You did it wrong.

One Sv increases your absolute risk of fatal cancer by an added 5% or so. It doesn't multiply it by 1.05.

Quoting Wikipedia: "According to the International Commission on Radiological Protection (ICRP), one sievert results in a 5.5% probability of eventually developing fatal cancer based on the disputed linear no-threshold model of ionizing radiation exposure."

Also, where on earth did you get 1% as a "depressing" upper bound from? For lifetime risk of dying of cancer? It's over 15% in the US.

The real logical problem with his approach is not the relative risk. It's not the linear no threshold model.

It's the use of effective whole body dose to estimate the risk associated with a dose to part of the body. Exactly zero radiation biology organizations recommend this. Most explicitly caution against using effective whole body dose to estimate radiation risk. Effective whole body dose is only used for population-level estimates.

For example, one of the most radiosensitive (wrt cancer) organs is the thyroid. But his thyroid is not in the beam. Also the skin is exposed more than the interior on CT, which increases the risk of skin cancer. These corrections are standard, while alternatives to LNTM are not standard.

Then there is the effect of age. Most radiation related cancers are delayed by a long time, and the faster that cells are dividing, the greater the risk of DNA damage. But Scott is old, which is also why older workers were preferred for cleanup at Fukushima.

D_eff can get you within an order of magnitude I suppose, but you shouldn't express it with two significant figures — it's misleading precision. You could say 1/1000 or maybe 1/700? But you really need more detail for any kind of meaningful medical decision.

Anyway, that's my rant as someone studying for the board exam.

I tried googling the risk and it's all a bit inconclusive but:

>The linear no-threshold model is disputed by several health organizations, including the American Association of Physicists in Medicine and the Health Physics Society, both of which concluded that cancer risk estimation should be limited to doses greater than 50 mSv. Both organizations state that risks from doses below this threshold are too small to be detectable and may be nonexistent.

"the risk of dying from the screening exam was 1/660"

For someone as smart as Scott Alexander, this is an astonishing mistake.

If CTs were such death machines, we would have seen a worldwide epidemics of CT-related cancers. There is no way you can cover up such a strong signal, given that people are screened all the time.

Edit: thanks for unleashing such an interesting debate. I guess the problem is in my perception. "Risk of dying from the exam" means lifetime risk, while my perception was "1 of 660 people who get the exam drops dead pretty soon afterwards".

It would be astonishing if it were a mistake.

And yes, it's a detectable signal. "in a large population-based cohort it was found that up to 4% of brain cancers were caused by CT scan radiation" --somewhere on Wikipedia

CT scans vary in dosage. Wiki gives ~10 Sv for an abdominal CT; I don't know where Scott got 30, but maybe the kidney screening is multiple scans or otherwise higher dose. Or he was wrong by a factor of 3, which is not a factor of 100.

CT scans aren't done frivolously, and the current rate of scans is hotly debated for exactly this reason. I'm a little surprised that kidney donation involves CT over MRI by default, but I'm not an expert.

> I don't know where Scott got 30, but maybe the kidney screening is multiple scans or otherwise higher dose.

Scott called it "multiphase abdominal CT". Quick searching on-line suggests[0] that the "multiphase" here stands for doing 3-4 scans within a minute or two of each other, as the contrast agent diffuses through the organ, giving you multiple images that inform you about different parts of the target structure.

> Wiki gives ~10 Sv for an abdominal CT; (...) Or he was wrong by a factor of 3

If what I wrote above is correct, then it tracks - ~10 mSv for one CT, multiplied by 3-4 scans done in a multiphase CT, gives you ~30-40 mSv, which matches the number Scott posted.

--

[0] - https://www.barnardhealth.us/dynamic-contrast/multiphasic-im... - First link I found; CTRL+F "multiphase", as the relevant information is spread throughout the comments section.

> I don't know where Scott got 30

The text where he says that is a clickable link! https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4635397/

> CT scans aren't done frivolously

As someone who works in the ED, we pretty much give CTs out like candy to avoid a lawsuit if we miss something.

I stand corrected.

