Dear experts,

When comparing MRI data of patients vs controls, I often want to take into account data that are only available in the patient group, i.e. disease severity and disease duration.
The overall statistical problem is typically something like "Are there differences between patients and controls and if so, how do the disease characteristics affect this difference?"

What is the most appropriate design for answering a question like this?

Usually, I will first try to compare the two groups without covariates, e.g.

(Design A)
Patients    Controls
1    0
1    0
1    0
0    1
0    1    
0    1

Contrasts
Pat>Con    1    -1
Con>Pat -1    1

Then I add the covariate (let’s say that the two groups are perfectly matched for age and gender, so I will not need to control for that).

(Design B)
Patients    Controls    Disease_duration
1    0    5
1    0    7    
1    0    6
0    1    0
0    1    0
0    1    0

Contrasts
Pat>Con        1    -1    0
Con>Pat     -1    1    0
Duration+    0    0    1
Duration-    0    0    -1

Should I demean “disease_duration”? I’m not really interested in the mean values of each group, so I don’t know if that is necessary. And if so, should I do it across the groups or within the patient group?
I guess it doesn’t really make sense to “control” for the effect of disease duration, when this is only applicable to one group.

A worked example:
Using design A, I find an area with a significant difference for contrast 1, i.e. patients>controls.

Using design B, I find no significant differences for contrast 1 but instead a significant difference for contrast 2, i.e. controls>patients, in the same area that was different using design A.
Also, contrast 3 is significant in this area, while contrast 4 is not.
How should this be interpreted?
Apparently patient values in the area are generally less than those of controls.
Also, the patient values in the area are linearly dependent on (increase with) disease duration.
It would not be fair to only run design B and conclude something like “Patient values are larger than control values, when you take their disease duration into account, and this difference increases with increasing disease duration”.
(I have seen published papers, that present interpretations like this).

Another example:
Using design A, there are significant differences for contrast 1.
When using design B, these differences are no longer present, and none of the other contrasts reach significance. Interpretation?

All best,
Pernille