The name is absent

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event, we assume each subject has unit mass, while after the occurrence, we assume
each subject has zero mass. Next step before fitting the model is to sort all the ob-
served time points in ascending order and let the smallest be on the far left. Assuming
independent censoring, the mass of a censored subject is redistributed uniformly to
all the event time points on its right. Applying this procedure to all (independently)
censored subjects from left to right, the mass should be distributed on event time
points only. Such procedure resulted in the Kaplan-Meier estimator.

Zheng and Klein’s research (1994) applies this idea of “redistribution of mass” to
obtain self-consistent estimators for the marginal distribution functions and modeled
dependent competing risks under an assumption of a copula-based conditional survival
probability function. Unfortunately, under the constraint of a copula function for the
joint distribution, the redistribution of mass to the right is no longer uniform for
dependent censoring. Here we further extend Zheng and Klein’s method to the Cox
proportional hazards model. For a dependently censored subject, we show below how
its mass is redistributed to the right.

Assume that x_i, i = l,...,n, are sorted time points in ascending order without
ties. If the subject i is censored (dependent censoring) at time x_i, then for each event
time point Xj > x_i, we want to compute the probability that this subject i fails at
time Xj. With some calculus (Zheng and Klein, 1994) under the joint distribution

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