Yann LeCun, now of Facebook, was interviewed by The Register. It is interesting that his view of AI is apparently that of a prediction tool:
"In some ways you could say intelligence is all about prediction," he explained. "What you can identify in intelligence is it can predict what is going to happen in the world with more accuracy and more time horizon than others."
rather than of a world optimizer. This is not very surprising, given his background in handwriting and image recognition. This "AI as intelligence augmentation" view appears to be prevalent among the AI researchers in general.
This is not biased data. No one tampered with it. No one preferentially left out some data. There is no Cartesian daemon tampering with you. It's a perfectly ordinary causal problem for which one has all the available data. If you run a regression on the data, you will get accurate predictions of future similar data - just not what happens when you intervene and realize the counterfactual. You can't throw your hands up and disdainfully refuse to solve the problem, proclaiming, 'oh, that's biased'. It may be hard, and the best available solution weak or require strong assumptions, but if that is the case, the correct method should say as much and specify what additional data or interventions would allow stronger conclusions.
I'm not certain why I used the word "bias". I think I was getting at that the data isn't representative of the population of interest.
Regardless, no other method can solve the problem specified without additional information (which you claimed). And with additional information, it's straightforward prediction again.
That is, condition on their prior health status, not just the fact they've been given the drug. And prior probabilities.