Difference in difference, controlled interrupted time series and synthetic controls

We thank Benmarhnia and Rudolph [REF] for their critical appraisal on our recent article on the use of controls in interrupted time series (ITS) studies. This offers the opportunity to clarify some important issues related to ITS and controlled ITS (CITS) designs and their comparison with other methods applied for public health evaluation. In particular, we argue that Benmarhnia and Rudolph based their assessment on three incorrect premises: that ITS without control is not a valid design for assessing causal relationships; that CITS is just another name for the difference-in-difference (DID) design that they advocate; that the synthetic control methodology represents an alternative to CITS.