8: WHEN CAN I IGNORE THE METHODOLOGISTS
Section 8 discusses when standard analytic approaches are fine (aka time-varying confounding isn't as issue for us). Keeping with the occupation theme, it is presented in the context of when employment history can be ignored https://twitter.com/PausalZ/status/1307390416619212807

First we go through the simpler case of point-exposures (ie only treatment assignment at baseline matters). Note that while we get something similar to the modern definition, I don't think the differentiation from colliders is quite there yet (in the language)

Generalization of the point-exposure definition of confounding to time-varying exposures isn't direct

To generalize confounding to time-varying settings, Robins first sets up the conditions for L to be a predictor of the outcome and exposure (at baseline and varying exposures over time)

Again, I think tools like DAG/SWIG are a massive improvement (or an enhancement) to definitions like this. It clarifies colliders and gives a way to /a priori/ specify the causal model. I think it is preferable than calculating to coefficient between various possible L's and Y

But back to the main question posed by this section, when can be _correctly_ ignore time-varying confounding. We get two sufficient conditions: (1) L does not predict exposure, (2) L does not predict death

Again, we can easily show this in causal diagrams by lack of an arrow between L_{t-1} -> A_{t} for the 1st condition or L_{t-1} -> Y(t) for the 2nd condition. So if there exists no L such that both of the above aren't true, you can safely ignore me

The next question is when can be ignore the g-methods and use standard approaches for adjustment of time-varying confounding

This is valid when previous exposure does not predict future L (ie A_{t-1} -/-> L_{t}). Another way of phrasing is that A effects Y not through modification of L

That's great and all, but when can be *completely* ignore L for the null test? Well now we only need both L -/-> A and A_{t-1} -/-> L_{t} (when L is predictive of Y

Now that is all a lot of arrows and letters, so Section 8 closes with an example regarding cigarette smoking history. I think it highlights the implausible nature of the previous assumptions that allow you to ignore L (and my methods concerns)

The example provided seems to indicate the difficulty of making any of these assumptions in a defensible way. Robins goes through these in explicit details

Another worthwhile mention from parts I didn't highlight in this thread: 'faithfulness' outside of DAGs