## Pilot study (independent from software) [Power / Sample Size]

Hi dennis001,

❝ However, could we conduct the Pilot Study based on the sample size? (eg. A total of 30 patients, 10 in each group, were included in our study.)

We need more information. Are you interested in all pairwise treatment comparisons (i.e., A vs B, A vs C, and B vs C) or is one of them a standard treatment acting as a reference (i.e., A vs R and B vs. R)? Are you interested in superiority or equivalence? At least, since this is a pilot study, you must not be worried about multiplicity issues.
Biomarkers are lognormal distributed. Hence, you should apply a multiplicate model $$\small{\mu_\text{T}/\mu_\text{R}}$$ or – easier – an additive model $$\small{\log_{e}\mu_\text{T}-\log_{e}\mu_\text{R}}$$. For any sample size estimation you have to assume treatment difference(s) and variance(s). Note that all versions of PASS require the standard deviation of the treatment difference as input.

The purpose of a pilot study is to obtain estimates of the treatment difference(s) and variance(s) in order to design a pivotal study with a desired power. Estimates are always uncertain. The larger the pilot study, the more certain (i.e., reliable) the estimates will be (the uncertainty decreases roughly with $$\small{1/\sqrt{n}}$$).
In the sample size estimation of the pivotal study you must take these uncertainties into account. Hence, the smaller the pilot, the larger the pivotal. For background in the equivalence setting see this article. Finding an ethical / economic optimum $$\small{(n_\text{pilot}+n_\text{pivotal}\rightarrow \text{min})}$$ can be tricky.

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