survival probabilities in robust design

[storrence]

I have a question regarding robust design survival probabilities.

I have weekly survival estimates. Let's call them wk1 wk2, etc. Assume 4 weeks.

Since the population is considered open between primary periods, is the following reasoning correct?

The survival estimate for all individuals caught in week one to the end of the 4 weeks is wk1*wk2*wk3*wk4. But, this is ONLY for those individuals caught during week 1. Survival for those first caught in week 2 would be wk2*wk3*wk4.

Therefore, I CANNOT come up with 1 survival estimate of individuals from week 1 to week 4 because new individuals are coming into the population (allowed because open between primary periods). Is this correct?

[Bill Kendall]

First, if you have a robust design where the primary periods are weeks, I'm assuming you don't have more than two closely spaced secondary samples. If your sampling for a given week takes almost a week, then you are coming close to continuous sampling. This violates assumptions, but the effect of this on survival has not received great attention.

Second, it appears to me that this question does not apply just to the robust design.

Now to the question. If you are modeling survival in the "usual" way (i.e., as a function of time, not cohort), then it doesn't matter whether or not new animals are entering the study as you go along. Under time dependence you assume that their survival probability is the same as that for the animals first captured in the first week. If you don't trust that, you can manipulated the PIMs or design matrix to get the model you want (e.g., model in transience, age dependence, etc.). Then take whatever product of estimable survival probabilities you are interested in.