Known-fate Censoring Questions

questions concerning analysis/theory using program MARK

Known-fate Censoring Questions

Postby tracker » Sat Jan 13, 2018 3:58 pm

When putting together encounter histories for Known-fate modeling, why does it result in bias if you record an animal as alive during an interval when it was missing but it must have been alive because you found it at a later date?

I have read and re-read Chapter 16 and section 16.7 on censoring in the MARK book, including the explanation that "The reason for this bias is because a dead animal is less likely to be encountered at a later occasion than if it lives. So, you have a biased sampling process – animals are mostly encountered because they are alive, and hence estimates of survival become too high if the ‘00’ values are replaced with ‘10’." I don't really understand this explanation and would appreciate it if someone could give me more information.

I am largely concerned about this because I would like to estimate survival from a dataset wherein a few telemetered animals were missing during an entire weekly interval, were located during the following weekly interval alive, and then were found dead during that same second interval (animals were tracked thrice weekly). From what I understand of Chapter 16, because these animals were missing/censored at the end of the first interval, I should therefore censor both intervals even though I know the exact interval in which the animal died. I am worried that censoring deaths from my dataset (which is relatively small) could lead to worse bias than including at least the death intervals, if not the earlier ones in which the animals were missing but must have been alive.

Additionally, this work is done at a military base where one of the primary reasons that the animals occasionally go missing is simply because the team could not access the areas on a given week because of military operations that barred them access. So, it seems very odd to me to have to censor these intervals when I am almost 100% certain that these animals would have been located if we could have looked and when they were found again at later dates.

Any advice on how I should handle my encounter histories formatting with respect to censoring would be much appreciated!
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Re: Known-fate Censoring Questions

Postby cooch » Sat Jan 13, 2018 6:08 pm

Take the following encounter history for a known-fate analysis:

Code: Select all
10 00 00 10

Interpretation -- alive at start of interval 1, didn't find it in interval 2 -- so, if we stopped there, you don't know the fate in that interval), detected it again at some point during interval 3, so we make it 're-appear' at the start of interval 4. The correct probability expression for this would be S_1S_4.

The natural question (which you're posing in a fashion) is 'why not S_1S_2S_3S_4?' -- which would seem to be correct if you back-filled the encounter history to

Code: Select all
10 10 10 10

The assumption you'd be making here, if you did this sort of 'back-filling', is that you're detecting live animals with the same probability as you would in finding dead animals. In other words, that the probability of them 'coming back into the system' is the same if they were live or dead, which is clearly not logically possible. Generally, if an animal departs the study area and dies, chances are you won't detect it again. On other hand, if it temprarily emigrates from the samplng region and then returns, then you will detect it with some probability. So, putting the S_2 and S_3 into the encounter history ('back-filling'), you'd bias your survival estimates high.

Hope that helps.
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Re: Known-fate Censoring Questions

Postby tracker » Sun Jan 14, 2018 1:32 pm

Thank you for your reply and advice!

What you're saying about back-filling being improper makes sense for animals that aren't detectable off-site, but what if you don't really have an issue with detectability, even if the animals die? Our study animals are terrestrial snakes that don't have terribly large home-ranges, and I don't believe that we really have issues of emigration like may be the case for certain species of birds or mammals that might move longer distances. It seems as though the possible bias from back-filling could vary depending upon study site and species.

For instance, sometimes the snakes go "missing" because we can't check certain areas of the military base for a few weeks due to training activities, but we typically find them once we're given access to return, whether they're dead or alive. As I alluded to in my first post, we have on multiple occasions found the transmitters of dead snakes along with their remains, so I don't think that the detectability of dead animals at our site is necessarily lower than live because we can still find their transmitters once we are able to look for them again (though it is possible that some transmitters could malfunction and be undetectable if they were too damaged by predators, but transmitters sometimes malfunction in live animals also).

Essentially what I'm wondering is, wouldn't I be biasing the survival rates even higher if I exclude known deaths than if I were to back-fill so that I could include them?
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