Interrupted Time Series Design with multiple groups More of a conceptual question
The standard ITS design is pretty simple, regress:
Y ~ Time + Treatment_Dummy + Time_Since_Treatment
However, what if the scenario was that there's multiple employees with sales data over time and we are looking to ascertain the effect of a certain training T on sales?
Employees could take treatment T at different times and there could be 100 employees - each one could become an individual ITS analysis.
Is there a way to modify ITS such that it could account for this?
 A: A straight-forward solution is that we can define the time-point intervention was take as $t=0$ as in standard literature and the use employee pre-treatment information as fixed effects, including known time-varying confounders and seasonality, and finally allowing employee ID to be a random effect. i.e. we have something like:
Y ~ Time + Treatment_Dummy + Time_Since_Treatment + Pretreatment_feature_1 + ... + Pretreatment_feature_n + (1|EmployeeID). Use of such "fixed effects" variables is not uncommon (e.g. see The effect of the late 2000s financial crisis on suicides in Spain: an interrupted time-series analysis by Bernal et al. (2013), similarly the use of the mixed effects approach can be seen in for example Segmented generalized mixed effect models to evaluate health outcomes by Saeed et al. (2018)). In any case, do check on residual autocorrelation though, we might need to define a more involved error structure to get accurate standard errors (or potentially bootstrap, in which case I suggest bootstrapping the employees rather than the rows of your dataset generally).
