pooled variance of parameters calculations

[nlsanto2]

Hello I have a question related to CMR data analysis. I hope there is somebody who has already faced these problem who can give me a hint.
I have used POPAN package and I obtained the following parameter estimates:

Parameter Estimate Standard Error Lower Upper
1:Phi 0,9934022 0,0024054 0,9865480 0,9967754
2:p 1,0000000 0,6254106E-003 0,9987742 1,0012258
3:p 0,3726369 0,0547070 0,2729743 0,4844407
4:p 0,5227892 0,0621026 0,4021108 0,6408644
5:p 0,4705237 0,0616675 0,3536116 0,5907623
6:p 0,5305776 0,0621577 0,4093428 0,6483078
7:p 0,7807760 0,0523811 0,6615884 0,8664592
8:pent 0,2665353 0,0519947 0,1774727 0,3796625
9:pent 0,1255567E-008 0,0000000 0,1255567E-008 0,1255567E-008
10:pent 0,4800321E-007 0,5403719E-004 0,4732962E-311 1,0000000
11:pent 0,0770509 0,0490104 0,0211674 0,2437342
12:pent 0,0848453 0,0480018 0,0268584 0,2374746
13:N 99,725594 2,7592006 96,634620 108,66143

I want to estimate an average p and pent across the capture occasions.
The question is
How do I calculate a pooled variance of the mean p and pent? Should I use this formula (http://en.wikipedia.org/wiki/Pooled_variance)? If the answer is yes what values should I use for the sample sizes(n1,n2 etc), the total number of individuals captured during the study?

I hope the question is clear and that there is somebody willing to help me
Thank you in advance,
Nina

[AdamGreen]

I would think that the Delta Method should work here. Take the derivative of the derived parameter (in your case, the average) with respect to each parameter (i.e., p or pent). Multiply a vector of those derivatives by the variance-covariance matrix for those parameters, then multiply that answer by the transpose of the vector of derivatives.

Using the average of p as an example...
The derivatives for the average with respect to each p is 1/6. So your vector of derivatives will be:
[1/6 1/6 1/6 1/6 1/6 1/6]. Multiply that vector by the VC matrix for those 6 p parameters obtained from the Output menu in MARK (be sure to transpose the bottom half of the matrix to the top before multiplying because MARK puts the correlations on the top half). Then multiply that answer by the transpose of your vector of 1/6s.

Another simpler option would be to run a dot model for those 2 parameters.

Adam