Sample size for creating a reference interval

I am a member of a governmental ethics committee where we receive all sorts of applications that involve human subjects.

The application procedure is quite formal and the applicants have a number of key topics they must address, including accounting for the "statistical basis for the study population. This is however not the main focus of the ethics committee and if the underlying statistics, or some other purely research related component is erroneous ("the researchers can not answer their research question with this design"), this is not in itself sufficient for rejection. Rather, our main focus is to protect the integrity and well-being of study participants. That said, it is not unimportant and if the ethical consequences are grave enough it can be enough to reject an application.

A recent application concerned the use of biomaterial from deceased individuals to establish reference values / intervals for a number of elements (e.g. silver, arsenic and so on) in urine and blood. The application was from an official forensic unity and could potentially have implications in real Surprisingly, there are no such standard reference values for post mortem measurements, which of course complicates determining if the cause of death is natural or not.

In their application they referred to a document from the Clinical Laboratory and Standards Institute stating that 120 samples / participants are recommended per group when creating a reference intervall. They write that optimally they would have this sample size for different relevant groups (gender, age categories etc) but in a compromise between what is optimal and practically feasible they decided to sample from 120 individuals, and creating a reference interval from such a sample is better than having no reference at all.

As far as I understand the number 120 has to do with it being the sample needed to create confidence intervals for the big and low end percentiles in however the population is distributed.

From the perspective of a non-statistician I think that perhaps the levels of natural elements used for poisoning humans are normally so low that even a biased reference will be good enough, and maybe this or other similar arguments are valid.

I would appreciate some input from the statistically more skilled on how you view the creation of such a reference interval using that kind of sample size. And that in fact a large number of reference intervals will be based on it as they will measure 65-70 elements.


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Without seeing the data, it is impossible to say what sample size would be sufficient for a prespecified accuracy. However, based on many data analyses I have performed over the last decade, 120 observations is unlikely to be sufficient for studying very low concentrations of some of the elements in human body... You are given a "manual" where they have already made the key decisions. Without them revealing their thought process, it is impossible to assess its quality.
@Forskare, you need to specify how precise you what your estimate to be. (That is something that is outside of statistics.) After that, and when you have specified how the randomness works, then you can calculate (or simulate) the needed sample size.

It depends on the situation for how precise you want the the estimate to be. If you want to know which party will win the next election, then you want to know the result to be within a few percentage points. But if you want to know how well known your local company is, then maybe it is known by 30% of the population, or of maybe by 80%.

So it is impossible to say if it is enough with 12, 120 or 12000.