I'm trying to find a calculation that will allow me to calculate both:
- the number of farms and
- 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...