Individuals reentering a population after a treatment

[cnicolai]

I'm trying to look at the effect of a treatment on the probability that an individual will reenter the population. First, individuals have to be in the population, in this case they have to breed once. Then, a treatment is invoked and I'm interested in their reappearance rates (start breeding again) over the next 8 encounter occasions. The treatment consists of a single level treatment and non-treatment control.

The issue I have is for individuals that are never seen again after the treatment is invoked. This is important, as the treament may have casued permanent emigration. What is happening is I know an individual was available for treatment, but I have no further information.

I'm using a pradel survival and seniority model. Individuals are conditional on breeding once, then allowed to enter the sample. A treatment is invoked upon a sample, then a capture history is built from the 8 subsequent encounters.

I know I need to deal with these individuls that are released after the treatment and never seen again, but in this case, their capture history would be 00000000 and thus are never released. Anyone have any suggestions? I do have an option to include a capture in the final encounter occasion from encounters from the global population, but I'd like to deal with this initial problem before I start dealing with this extra data.

Thanks,
Chris Nicolai
University of Nevada Reno

[gwhite]

Chris:
You need to enter the animals with both the pre-treatment and post-treatment encounters (or lack thereof), and code the treatment effect as a time-varying individual covariate for each animal. So, if you have, say, 5 occasions, and the treatment occurs on occasion 2, you would code the 5 individual covariates as 0 1 1 1 1.
If you call these Treat1, Treat2, Treat3, Treat4, and Treat5, the coding for the design matrix for phi would be:
1 Treat1
1 Treat2
1 Treat3
1 Treat4

(only 4 phi estimates for 5 occasions).

Gary

[cnicolai]

Well, I guess this is where I question whether use of a pradel model is appropriate. I am trying to use the gammas to examine when individuals return to the breeding populaiton after a treatment, rather than a detection probability approach.

I may be confused, but by even using the covariate technique, I will be using individuals that already were in the population prior to the treatment, therefore already recruited.

What I have is a list of individuals seen breeding across 20 years. As is typical, some are seen often, some only seen once. I have about 2500 individuals in the sample with a total of 7000 encounters. A treatment is invoked randomly to some individuals (51 individuals in total).

I built the capture histories with the following criteria:
1) An individual is assigned to control, or treatment.
2) Control birds enter the sample when first seen breeding
3) Treatment birds enter the sample when treated
4) I built a capture history for the next 5 capture occasions as all individuals who did return as a breeder did so within 4 years. That is, the are conditioned to enter the sample after the initial encounter
Modeling:
1) Each cohort of releases was a group, crossed with treatement
2) I allowed survival and capture probability to be year specific
3)gammas are constrained to be cohot specific for control birds, and due to small sample sizes of treatment birds, they are treated as one cohort.

Goal:
To estimate gammas such that they reflect reappearance rate after treatment. My hypothesis is that treated birds will take longer to reappear and do so at an overall lower rate

Problem:
By taking this approach, that is, conditional on entering the sample the first time seen after treatment, an individual who never returns after treatment is not in this analysis because their capture history is 000000. This causes major problems as I am interested in birds never returning following treatment.

As a side note:
I do have access to data from wintering areas and do know that a high percentage of these birds are still alive >=5 years following treatment

Thanks in advance for any suggestions,
Chris