G comp chapter

[LucyMcGowan]

No description provided.

[LucyMcGowan]

@malcolmbarrett & @tgerke can you please review this -- I took out the Monte Carlo piece because I don't think we really need it but please let me know if you disagree!

[malcolmbarrett]

Thanks for getting this in! I added some requests for other areas of content as well as some stylistic things. I don't focus so much on the latter as I will give this a polish later.

[malcolmbarrett]

I slept on this, and there are a few other things I wanted to include in this chapter:

• I'd like to include better intuition for cloning. I often talk about how we are simulating the counterfactuals. My idea here is to have a table showing a difference in the cloned sets but also a scatter plot with the predicted outcomes by cloned dataset
• Relatedly, I want to make it a bit clearer that we are averaging over covariates that are not the treatment variable, as well as the connection to marginalization.
• Show how to do different estimands (see https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-016-0282-4 and https://stats.stackexchange.com/questions/613569/estimating-and-interpreting-the-att-with-regression-adjustment-and-marginal-effe/613587#613587 and https://marginaleffects.com/chapters/gcomputation.html).
• Related to my comments about intuition for marginalization, we can also use this as an opportunity to show that different estimands are averaging over different covariate distributions
• I want to revisit positivity here because of the strengths of g-computation in this aspect. My idea is to 1) simulate good and poor overlap to show how IPW struggles but g-comptation does not 2) emphasize that we are gaining this by extrapolation with information from the outcome and how we become strongly dependent on getting the functional form right to resolve the positivity issue

Also see #240 (comment) re: variance with marginaleffects

[LucyMcGowan]

@malcolmbarrett @tgerke if y'all want to take another look at this that would be great! (@tgerke if you could please take a closer look at my time varying section to make sure it looks ago that would be awesome).

[malcolmbarrett]

I'll take a look in the next day or two! the failures on CI should resolve with the new WeightIt release which fixes an error related to a dependency and unrelated to your changes

[malcolmbarrett]

stellar 🤩