I have several years worth of individual level data on several thousand individuals and a corresponding measure. During those years several hundred individuals underwent an intervention with the hope of changing the result of this measure - this intervention could occur on any day in that timespan.
My first approaching to analyzing this dataset was to look at the change in this measure before and after the intervention; however, I wanted to incorporate those who did not receive an intervention in that analysis. My first thought was to conduct a Difference-In-Difference analysis (or the generalized form of it due to the intervention occurring on any one of several hundred dates); however, I am struggling with how to properly set up the control group since there is no single period in which to demarcate Pre/Post. Individuals can show up in the dataset at any point in that timespan and also leave at any point. Also, the intervention occurs somewhat randomly and is not necessarily related to when the individual enters the dataset.
Does the nature of this treatment set-up preclude difference-in-difference since there are no specified treatment periods? What other options are available to set up a control group to compare my intervened individuals against?
