7: MORE ASSUMPTIONS
Section 7 adds some additional a priori assumptions that can allow us to estimate in the context where we don't have all necessary confounders.
We have the beautifully named: A-complete Stage 0 PL-sufficient reduced graph of R CISTG A
We start with some rules for reducing graph G_A to a counterpart G_B. Honestly the language in this section isn't clear to me despite reading it several times...
I do think the graphs help a bit though. To me it seems we are narrowing the space of the problem. We are going from multiple divisions at t_1 and t_2 to only considering the divisions at t_2 for a single branch. The reduced STG is a single branch
The purpose of our graph reduction is that G_A is identifiable given G_B and the listed assumption R
So we can think about G_B as either everyone being set to the same value at t_1 OR everyone was off their assigned protocol (and then returned to it at t_2).
The section ends with the note that we can see if the observed G_B is compatible with a proposed randomization scheme. Section 8 goes on to discuss this and when standard analyses (ignoring time-vary confounding) are valid
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