet recovery among bone marrow transplant patients are used as demonstrations on how the two estimation methods work in practice. Our analyses show that the Datta-Satten estimator performs well in estimating stage occupation probability, but that the censoring mechanism has to be quite selective before a deviation from the Aalen-Johansen estimator is of practical importance.