References

aim Present different approaches for the estimation of transition probabilities in multi-state survival data. The central question here is: what is the probability that a randomly selected person is in stage j at time t, conditionally on being in state h at time s: Multi-state models (MSM) A MSM is a model for a stochastic process in continuous time allowing individuals to move between a finite number of states. An individual moves from one state to another through time. The next state to which the individual moves, and the time of change, are specified through transition intensities that provide the instantaneous hazard for movement out of one state into another. Nonparametric approaches Illness-death model Aalen–Johansen estimators of transition probabilities: This approach can be thought of as the generalization of the Kaplan-Meier estimate of the simple mortality model (assumes the process to be Markovian): Markov-free estimator: alternative estimators which do not rely on the Markov assumption are expressed as: Conclusions ÎThe “Markov-free ” estimator, have fewer jump points but with bigger steps. The number of jump points and the size of the steps are related to censoring and to the sample size. ÎWith regard to the survival prognosis, we observe serious departures between both survival curves for individuals who have had recurrence