Bland-Altman is for comparing measurements from two different approaches.

It sounds like you are looking to calculate the confidence intervals for your sampling approach, but it is hard to provide more direction without more details on the measurements you will be making.

• Generally speaking, a sample is always representative of the population from which it was selected. However, the measurement of any single sample can not be used to estimate the population value with any certainty. The same can be said for a single sampling measurement from an individual.
• Is the "n=8" the number of mares you will be sampling or the number of biopsies from each mare?
• Uteri can be highly variable in histological appearance depending on biopsy location, estrous cycle timing, gestation timing, and gravidity. Defining your sampling strategy (timing and biopsy location) to minimize variability among your animals is likely more important than minimizing variability among biopsies from a single animal.

Thank you John. Eight biopsies will obtained from each mare (after slaughter), and cycle stage will be determined based on findings on the ovaries. H&E slides will be evaluated for degenerative changes (mainly fibrosis). Several studies have evaluated whether one biopsy is representative for the entire uterus, with very different results, mainly due to small sample sizes, different classification of histological changes etc etc. I am aware, that degenerative changes depend on age, parity, repeated inflammation in relation to breeding etc.

We will try to answer this research question using slaughter house material and hopefully a proper sample size.

Other studies have found that the histological "score" (based on different categories) varies among the biopsies (obtained from the same mares) in 0-30% of the mares. The number of mares in these studies varied from 40-110.

So my question is, how to calculate the correct sample size for this. Let say, that we will accept that up to 10 percent of the mares may differ in biopsy score.

I don't know that I can give you a good sample size estimate for that. The most straightforward calculation, estimating sample size for detecting discordant scores in a sample, gives an n=1383 with a (assumed) prevalence of 10% at a 95% confidence level and a 5% margin of error with a 0.90 assay sensitivity. This would be quite the undertaking (>11,000 H&E stained slides to prepare and score).

I don't know that this is the proper calculation for your question, and perhaps I am misunderstanding what you are looking to do.

I would consider establishing an arbitrary, large sample size (e.g. n=100) and determining the proportion of discordant biopsies that you obtain. It's going to be difficult to determine biopsy sampling error without being able to analyze the entire uterus.

Some things to consider:

• If you perform more biopsies from a single uterus, you are more likely to find discordant scores. How many biopsies from a uterus need to have a different score to consider the results discordant?
• Is this discordance meaningful? Enough to warrant multiple biopsies?