I am a service-connected disabled veteran and for a veteran to be approved for a service-connected disability they must show a current diagnosis, some in service injury for event, and a medical nexus or link between the current diagnosis and the in service injury/event. There is a concept of a "secondary condition" as well. This where one disease or injury that is already service connected causes or makes some other condition worse. In those cases it can also be service connected on a secondary basis. Examples of this might be how there is a pretty high correlation between service members with tinnitus(ringing in the ears) and a bunch of mental health issues ranging from insomnia, to major depressive disorder, to various types of anxiety disorders. The VA operates under what they call the "benefit of the doubt doctrine" which basically says that a tie in evidence goes to the veteran. So as a veteran trying to service connect some condition we only have to meet a 50% threshold to get a condition service connected. Proving something caused something else can be really difficult and in practice within the VA just meeting the 50% threshold for showing a link between a previously service connected condition and a new condition is enough to get a grant of secondary service connection.
Lets take an example where a veteran has a service connection for tinnitus and also has a diagnosis for chronic insomnia. What variables would I need here to use bayesian reasoning see if we meet the 50% or greater probability that the insomnia was caused or made worse by the tinnitus? I've seen several studies, and one meta study, that basically suggest that the prevalence of insomnia in people who have tinnitus is over 40%(one study showed over 80%). The overall prevalence of chronic insomnia in the general US population is 6.25%. The prevalence of tinnitus in veterans is 11.7% and 5.4% for the general population. Is there enough information here to solve this? If not what do you think I am missing? How would one structure this to show a link? It just seem logical from these numbers that there is pretty obviously a link but it would be nice to put a number, if even fairly subjective number, to it. Also I picked this example because it was a pretty obvious/easy one. There are plenty that aren't so obvious.
This would be useful for a lot of reasons. One of which is to show a veteran if they have enough evidence to meet the threshold and if not then they can work on obtaining that evidence and another is to paint a clear math based picture for the rating specialist at the VA. The easier we can make their job the better things are for them and veterans alike in the long run.
edit
That example was really just used because intuitively the link seems fairly obvious. Without doing a controlled experiment determining actual causality is hard. Since a person can answer "What is the probability that someone has insomnia given that they have tinnitus?" and "What is the probability that someone has tinnitus given that they have insomnia?" then that means that either tinnitus can cause insomnia, insomnia can cause tinnitus, or some other unidentified condition, or set of conditions, can cause them both. I'm just not sure how to say that there is a 50% or greater probability that, given a person has both, one of the following is true X causes Y, Y causes X or some unknown variable, or set of variables, can cause both