Hmm, is that a situation where there is no appropriate action to take, regardless of the outcome of the screen? If that were the case, then there would be no point in doing the screen even if all actors were fully rational. But I'm guessing it's more like, the correct action is to wait N months and do a followup test.

Does it not work to say "If we take a biopsy, assuming normal treatment plans and outcomes for someone in your reference class, there's a 0.1% chance the biopsy kills you, and a 0.05% chance it saves you from cancer compared to the plan I'm recommending", or whatever the truth is?

(If the next possible step is a biopsy, under what circumstances does the calculus imply one should do the biopsy? When the screen results look sufficiently bad? Then maybe they shouldn't be presented as a binary "positive"/"negative".)

> Does it not work to say

No. It does not.

A diagnosis of "you might have cancer but the probability is low and we should just watch it" is not something that most people can psychologically take.

For more than half of the population, that kind of understanding is simply untenable.

And, even for people I knew who could understand it, several of them had so much anxiety that it drove their blood pressure up and it was better to just go get the biopsy so they didn't wind up with a stroke or heart attack.

In addition, "mortality probabilities" are a lot harder to psychologically absorb when you are 50 than when you are 20.

By the time you are 50, you've probably had more than a few of your friends and family in a coffin from a "low probability event".

Emotions are difficult. At some point, I will get diagnosed with a positive prostate screen (practically all men who live long enough do) that will almost certainly be "We should keep an eye on it." I hope I can weather it with the aplomb of my engineering background. We shall see.

Upvoted, but I remain skeptical. "You might have cancer but the probability is low and we should just watch it" is true for everyone who hasn't been screened, just the "might" is somewhat higher for those with a bad test result. Benign-looking moles on your arm could be cancer. Things you can't see or feel in your organs could be cancer. Also, plenty of other things could kill you practically without warning—heart attack, stroke, car crash, and the chance of the first two (and cancer) goes up over time. It seems to me that people have to come to terms with these things eventually, and "you have a low probability of having this type of cancer" just doesn't seem that different to me (perhaps it's best phrased as "you have an x% chance of being killed by this cancer"). If you've seen several people respond badly despite understanding probability, well, it's hard to argue with that, but I can't help wondering if it's fixable through slightly better communication or education.

Doing some reading about prostate cancer specifically, it seems like it actually is of the form "there is no appropriate action to take, regardless of the outcome of the screen"—or at least it's close enough that some experts think so. "In 2012 the United States Preventive Services Task Force (USPSTF) recommended against prostate cancer screening using PSA.[39] As of 2018 a draft for new recommendations suggests that screening be individualized for those between the ages of 55 to 69. It notes a small potential decrease in the risk of dying from prostate cancer, but harm from overtreatment." And: "A study in Europe resulted in only a small decline in death rates and concluded that 48 men would need to be treated to save one life. But of the 47 men who were treated, most would be unable to ever again function sexually and would require more frequent trips to the bathroom." https://en.wikipedia.org/wiki/Prostate_cancer_screening#Guid...