Basic questions about the best way to report precision in quantitative assay validation study

Question

This feels like a very basic question, but I'm feeling stuck on it. I'm writing up a biological assay development/validation study for a method of quantitating multiple organisms from a mixture simultaneously. One of the experiments was set up to be a precision study. Essentially, three users each followed the protocol to measure the same batch of material three times each (on separate days), for a total of 9 different measurements. And in this case, 8 different organisms were quantitated with each measurement. I think it's the nested structure that's are tripping me up.

My current plan is to report mean and SD of each organism for each user, along with an overall mean and SD of each organism at the end. My question is about how I should be calculating those overall SD values in my final column. Should I be using all measurements collected (n=9) to describe overall variation between measurements? Or, because of the nested structure, should I be using the average values of each user (n=3) to describe variation between users? Or, is there a meaningful way to report both and discuss the significance of each?

I should probably mention that all of the calculations are performed on log transformed values, which is also how they will be reported.

Answer 1

This is a typical application of linear mixed models (LMM). For each organism, you could consider applying an LMM with a random intercept for each individual plus the usual error term.

In this way, you are decomposing the overall variability in two components, where one of them is due to the variability of the users.

Assuming mydata is the dataset for a single organism, in R you could do something like this

mylme <- lme(resp ~ 1, random = ~1|user, data=mydata)
summary(mylme)

here resp is the response and user is the user id.

Note: you can't estimate variability for the batch material since you don't have replication within each batch material.