Happy to help out here!

Thanks to @jwdebelius and @Nicholas_Bokulich for the help below:

This is pretty standard for regression equations. Your model is testing four things:

- Is the reference group (intercept) different from 0. (Intercept term)
- Is there a difference at time 0 between your treatment and reference group (Treatment[T.X] terms)
- Is there a change over time in the reference group (time)
- Does the rate of change differ over time with different treatments? (time x treatment)

You could re-code the model (check the statsmodels formula documentation) to test the hypothesis that there's a difference in each of your groups compared to 0, but I don't actually think this is what you want. So, the group you're missing (A), is what we're treating as the reference and it's rolled into the intercept. What you may want to do is either create a dummy variable that codes your treatment as numbers with K=0, add a prefix (1-K, 2-A, etc) or in some other way indicate that K is your control group when you run the model.

This is only a diagnostic plot showing the trend line. So it is working as intended.

Yes - I'd probably advise a delta. The other option would be a three level model - `time*treatment*treated`

and that would suck to interpret.

Hope this helps! Cheers