Difference between regression between groups vs across all subjects (continuum)? I'd like to understand this better in terms of drawbacks and suitability. 
For example, if my data includes investigating differences between 2 patient groups and a control group (3 groups in total), how can I tell which is a more appropriate method to use and maybe, adding strength to the model?
Thank you very much.
 A: I'm not entirely sure on this one, so I hope somebody else can join in the discussion.
One option is to do a standard linear regression with indicator variables for patient groups (i.e. x1 is a binary variable with 1 meaning patient group 1 and 0 meaning patient group 2 or control and x2 is a binary variable with 1 meaning patient group 2 and 0 meaning patient group 1 or control) and the other covariates as you please. You will then compare both patient groups to the controls but you will not compare the patient groups with each other. You can do this by changing indicator variable x1 for another, we can call it x3, which is constructed so that 1 means control and 0 means patient groups 1 or 2. However, the drawback of this model is that you do not take the matching in account, and that's where I'm not sure.
Since you did the matching only by age and gender, including these variables (and possibly their interaction term) should be enough, provided the assumption of a linear relationship between age and the DV holds (if there is a relationship). If not, you need to add a non-linear variable.
Anyway, I'm not sure this is the best way to handle the case-control design. Perhaps a linear mixed model could be used, so that each patient and its control(s) will share the same level in a factor variable and this factor acts as a random intercept, but I'm not sure this would be appropriate.
Hope this helps.
