[apathy]

I hate to take “both sides” but in the absence of confounding by indication, you can often use propensity scoring within robust models to decrease these impacts.

Mind you, the problem with non random and undetected sampling bias is that it can be subtle. See for example https://www.nytimes.com/2018/08/06/upshot/employer-wellness-...

[AnthonyMouse]

Propensity scoring is a method of applying statistical controls. How does it address the issue of controls compounding measurement error?

[apathy]

That’s the whole point of doubly robust models. However, in the event of confounding by indication or sampling misspecification, my experience is that nothing can save you.

I am a rather strong proponent of randomized trials for this exact reason. (They can also have sampling bias, but some degree of noise is inevitable)