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Is there a problem with overdoses?
Acetaminophen

I have to claim supreme ignorance here. As far as I can tell the main advantage to dosing by weight is to make sure each child gets enough to reduce the fever.

I have seen, but not researched, the issue of overdoses. I will give you a few remarks that do not have details. However, the safety statistics at the bottom are the most relevant.

Just below is a link to an infant Tylenol overdose warning (and an admonishment to only use their dropper) ("... multiple overdoses of acetaminophen, the active ingredient in Tylenol and other pain relievers, can damage the liver and cause death, says Anthony Temple, M.D., executive director of medical affairs for McNeil Consumer Products."): (You'll have to use your back button to return.)

Tylenol overdose warning

And here is another, for adults, with "The window between therapy and toxicity is much smaller with acetaminophen than with most other compounds, [from Dr. Lee]": (You'll have to use your back button to return.)

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Safety statistics: "Dr. Temple said that between 1992 and 1997, 4.7 billion doses of Tylenol were shipped and 30 serious adverse events in children under age 12 were reported to the company." (See Mechcatie in references.)

References

Cup product

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