Janessa Benson

2022-10-07

Probability of infection by staphylococcus aureus
Please forgive my innumeracy, but I have a question with which I am hoping someone might be able to help me.
Suppose the following be true. The chance of a prosthetic hip joint becoming infected by staphylococcus aureus is one per cent. The chance of a natural hip joint becoming infected by staphylococcus aureus is 0.1%. In other words (in case I am misusing the word 'chance'), one in one hundred people with prosthetic hip joints will become infected by staphylococcus aureus, whereas only one in one thousand people with natural hip joints will become so infected.
Now suppose that X has a prosthetic hip joint and that X's hip joint becomes infected by staphylococcus aureus.
Given only the information provided here, is it correct to say that X's hip joint probably would not have become infected but for the fact that X has a prosthetic hip joint (instead of a natural hip joint)? In other words (to make it clear what I mean by 'probably'), is it correct to say that there is a greater than 50 per cent chance that X's hip joint would not have become infected but for the fact that X has a prosthetic hip joint? Why or why not?

Marshall Horne

It is tempting to think of the cases where infection and prosthetic hip joints occur as a superset of the cases where natural hip joints contract the infection. This way we could reach a result that "Only 10% of prosthetic hip joint infections would have been infected with a natural hip joint" but this is not a valid conclusion. The two groups aren't directly comparable. We'd need some data about the correlation of these percentages, which is impossible to acquire because we can't simulate alternate universes where person X who has a prosthetic hip joint doesn't have the prosthetic hip joint.
Even if we could correlate the percentages of people that get a staphylococcus aureus infection in either group, the statement "X's hip joint probably would not have become infected but for the fact that X has a prosthetic hip joint" implies a causal link. We know that correlation doesn't imply causation.
In fact, given that X was any other person with a prosthetic hip joint, they would probably not have acquired the hip joint infection. The probabilities in this case work out similarly.

Do you have a similar question?