Bayesian Probability and Confounding Variables
I thought of an interesting problem with bayesian probability. I’m going to use an example not related to clinical research, but it applies to clinical research too since Bayesian theory is used for it. Let’s say you’re trying to find the chances that someone with a certain trait doesn’t have a certain capacity. 99% of people without the capacity have this trait and 2% of people who may have the capacity (which is currently being questioned) have this trait. That should produce a LR of around 50, right?
But this would produce an abnormally high chance that people with this trait do not have this capacity, which seems unintuitive. Upon thinking about it, I realized that it’s because the 99% of the people who don’t have the capacity don’t have it due to a confounding variable, other illnesses that may cause the trait.
So my question is, do confounding variables reduce the reliability of bayesian probability models? If the 99% figure is possibly caused by other factors, does that change things?