Alternative titles:

• … earns you a high-risk pregnancy
• … earns you an ascent of Matterhorn
• … earns you 10,000 km on a motorcycle
• … earns you two base jumps
• … earns you a day on the frontline in Ukraine

These are all about equivalent to the risk of one year of smoking.

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I’m skeptical of submitting asymptomatic people to medical tests. Almost any time I look into the evidentiary power of medical tests, I’m struck by how much work is performed by the base rate. The tests only work because we perform them on people who appear sick, i.e. have a higher probability of actually being sick in the first place. If we would perform them on seemingly-healthy people we would get nonsensical results.1¹ Note that this is not a criticism of the tests. They are optimised for the thing they need to do.

Thus it was with interest I read Scott Alexander’s breakdown of the benefits and costs of a routine full-body mri as a way of screening for cancer. However, I felt like the conclusions weren’t put into an understandable context. Here’s my attempt at doing so.

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First, a quick recap of the main points of the article. I’ll ignore the exorbitant financial costs of us healthcare, and focus on the benefit and cost in terms of health. This is measured in quality-adjusted life years, or qalys. Of the hypothetical thousand people who get scanned, the estimation is that

• 680 people will be fine, and this costs them only the doctor’s visit, which is around 3 hours, or 0.0003 qalys.
• 296 people will undergo additional waiting and testing unnecessarily, at a total cost of 0.02 qalys coming from side effects, anxiety, and patient time.
• 10 people will have unnecessary biopsies on top of the additional waiting and testing above, bringing their total cost to 0.06 qalys.
• 6 people will detect a real problem, but in a way that doesn’t help them. We’ll count this as no benefit, but also no cost.2² They would probably have gone through this circus eventually anyway.
• 4 people will benefit from early detection already at the mri stage, and gain an average of 4 qalys from this, and at a cost of 0.007 qalys after patient time and side effects, this is still a gain of 3.99 qalys.
• 4 people will benefit from early detection only after additional rounds of testing. They still gain the 4 qalys but their cost is ten more hours of patient time and some additional anxiety. It still ends up being a net benefit of 3.99 qalys.

Tallying up the costs and benefits into an expected value, we get a net benefit of 0.025 qalys per person, after accounting for medical time.3³ This is the figure Scott Alexander reports as “25” in sum across all 1000 people. I just didn’t find its very clear so I had to replicate it to make sense of it. This doesn’t tell me a whole lot, because my intuition for qalys is weak. How strongly should I prefer an intervention with a net benefit of 0.025 qalys over other things I might do with my time? No idea!

However! When marketing the effect of global health interventions, a count of 27 qalys is typically considered “a life saved”. A life also happens to be a million micromorts, and I have a much better intuition for micromorts! When we run that maths in reverse, we get a very cheeky exchange rate between qalys and micromorts:

One qaly is 37,000 micromorts.4⁴ The equivalence between 27 qalys and a life saved is based on global demographics. For people in developed countries, where the life expectation is longer, a qaly probably corresponds to a lower number of micromorts – probably around 30,000 or so.

Thus, an intervention that has an expected benefit of 0.025 qalys – like a routine full-body mri – corresponds to an intervention that has a benefit of 926 micromorts. The alternative titles indicate activities that carry roundly a risk of around 1000 micromorts:

• a year of smoking,
• a high-risk pregnancy,
• an ascent of Matterhorn,
• riding 10,000 km on a motorcycle,
• two base jumps, and
• one day on the frontline in Ukraine.

So the same effort you would expend to get out of those activities on account of their risk, the same effort you should be willing to expend to get a full-body mri.

Note the on account of their risk phrasing. I have no interest in doing any number of base jumps and will work hard to get out of doing them, but that’s because I wouldn’t enjoy the activity, not because I’m worried about the risk. If I was put in a situation where it seemed like I had to perform two base jumps to reunite with my family, I would spend some effort on finding alternative ways of getting there, but perhaps not all that much before I decide to just eat the base jumps and getting it over with.