I have a dataset of about 90,000 cases. In something like 10% of these cases, an intervention was applied to hopefully bring about a specific outcome. The intervention was not equally applied across geographical regions. (One region used it a lot more often than the other two.) The outcome is binary - we know whether or not it happened, and when it happened in relation to the intervention.
But, that same outcome also happens without the intervention. In fact, the intervention is only used on "difficult" cases that wouldn't achieve the outcome on their own. And what we don't know is whether or not the case would have that outcome even if we hadn't applied the intervention.
What I want to be able to identify is one or both of two things: 1. If the intervention is effective. (It probably is.) 2. In which circumstances it is effective - meaning which factors in the dataset (age of case, type of case, gender, occupation, region, etc.) are more likely to bring about the desired outcome in conjunction with the intervention.
Ideas? I have a few, but don't want to limit responses.