Survival estimates of 0

[mgroner]

I'm running a Multi-state mark-recapture analysis on a dataset where states are represented by health (healthy, mild, moderate or severe disease). In several of the time points, the healthy state is not present. The best fit model includes an effect of time and state on survival ('from.to+time'). However, the model is estimating survival as close to 0 for the time steps when the healthy state is not present. (Biologically we know that this is because the healthy individuals are becoming diseased, not because they are dying). For all other time steps the survival estimates are quite high. (This issue also occurs if specify survival as 'from.to.time', and the survival of the healthy individuals is also very low when I specify survival with 'from.to'). I'm wondering if the lack of data in all states at all time points is leading the model to converge on a biologically implausible result. Can I constrain the survival to be within a specific range (for example survival of healthy> survival of mild disease)??

Thank you!

[simone77]

This situation does seem unusual, assuming I’ve understood your data correctly. Let’s consider an example like this:

10202
10234
13204
...

Here, 1 represents individuals detected as healthy, 2 as mild disease, 3 as moderate disease, and 4 as severe disease (since you’re working with a multistate model, I assume you don’t have a fifth event for undetected individuals).

Now, if in your second occasion you never observe a 1 (healthy individuals), the first thing I would ask is why. Is there a biological reason for this absence of healthy individuals at that time point? If so, it could imply a structural absence, meaning that there’s a biological mechanism preventing individuals from remaining in or returning to the healthy state at that time. In such cases, you might be able to constrain the initial state probabilities, fixing them to zero for healthy individuals at that/those specific time point/s.

However, without more details about your data, this is just a general suggestion. If this lack of healthy individuals isn’t biologically plausible, the model might indeed be struggling due to the absence of data in certain states at particular time points, leading to unrealistic survival estimates.

[mgroner]

Thank you for your help Simone.

These are tagged plants, and they have an endemic disease with high prevalence, so I think the absence of healthy plants is biologically plausible and occurs at the peak of the epidemic.

You mentioned this: In such cases, you might be able to constrain the initial state probabilities, fixing them to zero for healthy individuals at that/those specific time point/s.

Can you explain how I would constrain the initial state probabilities for a specific time point? Should I add a time effect to the Initial State GEMACO and then fix the parameter to 0 for the specific time/state combination?

Thank you!

[simone77]

Can you explain how I would constrain the initial state probabilities for a specific time point? Should I add a time effect to the Initial State GEMACO and then fix the parameter to 0 for the specific time/state combination?

I am sorry for the delayed reponse: yes, you can definitively do that. If, for example your Initial State in GEPAT looks like this:

p p *

Representing the probability of initial state in state healty, mild, moderate/high. Imagine you have five occasions and you know that probability for healthy is 0 at time 2 and 3 you can write in GEMACO
to.time
and fix to 0 the corresponding parameters (to 1 time 2, to 1 time 3) in the IVFV.

You can adopt other strategies too. For example, you can assume the probabilities keep the same over all the occasions except at time 2 and 3 when it is different because healthy probability is 0 (but mild and moderate are the same), then in GEMACO you can write:
to.time(1 4 5, 2 3)

and fix to 0 in the IVFV the corresponding parameters (to 1 time 2 3).
Just a couple of examples, several other approaches are feasible, they depend on your biological criteria.