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I apologize in advance if the question is rather simple, but I have been having a difficult time figuring it out.

I am an experimental scientist interested in modeling human disease with induced pluripotent stem cells. The disease is fairly common, but doesn't have a common genetic basis. It is mainly driven by rare genetic variants of high penetrance but in a small number of individuals.

For (let's say) 5 patients out of 1000 screened affected cases, we are able to strongly associate mutations in one gene with the condition. These mutations are completely absent from a control population of 5000 individuals.

We have made stem cells from 2 of those individuals to determine whether these mutations result in cellular dysfunction (let's call this phenotype A) when compared to controls. We have several stem cell lines per individual. In this situation, phenotype A is an 'intermediate phenotype'.

The big conceptual question for me is this: Am I modeling the disease or am I only modeling the effect of the disease-associated mutations on cellular function? How can I determine the sample size to test the former claim with, say, 80% power?

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You can already see the Wikipedia article on power calculations, so I won't repeat it here.

Let's take the parameters you probably already know:

  • You already have the base rate - the rate at which the disease will occur in a population that doesn't have this particular mutation.
  • You've got a beta value (you want an 80% chance of not making a type II error / missing a real effect)

Before you can arrive at your value for n, you still need to choose:

  • The rate at which you expect the disease to occur in a sample population which has the mutation
  • The variance that you expect that rate to have - so, you are characterising your sample mean and sample variance, for the population with the mutation, given that your hypothesis is true.

Visualise what you are doing as picking sufficiently large value for n that the curves describing the mutation-free, low-disease rate population and the mutation-bearing high-disease rate populations don't overlap much (the overlap is where your Type II error would happen - a mutation-effect-mean that happened to fall too far inside the general population's distribution).

If your variance happens to be small (you mention a high penetrance), that helps a lot - your sample size can be surprising small, if the distribution in the "effect" population is really tight.

Does this help?

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