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I'm trying to find a calculation that will allow me to calculate both:

  1. the number of farms and
  2. the number of sheep per farm

I would need to sample to determine the absence of a disease for the South of England, or at least determine that the prevalence is below 1%.

Information available to me:

We have a rough idea of the total number of farms per county, and the number of sheep within each county, but not how many sheep are on each individual farm.

Additionally we know that the disease varies between farms (40-90% prevalence) and on farm (10-80% prevalence).

The test that we would use to diagnose the disease has a 95% sensitivity and 99% specificity.

I have already considered two-stage sample strategies, of which limited sampling seems to be the most feasible in terms of cost, however as I have no ability to find out the number of sheep per farm in advance (necessary for the home office licence application). I have also looked at FreeCalc, however this doesn't seem to take into account the within cluster variance in disease prevalence...

Any ideas?

Many thanks

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In case anyone else is looking for the answer:

I ended up using an R programme called FFD. It has a nice GUI for those not particularly familiar with R.

The details can be found here: http://cran.r-project.org/web/packages/FFD/vignettes/FFD-intro.pdf

It allows you to do two-stage cluster sample size estimations for an imperfect test. Furthermore it allows you to include cost considerations. I ended up doing individual, rather than limited sampling, as this takes into account the size of the farm in terms of animals/farm to sample. The FFD programme outputs a table for you to tell you how many animals on different farm sizes you would need to sample (i.e. 0-10= all animals, 11-50=5 animals 51-100 = 7 animals, >100= 9 animals), unlike FreeCalc, which you would have to calculate yourself.

The only downside of the programme is that you need to have a list of all the herds with the number of animals on each farm in advance- for me this was possible through a APHA information request.

Hope this helps someone else.

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