Thread by @PausalZ

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

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