We investigate two population-level quantities (corresponding to complete
données) related to uncensored stage waiting times in a progressive multi-stage
model, conditional on a prior stage visit. We show how to estimate these
quantities consistently using right-censored data. The first quantity is the
stage waiting time distribution (survival function), representing the
proportion of individuals who remain in stage j within time t after entering
stage j. The second quantity is the cumulative incidence function, representing
the proportion of individuals who transition from stage j to stage j’ within
time t after entering stage j. To estimate these quantities, we present two
nonparametric approaches. The first uses an inverse probability of censoring
weighting (IPCW) method, which reweights the counting processes and the number
of individuals at risk (the at-risk set) to address dependent right censoring.
The second method utilizes the notion of fractional observations (FRE) that
modifies the at-risk set by incorporating probabilities of individuals (who
might have been censored in a prior stage) eventually entering the stage of
interest in the uncensored or full data experiment. Neither approach is limited
to the assumption of independent censoring or Markovian multi-stage frameworks.
Simulation studies demonstrate satisfactory performance for both sets of
estimators, though the IPCW estimator generally outperforms the FRE estimator
in the setups considered in our simulations. These estimations are further
illustrated through applications to two real-world datasets: one from patients
undergoing bone marrow transplants and the other from patients diagnosed with
breast cancer.

Cet article explore les excursions dans le temps et leurs implications.

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