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E.g.

Fentanyl is a synthetic opioid that is 80-100 times stronger than morphine.

What does that refer to?

According to https://en.wikipedia.org/wiki/Potency_(pharmacology):

The IUPHAR has stated that 'potency' is "an imprecise term that should always be further defined", for instance as EC50, IC50, ED50, LD50 and so on.

I guess effective dose is the relevant notion here, but which version does the DEA use ED50, ED95 (does it matter which)?

Presumably they are not talking about receptor affinity which would be mostly irrelevant from DEA's perspective (although the FDA suggests otherwise). The latter ratio between fentanyl and morphine is only 1.35 to 1.14 on the μ-opioid receptor. Even that is not really a good way to compare, because actual measurements of affinity have a large margin of error:

enter image description here

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  • $\begingroup$ Apparently the CDC itself has been criticized for making weaker/stronger-than-morphine comparisons. But let's take one claim at a time. $\endgroup$ – Fizz May 12 at 16:47
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At least the 100 number seems based on the CDC parenteral dose conversion:

enter image description here

(Fentanyl has poor oral bioavailability, so it's not intended to be used that way.)

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