Dear Anderson, PALM and permutation experts
I have some questions about the possible permutation strategies in the following design using PALM:
I have 3 equally spaced timepoints for the patients and two timepoints (the first and third) for the controls. The main goal is to compare patients and controls. I think I can’t use the second timepoint from the patients in this direct comparison in a meaningful way, so I decided to compare the patients and controls in the timepoints 1 and 3 (pre post) as the main analysis.
I then have a 2(group)*2(factorA)*2(factorB)*2(time) design. I’m interested in the group*factorA interaction, the group*factorB interaction and the group*factorA*factorB interaction at each timepoint, as well as the changes over the timepoints (group*factorA*time interaction, group*factorB*time interaction and group*factorA*factorB*time interaction)
As I understood it, for between group comparisons the subjects could be permuted as a whole using either ee (assuming the same covariance structure in each subject) or ISE (assuming symmetric errors) or both together. So, are these interactions I want to test between group comparisons and this would be a valid option, or do I need within permutations to test these?
The second option I was thinking about would be to assume compound symmetry anyway in all the within subject factors (and also over time) and permute subjects within and whole (using whole within with the options –ee –ise (as I understood sign flipping still occurs only over whole subjects?).
And as a third option I was thinking to do something inbetween by assuming compound symmetry in the within subject factors in each timepoint, but not over the timepoints and then working with exchangeability blocks. So I would permute data within each time point and also permute whole timepoints and whole subjects.
As I understood it, the more permutation possibilities -> the more power, if the assumptions are met. Any opinions which permutation strategy to use is greatly appreciated. Thank you very much for the help.
Best wishes,
Silvano
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