For all (most?) cancers, you need many mutations in one cell.
There is some probability that a mutation will trigger an internal check in the cell to detect bad mutations, and the cell will commit suicide.
There is also some probability that the cell will die accidentally before the second mutation.
There is some probability that the immune system will detect something fishy and kill the cell just in case.
If the time between each mutation is bigger, then you have more time to get lucky and remove the cell while it has a single mutation, before it can accumulate more mutations and become dangerous.
So a lower dose will increase the time between mutations and make the case of two accumulative bad mutations less common. Then at small doses, the effect is not linear and perhaps below some threshold the ability of the body to detect problems will fix all the cases before you notice.
The problem is that it's very difficult to measure the effect of very low doses for a long time. (You have to test the drug in some animal that lives for a long time like elephants instead of mice.) (And it's difficult to get funding and graduate students for a 20 year experiment.)
So the "linear non threshold model" is slightly pessimistic, it err on the side of caution, but it's probably good enough and not too alarmist.
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Technical note: There are actually no cells with zero mutations. All cells have some mutations. Some have less, some have more. Some mutations are dangerous, most are innocuous, a few may be advantageous. But to simplify the discussion, I just ignored this and imagine that usually the cells have no mutations.
There is some probability that a mutation will trigger an internal check in the cell to detect bad mutations, and the cell will commit suicide.
There is also some probability that the cell will die accidentally before the second mutation.
There is some probability that the immune system will detect something fishy and kill the cell just in case.
If the time between each mutation is bigger, then you have more time to get lucky and remove the cell while it has a single mutation, before it can accumulate more mutations and become dangerous.
So a lower dose will increase the time between mutations and make the case of two accumulative bad mutations less common. Then at small doses, the effect is not linear and perhaps below some threshold the ability of the body to detect problems will fix all the cases before you notice.
The problem is that it's very difficult to measure the effect of very low doses for a long time. (You have to test the drug in some animal that lives for a long time like elephants instead of mice.) (And it's difficult to get funding and graduate students for a 20 year experiment.)
So the "linear non threshold model" is slightly pessimistic, it err on the side of caution, but it's probably good enough and not too alarmist.
--
Technical note: There are actually no cells with zero mutations. All cells have some mutations. Some have less, some have more. Some mutations are dangerous, most are innocuous, a few may be advantageous. But to simplify the discussion, I just ignored this and imagine that usually the cells have no mutations.