Twice as likely or twice more likely

Recently I read about a sentence on a test.

"Men suffering anxiety are twice as likely to get cancer."

I wonder if I can also use 'twice more likely' in the sentence. If not, please tell me why 'twice more likely' is grammatically incorrect.

My immediate reaction is that people just don't say "twice more likely." I am not sure if it is ungrammatical (I can't think of any reason why it would be), but it definitely seems wrong to me.

But for some reason, even though "twice" and "two times" are generally interchangeable, "two times more likely" does sound OK to me. In general, I think people use "two times more likely" to mean the same thing as "two times as likely" and "twice as likely," but I believe I've encountered a peeve where people object to this use of "two times more likely" and say that it "logically" should mean "three times as likely" (because one plus two is three).

Here is a Google Ngram chart that shows that the difference between "twice as likely" and "twice more likely" is much greater than the difference between "two times as likely" and "two times more likely" or "three times as likely" and "three times more likely."

image of the ngram chart

You can see that "twice more likely" is at the very bottom. However, if you click through to the Google Books results, you can see there are some examples of "twice more likely" being used in published works (a surprisingly large number from my perspective).

Here are some relevant questions dealing with the distinct, but related question of whether to use "X times more" or "X times as many" in general: