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Observational Studies

This is where the pain begins. Sort of. People love Randomized Studies for a reason. The trick here is to make the Observational Study resemble a Randomized Study as much as possible during the design phase. More on this later.

I am yammering

Remember The Game. We want to recover/estimate:

ACE=E[Y1−Y0]ACE = E[Y^1 - Y^0]

from the Observed Association

Observed Association=E[Y∣A=1]−E[Y∣A=0]\text{Observed Association} = E[Y\mid A =1] - E[Y \mid A=0]

Randomization made this easy by virtue of what it is (its design: “No causation without manipulation.”) Observational studies require additional assumptions and analytical methods because lack of control means confounders 😵‍💫

Perfect Doctor Visits Again​

The canonical setup here: A doctor might prescribe a medication because someone has severe disease. And people with severe diseases often have worse outcomes regardless of treatment.

Actual example: You prescribe antiretroviral therapy (ART) to patients with lower CD4 counts. Now:

  • If they have a low CD4 count, they have a higher chance of poor outcomes.
  • If they have a low CD4 count, they have a higher chance of receiving treatment.

What are the ‘entities’ at play here? Can we draw a graph so we can see shit?

So CD4 affects (has pointy lines to) both the treatment and outcome. It’s a Confounder 😵‍💫 And this is Confounding by Indication.