Abdominal stuff often involves CT scans that need to be done in phases. For brain stuff, some things require CT vs MRI.

Another risk is the contrast dye that’s often used in these studies. If you’re dealing with cancer monitoring or something that requires monitoring, you can develop allergies and poor reactions to that as well.

The paper he links to [1] broadly agrees with his statement, eg "An estimated 1 in 270 women who underwent a coronary angiography CT at age 40 will develop cancer from that CT (1 in 600 men), compared with an estimated 1 in 8,100 women who had routine head CT at the same age (1 in 11, 080 men)".

1. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4635397/

I felt less compelled by the paper after reading " 1,119 " as the sample size - how the fin f they think that they can get to estimates like 1:11,080 with a sample size of 1,119 I do not know.

Going the other way: on the internets I read that there are 5 million CT scans in the UK every year. If there was a 1:10k rate of cancer from these we would see 500 fatal cancers a year. If there was a 1:600 risk then we would see 8300 cancers a year. There are 400k cases of cancer per year in the UK as it is. So, at the top end about 2% of cancer could be hypothesized as from CT scans based on these numbers however they were extracted kicking and screaming from the case notes.

There is an interesting twist on this though - the mortality of people who get CT scans is probably much higher than the mortality of people who don't as there is probably a reason why they are getting the scan. One reason I have seen for people to get a CT scan is that they have metastasizing cancer. If you have metastasizing cancer you are probably going to get radiotherapy. Now, radiotherapy doses are quite difficult to understand as there is a big difference in the way it gets absorbed and handled, but as a layperson I look at the numbers and think that radiotherapy doses seem much bigger than CT scan doses. But I don't even know how I would go about comparing them and controlling for them in the stats.

I personally would have to sit and think for a long time about how to sort the causal factors out in the stats around this, I think I would not be doing that on a sample of 1k people.

> The paper he links to [1] broadly agrees with his statement, eg "An estimated 1 in 270 women who underwent a coronary angiography CT at age 40 will develop cancer from that CT (1 in 600 men), compared with an estimated 1 in 8,100 women who had routine head CT at the same age (1 in 11, 080 men)".

Develop cancer, or die of cancer? Alexander seems to be claiming the latter.

The thing I don't understand is that if the CT scan is more dangerous than having a kidney removed, then surely they'd take the kidney out to see if it was compatible with the recipient rather than give you such a dangerous scan.

The kidney surgery only looks so low risk (partially) because they only do it on people that passed the CT scan.

(To give an even more extreme example for illustration:

Suppose the scan could perfectly predict who will die from the surgery and who will live without any side effects. Suppose 90% of people fall into the former and 10% of people fall into the latter category. Suppose further that the scan has a 0.1% chance of killing you.

If you scan people beforehand, it will look like the surgery has 0% chance of complications against 0.1% of the scan. But if you dropped the scan, all of a sudden the surgery would have a 90% death rate.)

One of the reasons they do the scan is that they look at both kidneys only take your WORST one

If that's the case, is it possible Scott is lying or leaving out information on what kidney it was?

I'm guessing that <CT scan> is more dangerous than <having a kidney removed, given you've cleared the CT scan and other tests>. Plus, <having a kidney removed, studied, and then reinserted after failing some tests>, might be more dangerous than either.

> Conclusion: this is not your risk of dying, but the increase of your risk of dying.

No, it does not increase your risk of dying. Your risk of dying was 100% before the procedure and is 100% after it. We all die at the end with certainty. Risk of dying is only meaningful when you qualify it with a timeframe (let say next 5 years) or cause (let say getting terminal cancer).

Um, yes, the entire point of that section of the article was to talk about the increase of risk of death by cancer.

You're not wrong, but he's probably farther off that that. Danger from radiation doesn't scale linearly, although (to be extra safe) standards are set as if it is. In fact, there is some evidence that small doses of radiation can even be beneficial (hormesis).

That discussion is already in the linked article.

He also assumed that the risk increases linearly.

Not blindly; there is a pretty extensive footnote (footnote 2) covering the linear-risk assumption.

I think you are correct.