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I am currently trying to fit a survival analysis model. After reading through several books, I have still not come across the theoretical implications of implementing survival analysis on data that only contains deaths.

For example, usually some data, such as the one described here:

http://www.utdallas.edu/~pkc022000/6390/SP06/NOTES/hmohiv.txt

has a censoring variable that assigns the value 1 if the patient died during the study, and 0 if the patient didn't die during the duration of the study.

However, I have data that records everyone as having died. The other people who survived indefinitely were not included in the dataset and I cannot obtain it as it is now completely lost. In this case, would it theoretically make sense to put a censoring variable of 1 for every single observation? Thank you!

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    $\begingroup$ When you say "The other people who survived indefinitely were not included in the dataset" do you mean even the knowledge of how many there were is not included? $\endgroup$ – Glen_b -Reinstate Monica Aug 26 '14 at 12:40
  • $\begingroup$ yes, that is absolutely correct, the data of how many there were doesn't exist because no one recorded it. thanks! $\endgroup$ – James Schwartz Aug 26 '14 at 12:49
  • $\begingroup$ i guess what i am trying to ask is if the results from a surivival analysis is the same between a dataset where EVERYONE actually died, and one where it SEEMS like everyone died, but was only due to incomplete data. Thanks! $\endgroup$ – James Schwartz Aug 26 '14 at 12:53
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    $\begingroup$ Then all your censored data is all missing, and your results will be biased, potentially by a lot (after all you don't know how bad it might be, so you can't even bound the effect). $\endgroup$ – Glen_b -Reinstate Monica Aug 26 '14 at 13:18
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If you leave out the censored observations, your results might be very wrong. The example below follows ten people. Two died during the course of the study, and eight were alive when data collection ended (so their data are censored). The blue survival curve accounts for the censoring; the red one does not. They are very different!

enter image description here

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