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I have been working with a dataset that I would like to analyze using the Cox PH model in R. The data I have includes:

  • a start measurement year
  • an estimated mortality year
  • survival time that is the difference of these two
  • multiple complete case covariates (no NAs)

The problem I cannot seem to find an answer to is how do I deal with individuals who have survived beyond the study period (survival time = NA)? I am familiar with the concept of censoring, however I do not believe this is appropriate in this case - let me explain why.

I have data from 3 different states: Nevada, Colorado, and Arizona. Each of these contain approximately 120-250 individuals who experienced the desired event (in this case mortality) and 2000-4000 individuals who did not (survival time is listed as NA). Censoring this many individuals gives drastically different results, as expected. However, filling the NA's with a survival time equal to the study period also seems inappropriate - as I am assuming their death upon completion of the study. The inclusion of NAs in the Cox PH model removes these observations due to missingness, therefore censoring them automatically.

How should I approach this issue? Pseudo-filling survival time is likely affecting my analysis. Is it actually appropriate to censor this many observations? Is there a way I can correct this?

Thank you for your time, and please let me know if further clarification is needed - this is my first time making a forum post.

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    $\begingroup$ Censoring seems to be the right approach here. It seems like "administrative" censoring, i.e., you can't wait until every event has happened. $\endgroup$
    – Michael M
    Dec 13, 2023 at 21:01
  • $\begingroup$ Thank you for your comment, Michael! Maybe I am misunderstanding the concept of censoring. Is it not inappropriate to exclude this many observations? $\endgroup$ Dec 13, 2023 at 21:03
  • $\begingroup$ Censoring means setting the end time to the "end of observation date" and then setting the event flag to 0. You don't remove any observation. The response consists of a (time, event) tuple. $\endgroup$
    – Michael M
    Dec 13, 2023 at 21:05
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    $\begingroup$ I think your edits provided clarity that I am doing it correctly, thank you for your clarification. $\endgroup$ Dec 13, 2023 at 21:16
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    $\begingroup$ Agree with @MichaelM. This is exactly what censoring is for. They are censored in the sense that "the event happened/will happen after the conclusion of the study", and they should certainly be included in the analysis $\endgroup$
    – Alex J
    Dec 13, 2023 at 23:36

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Converting comments into an answer. As @MichaelM said:

Censoring means setting the end time to the "end of observation date" and then setting the event flag to 0. You don't remove any observation. The response consists of a (time, event) tuple.

In this situation, for an individual who hadn't yet experienced the event, you would set time to be the duration of the corresponding observation period, but event would be set to 0, indicating a right-censored event time (instead of to 1, which marks observed event times). Particularly with this "administrative censoring" at the end of a study period there is no problem with a high fraction of censored cases, provided that there are enough events during the study period.

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