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Dear Martin
You have a 2x2 factorial design at the between-subjects level: treatment (pre vs post) and group (subject set). So to fully encode this in your GLM, you could model the mean (expected by the PEB system to the first column), the two main effects (treatment and group) and their interaction. You could code the main effects as 1s and -1s as you suggest, making sure you mean-correct them, and to generate the interaction regressor you element-wise multiply the mean-corrected main effect regressors.

I am interested in determining whether its treatment 'A' which improves effective connectivity within a network for set 1, or its treatment 'B' which improves effective connectivity within a network for set 2.

Those are the simple effects – an effect of treatment in group 1 and an effect of treatment in group 2. If that’s all you want, you could just include these in the design matrix as you suggest (and mean correct them) but it doesn’t fully cover your factorial design without the interaction.
Q1: Whether I mean center 'age', 'sex', 'amount of dose' and 'time since stroke' from overall sample i.e., from both conditions together, or calculate mean centered values separately for treatments A and B.

From the overall sample (for age and sex). Just include non-zero values for dose and time since stroke in the patient group.

Q2: For M.X matrix, should I use mean centered 'dose used' values only for post-treatment conditions and put 0's for pre-treatment condition, because there was no dose used during pre-treatment condition? Correct?
Q3: For M.X matrix, should I use mean centered 'time since stroke' only for post-treatment condition and put 0's for pre-treatment condition? Or it will be same values for pre- and post-treatment condition because 'time since stroke' values are same for pre- and post conditions.

Yes but note, for every covariate you add, there’s a new parameter added for every DCM connection. So you’ll be using up your degrees of freedom for each new covariate. You might want to keep the number of covariates at a minimum.

Q4: If I want to compare connectivity for controls with post-treatment condition, then again should I mean center 'age' and 'sex' from overall sample or separately for controls and patients?

I think overall should be fine.

Also, should I include 'time since stroke' and 'amount of dose' used also as covariates, which will of course be zeros for controls.
Or there is no need to include 'time since stroke' and 'amount of dose' as covariates because I am comparing controls with patients. If so, I doubt then how to incorporate the variance as the 'amount of dose used' and 'time since stroke' values differ between treatments A and B.

See above comments – yes you can model them, but there could be a big cost in terms of model complexity.

Best
Peter