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The phrase "a substantially higher recurrence" is correct and usable in written English.
It can be used in contexts where you are comparing the frequency of an event or occurrence, indicating that it happens much more often than another reference point.
Example: "In the study, we found that patients with the condition had a substantially higher recurrence of symptoms compared to those without."
Alternatives: "a significantly greater recurrence" or "a markedly higher recurrence".
Exact(1)
Therefore, by reporting that trastuzumab-naïve HER2+ HR- patients have a substantially higher recurrence rate than HER2+ HR+ patients, we infer and show that HER2+ HR- will derive higher absolute treatment benefits from trastuzumab treatment.
Similar(59)
Or a substantially higher fine for littering.
You are simply getting a higher quality economy product, often for a substantially higher price.
In the event of complications from donation, women would receive a substantially higher payment than normal.
Natives experience a substantially higher employment status persistence than immigrants.
The uninsured have a substantially higher probability of dying (about 42% higher, compared to the insured).
IMPORTANCE Patients with schizophrenia have a substantially higher suicide rate than the general public.
Fifty percent were responded to -- a substantially higher rate than I'd ever experienced.
Thus, they had a substantially higher power than this cohort.
Several genes exhibit a substantially higher level of allelic diversity.
In a meta-analysis of studies reporting on the use of pre-operative breast MRI for the patient with an established index cancer, multifocal or multicentric disease was found on breast MRI in 16% of the patients, a rate substantially higher than the rate of local recurrence after breast conserving surgery plus definitive radiation treatment.
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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