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It is well acknowledged that we cannot extrapolate the lifespan T of the censored observation.

In the Kaplan-Meier estimation, the estimated $s(t)$ for $t∈[t_j,t_{j+1}]$ is estimated using:

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I am confused by the fact that the censored observation is excluded from the denominator n at the next event point. Since we are not sure if their lifespan is more than the observed lifespan, how could we treat them as dead during the past interval?

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