For a good understanding of this technique, check out Raj Chetty's work in social mobility in US. He starts with the data that some areas have high social mobility and some have less mobility. There is a possible confounding factor here - may be people of certain kind live in a place which results in higher mobility, and it has nothing to do with the place. The way to test this is to check those people, who have changed cities and see how their mobility varies. If a person shifting from low mobility area to high mobility area ends up having higher mobility, it can be inferred that mobility is due to place, not people. Further, if the extent of mobility is proportional to the number of years of exposure to high mobility areas, it's a further evidence. All of this proves causality. No RCT here.
Remember the RCT that assigned people to smoking (versus not) to see if it really caused lung cancer? Me neither…because it never happened. So, if you are a strict “correlation is not causation” person who thinks observational data only create hypotheses that need to be tested using RCTs, you should only feel comfortable stating that smoking is associated with lung cancer but it’s only a hypothesis for which we await an RCT. That’s silly. Smoking causes lung cancer.On alternative explanations - confounding factors
There must be an alternative explanation! There must be confounding! But the critics have mostly failed to come up with what a plausible confounder could be. Remember, a variable, in order to be a confounder, must be correlated both with the predictor (gender) and outcome (mortality). We spent over a year working on this paper, trying to think of confounders that might explain our findings. Every time we came up with something, we tried to account for it in our models. No, our models aren’t perfect. Of course, there could still be confounders that we missed. We are imperfect researchers. But that confounder would have to be big enough to explain about a half a percentage point mortality difference, and that’s not trivial. So I ask the critics to help us identify this missing confounder that explains better outcomes for women physicians