My question could be rephrased as "how to assess a sampling error using big data", especially for a journal publication. Here is an example to illustrate a challenge.
From a very large dataset (>100000 unique patients and their prescribed drugs from 100 hospitals), I interested in estimating a proportion of patients taking a specific drug. It's straightforward to get this proportion. Its confidence interval (e.g., parametric or bootstrap) is incredibly tight/narrow, because n is very large. While it's fortunate to have a large sample size, I'm still searching for a way to assess, present, and/or visualize some forms of error probabilities. While it seems unhelpful (if not misleading) to put/visualize a confidence interval (e.g., 95% CI: .65878 - .65881), it also seems impossible to avoid some statements about uncertainity.
Please let me know what you think. I would appreciate any literature on this topic; ways to avoid over-confidence in data even with a large sample size.