Which statistical tests are appropriate for estimating drug treatment effects in a crossover design (transition from medication to placebo)?

Hi all! I am interested in estimating drug treatment effects in a crossover design where I have a baseline, week 20 and week 40 measurements (1. univariate; 2. multivariate) for a set of 30 patients. 15 of these patients were treated with active medication during the first phase (baseline to week 20) and were on placebo for the second phase (week 20 to week 40). The remaining 15 patients were on placebo for the first phase and treated with active medication in the second phase. I am interested in evaluating if the medication helped this cohort while also accounting for baseline differences, age and gender, etc. As I mentioned earlier, the recorded measurements could be univariate (e.g. mental state scores recorded at each of the three timepoints), or multivariate (e.g. thousand-dimensional imaging features estimated at each time point). I would appreciate all informed suggestions for this research question. Thank you for your time in advance!


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It has been awhile since I used the MMSE, remind me how it is explicitly formatted and scored and what the distribution of outcomes look like. Is it the one where it is around 6 questions (e.g., US Pres, Count backwards, draw shape,...)?

Did you have inclusion/exclusion criteria related to the MMSE in the study and was looking at the MMSE the primary endpoint of the project or just some exploratory thing you all are looking at now that the study may not have been powered for or designed to analyze?
MMSE is a series of 30 questions testing of orientation, attention, memory, language and visual-spatial skills. Please note it is just one score; there are several other such cognitive/functional/behavioural scores recorded which I am interested in testing. Additionally, I would like to see if the imaging features (structural MRI which are 3D images hence multidimensional/multivariate observations) could inform us something on top of what these scores captured. Again, the cohort constituted people with mild impairments, and the purpose was to identify (1) if the active medication helped this cohort (which was studied with a crossover design, hence a bit complicated and should likely also factor in the treatment pattern i.e. active to placebo or placebo to active). Thanks!
Just wondering what all analysis would be meaningful and work towards setting up a complete report on this data. A. Timepoints T1, T2 and T3; B. Groups: A2P (Active medication T1 to T2; Placebo T2 to T1) and P2A (opposite pattern of A2P). C. Response variables: C1. Scalar clinical/behavioural/functional scores C2. Multidimensional imaging observations. D. Confounds: Age, Gender. I think probably baseline responses must be considered as covariates too.


Less is more. Stay pure. Stay poor.
Well if treatment was randomized controlling for confounders and baseline wouldn't be necessary in most studies. But given the small sample, there is risk of a single outlier patient being in a group. So what do the format of the MMSE look like? Is it a percentage score between 0 and 1 or what? And what is the distribution of its values. Can each values exist between 0 and 1 if that is how it is formatted?
Thanks so much! This example gave me good clarity about few things. Just worried about how to go about the baseline measurements. Or just work with difference in the measurements. I know there is a lot of debate on this, and most of the people I know prefer to work with actual followup measurements while accounting for the baseline measurements in their models, as opposed to working with difference of measurements. For example, the first approach would consider values at timepoints 2 and 3 while accounting for timepoint 1 in the used model, whereas the other would work with measurement differences between timepoint2 - timepoint1, and timepoint3 - timepoint2. Wondering what would be a more justifiable approach here..


Less is more. Stay pure. Stay poor.
In post #3 you state subjects were randomized. If you randomized you don't necessarily need to control for baseline, unless there is a very strong confounder that by chance ended-up disproportionally in a group.

Baseline is so important when you don't randomize since you won't have 'exchangeability'. So if I had a weight loss intervention, I would want to control for baseline weight if it was not comparable between groups.