It comes down to the scan and the age.
3 scans for a 1 year old? Strongly associated with cancers later in life. 5 scans of a 50 year old? Less so.
The 1 year old has an 80 year run way to develop cancer, along with cells already set in a state of rapid division, and a less developed immune system.
But the association is quite strong.
https://www.sciencedirect.com/science/article/pii/S0720048X2...
There's excellent reason to think LNT is accurate: at low doses, almost every cell is exposed to at most one radiation event. The dose affects how many cells experience a (single) event, but does not affect the level of damage to those exposed cells. Linearity naturally falls out of this.
To abandon linearity you have to imagine some sort of signalling system (not observed) that kicks in at just the dose we're talking about (not lower, not higher) to allow exposure to one cell to affect other cells.
There's also no good evidence that LNT is wrong. The typical things that are pointed to by anti-LNT cranks are cherrypicked, often involving interim results from studies the full results from which do support LNT, which is evidence it was statistical noise.
Someone being born with no legs is strongly associated with them using a wheelchair in later life.
Why are you giving a one-year-old three CT scans? For shits and giggles? Or because you think they might have cancer?
Maybe a full body MRI once a decade is fine until your 30s, then once every 5 years until 50, then once ever 2 years beyond 50.
The test should scale with the probability of cancer.
The mean effective dose for all patients from a single PET/CT scan was 20.6 mSv. For males aged 40 y, a single PET/CT scan is associated with a LAR of cancer incidence of 0.169%. This risk increased to 0.85% if an annual surveillance protocol for 5 y was performed. For female patients aged 40 y, the LAR of cancer mortality increased from 0.126 to 0.63% if an annual surveillance protocol for 5 y was performed.
So, a just-about-measurable increase, if you pick and choose your values carefully?
You are not going to die from cancer caused by getting a PET scan. This will not happen.
You're going to die of heart disease or as a not-too-distant second in a car accident.
Continuous scanning for months would give a dose many orders of magnitude higher.
https://www.facs.org/for-medical-professionals/news-publicat...
How are they determining "this cancer was caused by the CT scan" versus "this cancer was caused by the cancer we were originally looking for that was there all along"?
Other than comparing population groups, what method do we have?
Why is "We think this person has cancer so we gave them a CT scan and look! Now they've got cancer! It must be because of the CT scan!" the conclusion to jump to?
You'd have to be massively overexposed to CT or PET scanning to cause cancer, like in the region of spending months being scanned continuously with it at full beam current.