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I am working on a survival analysis problem and I am having trouble wrapping my head around the weighting on right censored data.

If I have a group of right censored data where the time is longer than the median time to event, shouldn't this data affect my survival curve more than censored data where the time is less than median time.

I am working on determining the reliability/lifetime of a component. I am focusing on one failure mode but there are multiple different modes which are affecting my data.

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Calculations for survival curves are based on the number at risk at each event time. If censoring is uninformative, then a censored case simply provides information that the event for that case happened at some time after its censoring time; it no longer contributes to the number at risk for later events. Thus the late-censored cases are already "weighted" more than early-censored cases in the following way: they contribute to the number at risk for more of the event times than do the early-censored cases. There is no need to add additional weighting if the standard assumptions about censoring hold.

With multiple failure modes, however, you have competing risks. As this article notes, in this context the assumption that censoring is uninformative might not hold. If there are multiple failure modes then you should analyze the competing risks directly rather than perform individual survival analyses for each mode of failure. This paper provides an introduction to the concepts.

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    $\begingroup$ Thanks, I made some fake data which also confirmed this. Thank you for the further reading about the competing risks. I was not aware of this potential issue. $\endgroup$ – Soxman Oct 16 '18 at 15:58

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