Small sample size survival analysis

[beasley]

Hi Folks,
I have run into a snag analyzing some mark-recapture data and am looking for some advice. My study design consists of 25 populations which have been monitored using mark-recapture for 6 years (1, 10-day mark-recapture session conducted at the same time each year) with reasonable capture probabilities (~50%). The problem that I am running into is that I have small samples sizes for most of these populations (<10), despite the fact that I have captured ~85-100% of the resident population during each year. I am specifically interested in estimating survival for each population to compare these values but because of my small sample sizes many of the model results do not appear to be very robust. Does anyone have any suggestions as to how I can obtain population specific values for these parameters with a limited sample size or whether it even is possible? My understanding is that when estimating N-hat using closed population analyses you can treat each population as a disparate attribute group to calculate overall estimates of p and c for the combined data set but still obtain population specific estimates of N-hat using the p and c estimates from the combined data set (of course by making a few assumptions about the populations). Is there a similar approach that can be used for survival analyses? Any information would be greatly appreciated.

Thanks,

Jim

[ganghis]

Hi Jim,

Since capture probabilities are so high, I think I'd start by pooling data for each of your 10 day sessions into a single session so you have 25 groups and 6 sample periods. Then you might think about sharing information on detection probabilities between groups in MARK using the CJS model ("Recaptures only" I think). However, you'll need to think carefully about what formulations make sense. For instance, does detection probably vary in a systematic way over time that effects all populations similarly? If not, it may not make sense to perform a combined analysis of all groups, especially if you're interested in separate survival estimates for each population (though it is probably worth comparing models with separate versus equal survival to look at this assumption).

With separate survival for each population precision will likely be quite poor on survival estimates. One thing that might help is to treat the population itself as a random effect - but I don't think that's possible in MARK. If interested in going that route, you might look at how Andy Royle has implemented some M-R analyses in WinBUGS (see his and Dorazio's book on "Hierarchical Modeling and Inference in Ecology" for a few examples). You'd probably need to make clever use of indicator variables to reference populations in order to code this efficiently.

Cheers, Paul