Hi Dexter, thanks for your question - I couldn't find the particular Campbell and Stanley paper you cite but in general, at least to my understanding, interrupted time series per se does not involve counterfactual analysis, but matched with non equivalent group design then we are in the standard diff-in-diff world with the Parallel Paths assumption. As far as I know, Ricardo and Iliana are the first to formalize the family of parallel assumption as the do. Ricardo also wanted to respond with the following:
Thanks Dexter for your interesting question. Interrupted Time Series
assumes the existence of time series before treatment. The longer the
better. You do not even need the existence of a control group or
It is true that ITS analysis may end up being equivalent to assuming
Parallel Paths, Parallel Growths, or both of them at the same time, but
it doesn't need to be so.
I personally view Parallel Paths assumptions as reasonable strategies
of identification when we only have a sequence of cross-sections,
treated and controls groups, and a small number of periods before and
after treatment (like less than 20 periods).