You can read a bit more about this weighted regression version of AIPW (in the context of confounding) in the following short commentary I like this approach since it's super easier to implement and you don't need to memorize the AIPW formula academic.oup.com/aje/article/... - ThreadSky

pausalz.bsky.social • 15 days ago

You can read a bit more about this weighted regression version of AIPW (in the context of confounding) in the following short commentary

I like this approach since it's super easier to implement and you don't need to memorize the AIPW formula

https://academic.oup.com/aje/article/173/7/739/104202

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pausalz.bsky.social•15 days ago

So now let's translate this procedure into estimating equations. First is our logistic regression model for R|X. This is simply the same as the previous post

pausalz.bsky.social•15 days ago

Step 2, is simply computing the weights (which doesn't need it's own estimating equation). Step 3 is a weighted regression model. While we haven't done weighted regression yet, it is simply the product of the weight with the estimating function. Below presents these stacked together

pausalz.bsky.social•15 days ago

Step 4 is again just predict some values from the model (doesn't require an estimating equation), so we only need Step 5. Step 5 is simply the mean of the predicted values from the outcome model (like for g-computation usually). The following is the full stack

pausalz.bsky.social•15 days ago

Again we can use the sandwich for variance estimation

Those of you familiar with AIPW or doubly robust methods might know that we can also use a influence function (IF) variance estimator. So you might wonder why bother with the sandwich here

pausalz.bsky.social•15 days ago

The IF variance assumes that both models are correct. So our point estimator is doubly robust but the variance estimator is NOT. To me, this diminishes the motivation behind using doubly robust estimators...

pausalz.bsky.social•15 days ago

But here the sandwich variance estimator IS doubly robust. So we can get both doubly robust point AND variance estimates

You can read more details in the following pre-print

https://arxiv.org/abs/2404.16166

edwardhkennedy.bsky.social•15 days ago

Hm not sure I agree with this logic…

To me the beautiful thing about the DR estimator is you can get away with estimating both nuisances at slower rates (as long as the product is < 1/sqrt(n))

This opens the door to using much more flexible methods - random forests, lasso, ensembles, etc etc

noahgreifer.bsky.social•15 days ago

A more detailed treatment here: https://doi.org/10.1002/sim.9969

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