I am wondering whether there is any relevant literature on how to best estimate the sample size of a hypothetical clinical trial with various treatment effects (10%, 20%, 30%) based on the scores of the first principal component in a PCA. The scores summarize changes of various markers over time which are standardised and which are associated with clinical outcome measures.
Many thanks in advance
I am not familiar with a principal component analyses to be used for sample size estimations. One normally calculates sample sizes based on power which is related to the likelihood to commit a type II error, but I am interested to hear what other people will post in relation to your question. .
The idea of PCA is not based on the same proposals and paradigms as sample size calculation effect size parameters. What you could do is likely plot an effect size based on the parameters for your fist study and from there derivate your sample size.
Now, on the topic on sample size FOR PCA analysis: https://content.sciendo.com/view/journals/eko/35/2/article-p173.xml?language=en
The idea of PCA is to gather big multidimensional datasets into comprehensible and more easily core information. I guess if the PCA is your outcome in itself you could use it as the effect and predict a PCA value for each group, from there the difference in values and therefore the important d value for sample size calculation, on a standard sample size calculation, that would likely be based on a continuous dataset test comparison, well, you get the mean. I hope this was helpful.
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