I have two groups.
Group 1 received intervention A and Group 2 received intervention B. I'm interested in seeing if intervention A is more effective than intervention B. People cannot be enrolled in both interventions at the same time.
Am I able to use difference in differences-in-differences to compare the two interventions, or would I need to include a third group where the people receive no intervention (control group)? What I have are the dates in which someone enrolled in their respective intervention and the pre-enrollment and post-enrollment outcomes. The outcome was measured every 3-6 months pre-enrollment and every 3-6 months post-enrollment.
Also, since people can enroll in any of the interventions at different times, I would like to standardize the time dimension as the number of days before and after enrollment into the intervention. If I were to include a third group, how would I standardize the time since there is no enrollment?