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Let's say I'm observing the mortality of flies.

Say I have 100 flies that are born throughout the year.

And also say I am recording the alive/dead status of a fly every single day, without fail.

So say I had a fly born yesterday. Today I observe that it is still alive.

Would I, or would I not include this data in a cox proportional hazards model? Is the fly considered "censored"?

I ask, because I am seeing a big uptick in the hazard rates on the very last day of my observations. This is clearly driven by the flies that are still alive (which I consider censored). I'm now leaning towards dropping them from the data entirely.

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    $\begingroup$ What do you know, precisely, about how long your hypothetical fly will live? What, then, will you record for the value of its lifespan? $\endgroup$
    – whuber ♦
    Commented Sep 14, 2018 at 3:09
  • $\begingroup$ So you're saying the appropriate thing to do is censor the flies that are still alive? $\endgroup$
    – JoeBass
    Commented Sep 14, 2018 at 3:15
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    $\begingroup$ I wouldn't censor the flies--please leave them unharmed. :-) Just note that the lifespans of the still-living flies are unknown, but you do have definite lower bounds for them. That's right-censored data, by definition. $\endgroup$
    – whuber ♦
    Commented Sep 14, 2018 at 3:33
  • $\begingroup$ It's pretty well known that non parametric hazard rate estimates/Kaplan Meier estimates/ baseline hazard functions from Cox regression become pretty unreliable, if your risk set becomes small. Perhaps that's the issue you have? Considering the flies as still alive (=live longer than current observation time = right censored) when they are indeed still alive is presumably not the problem. $\endgroup$
    – Björn
    Commented Sep 14, 2018 at 5:18
  • $\begingroup$ Could you explain in precise detail how you are doing your experiment. I would expect that your observe all flies for a fixed window of time from birth and that your cox's model is based on time from birth not current calendar day. Maybe due to practical constraints you may not be able to observe the same length each time? If we understand what exactly you are doing we can give appropriate advice, $\endgroup$
    – ReneBt
    Commented Sep 14, 2018 at 7:19

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In survival analysis, data are censored when you know that the animal lived up to the time of censoring but after that: you don't know (because it hasn't happened yet), don't know (because the animal disappeared or somehow got off treatment), or know but can't use the data (because the treatment wasn't given). Your situation is #1. You don't know survival after today because it is the future. But you know the survival until now. Don't remove those data! That would bias your results.

The "uptick" sounds wrong. My guess: You should be entering data for each animal once, on its day of death or censoring. It seems as though you might be entering data for some animals multiple times.

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