I am planning a 2x2 randomized crossover trial with about 20-25 subjects. There will be one measurement (continuous outcome) with period A (intervention) and period B (placebo) for each individual. There will be a sufficient washout period and I assume no carry-over.
I have 3 questions:
I will only have 2 outcome measurements per subject and a total of 20-25 subjects. I expect the effect size of my experimental intervention to be moderate. I do not expect the outcome to be normally distributed. Ideally, I would like to do a linear mixed effects model with treatment, sequence, and period as fixed effects and subjects as a random effect nested under sequence. Would this model be overfit?
If my assumptions are violated with the above model (I'm most concerned about non-normally distributed residuals) - should I log transform the variables? Or, given the minimal number of observations, should I just do a simple paired t-test instead?
I am considering the necessity of having a pre-randomization trial baseline measure. It makes the trial harder and more expensive to do, but would it be worthwhile for the possible statistical efficiency? The baseline measure could be used to calculate change scores (so that the primary outcome becomes difference in change scores) or could be used as a baseline covariate.
