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The phrase "a much higher dose" is correct and usable in written English.
It can be used when discussing medication, treatment, or any context where dosage levels are relevant.
Example: "The doctor recommended a much higher dose of the medication to effectively manage the symptoms."
Alternatives: "a significantly larger dose" or "a considerably higher dosage."
Exact(37)
Then, a much higher dose of radioactive particles is placed inside the blood vessels feeding the tumor.
I learned much later that I could have been prescribed a much higher dose of narcotics with no ill effect and much better pain control.
If an MRI label were added to the particle and that imaging technique were used instead, a much higher dose would be necessary.
The length of the anorexic effect achieved is comparable to other long-acting derivatives of OXM but it requires a much higher dose for administration.
Statins are out of patent and therefore now very cheap – a month's supply of 20 mg simvastatin costs less than £8, although the treatment for MS would be at a much higher dose.
"It is economic malpractice to give a much higher dose of an expensive drug than is required," said Dr. Ernest Beutler, an authority on Gaucher disease at the Scripps Research Institute.
Similar(23)
When we looked at the plasma concentration of genistein for the CD-1 mouse and F344 and S-D rats, we found a much higher dose-related response of genistein concentration in the plasma of S-D rats compared with CD-1 mice and F344 rats.
But it appears that the medicine is much weaker than he thought just a year ago, and that much higher doses will be needed to have the desired effect.
Pharmacologically, these data suggest that minimal amounts of ondansetron are needed to block 5-HT3 receptors in a vomiting patient, but that much higher doses are needed to block these receptors prophylactically.
For example, the animals in previous studies were reinforced with a much higher cocaine dose during self-administration training and PR testing (0.6 mg/infusion) than the dose that we used.
However, the complications were varied and not those typically seen when Avastin is used, at much higher doses, as a cancer treatment.
More suggestions(16)
a much higher exposure
a much higher radiation
a much higher intake
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com