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I am looking for a beginner-friendly explanation of what Robbins' G-computation and G-estimation are for estimating causal effects. What problem(s) do they solve. Ideally I would like an example of where multivariable regression fails to estimate the desired effect, but G-methods succeed.

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This is a short beginner-friendly guide to g-computation for estimating the average treatment effect https://github.com/kathoffman/causal-inference-visual-guides/blob/master/visual-guides/G-Computation.pdf .

A more in-depth introduction can be found at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6074945/ .

The g-formula is particularly useful when there is time-varying exposure and time-varying confounding. Standard methods, like multivariable regression, will yield bias effect estimates in these scenarios while g-formula based methods will remain unbiased.

As an example, here is a recent paper that compares using a method based on the g-computation formula, along with a "question-first" approach (i.e., starting with the estimand of interest) compared to using cox proportional hazards for estimating the effect of corticosteroids on covid mortality, https://www.medrxiv.org/content/10.1101/2022.05.27.22275037v4

The authors use an RCT as a benchmark for the "true" effect and show that the modern causal inference g-method recovers the truth where the standard approaches fails.

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