This estimating function is a little special, in that it actually does not directly depend on the data itself. As I've said before, we will return to the connection between the sandwich variance estimator and the delta method
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If you're like "sure, we've had one, but what about a second Rogan-Gladen?" I'm happy to let you know that is considered here, where it is applied iteratively (maybe will come back to this one on another monday)
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https://academic.oup.com/aje/article/192/3/467/6564140#412157886
https://pubmed.ncbi.nlm.nih.gov/38423105/
https://deli.readthedocs.io/en/latest/Examples/Cole-AJE-2023.html#Case-2:-Estimating-a-Misclassified-Proportion
https://pubmed.ncbi.nlm.nih.gov/39198907/