Most people are tested for cancer because they have one or more symptoms consistent with cancer. So the base rate of 1% “for the patient’s age and sex” isn’t the correct prior, because most of the people in the base rate have no symptoms that would provoke a test.
To clarify, the problem that Gigerenzer posed to doctors began with “A 50-year-old woman, no symptoms, participates in a routine mammography screening”. You’re right that if there were symptoms or other reasons to suspect having cancer, that should be factored into the prior. (And routine mammograms are in fact recommended to all women of a certain age in the US.)
We really need a computation whose result is a probability.
I agree—it would be ideal to have a way to precisely calculate your prior odds of having COVID. I try and estimate this using microCOVID to sum my risk based on my recent exposure level, the prevalence in my area, and my vaccination status. I don’t know a good way to estimate my prior if I do have symptoms.
My prior would just be a guess, and I don’t see how multiplying a guess by 145x is helpful.
I don’t fully agree with this part, because regardless of whether my prior is a guess or not, I still need to make real-world decisions about when to self-isolate and when to seek medical treatment. If I have a very mild sore throat that might just be allergies, and I stayed home all week, and I test negative on a rapid test, what should I do? What if I test negative on a PCR test three days later? Regardless of whether I’m using Bayes factors, or test sensitivity or just my intuition, I’m still using something to determine at which point it’s safe to go out again. Knowing the Bayes factors for the tests I’ve taken helps that reasoning be slightly more grounded in reality.
Edit: I’ve updated my post to make it clearer that the Gigerenzer problem specified that the test was a routine test on an asymptomatic patient.
To clarify, the problem that Gigerenzer posed to doctors began with “A 50-year-old woman, no symptoms, participates in a routine mammography screening”. You’re right that if there were symptoms or other reasons to suspect having cancer, that should be factored into the prior. (And routine mammograms are in fact recommended to all women of a certain age in the US.)
I agree—it would be ideal to have a way to precisely calculate your prior odds of having COVID. I try and estimate this using microCOVID to sum my risk based on my recent exposure level, the prevalence in my area, and my vaccination status. I don’t know a good way to estimate my prior if I do have symptoms.
I don’t fully agree with this part, because regardless of whether my prior is a guess or not, I still need to make real-world decisions about when to self-isolate and when to seek medical treatment. If I have a very mild sore throat that might just be allergies, and I stayed home all week, and I test negative on a rapid test, what should I do? What if I test negative on a PCR test three days later? Regardless of whether I’m using Bayes factors, or test sensitivity or just my intuition, I’m still using something to determine at which point it’s safe to go out again. Knowing the Bayes factors for the tests I’ve taken helps that reasoning be slightly more grounded in reality.
Edit: I’ve updated my post to make it clearer that the Gigerenzer problem specified that the test was a routine test on an asymptomatic patient.