There's a vaccine that purports to reduce the risk of a certain infection... some of the time.
After doing some investigation, you come up with the following statistics:
Roughly 10% of the population has taken the vaccine.
Of those that have taken the vaccine, the infection rate is 25%.
Of those that have not taken the vaccine, the infection rate is 10%.
P(Infection|vaccine) > P(Infection|~vaccine), so EDT says don't give your child the vaccine.
You do some more research and discover the following:
The infection rate for unvaccinated heterosexuals is 11%.
The infection rate for vaccinated heterosexuals is 9%.
The infection rate for unvaccinated non-heterosexuals is 40%.
The infection rate for vaccinated non-heterosexuals is 30%.
Non-heterosexuals are a small minority of the population, but are disproportionally represented among all those who are vaccinated.
Getting vaccinated doesn't change a person's sexual orientation.
EDT now comes to the ridiculous conclusion that heterosexuals should take the vaccine and that non-heterosexuals should take the vaccine, but people whose sexual orientation is unknown should not - even though everyone is either heterosexual or non-heterosexual.
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EDT chokes on Simpson's Paradox in general.
Consider:
There's a vaccine that purports to reduce the risk of a certain infection... some of the time.
After doing some investigation, you come up with the following statistics:
Roughly 10% of the population has taken the vaccine. Of those that have taken the vaccine, the infection rate is 25%. Of those that have not taken the vaccine, the infection rate is 10%.
P(Infection|vaccine) > P(Infection|~vaccine), so EDT says don't give your child the vaccine.
You do some more research and discover the following:
The infection rate for unvaccinated heterosexuals is 11%.
The infection rate for vaccinated heterosexuals is 9%.
The infection rate for unvaccinated non-heterosexuals is 40%.
The infection rate for vaccinated non-heterosexuals is 30%.
Non-heterosexuals are a small minority of the population, but are disproportionally represented among all those who are vaccinated.
Getting vaccinated doesn't change a person's sexual orientation.
EDT now comes to the ridiculous conclusion that heterosexuals should take the vaccine and that non-heterosexuals should take the vaccine, but people whose sexual orientation is unknown should not - even though everyone is either heterosexual or non-heterosexual.
EDT chokes because it ignores the obvious extra controlling principle: those with no sexual experience don't generally have the infection.
Add that, and you are fine. Vaccinate before the time of first expected exposure