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The phrase "a substantially higher probability" is correct and usable in written English.
It can be used when discussing the likelihood of an event occurring, particularly in statistical or analytical contexts.
Example: "The new treatment has a substantially higher probability of success compared to the previous methods."
Alternatives: "a significantly greater chance" or "a markedly increased likelihood".
Exact(4)
The uninsured have a substantially higher probability of dying (about 42% higher, compared to the insured).
Hence, conditional on being admitted to the hospital, the uninsured have a substantially higher probability of having been transferred from the Emergency Department to the hospital (about 90% higher, compared to the insured).
Older girls had a substantially higher probability of vaccination initiation than younger girls.
Other studies have shown that extensive intracranial bleeding requiring neurosurgical intervention is associated with a substantially higher probability of in-hospital mortality in comparison with non-surgical intracranial bleeding [ 36, 37].
Similar(55)
The final weight for the men was computed to account for the oversampling of subjects for the sleep laboratory study (phase II); those with larger counts of the four possible risk factors, i.e., snoring, daytime sleepiness, obesity, and hypertension, had substantially higher probability of being selected.
In the case of breast cancer, HER2 overexpression is typically associated with younger patients and generally poor prognoses with substantially higher probabilities of relapse after treatment [8], [9].
Comparing pretreatment groups by the probability of admission sets a substantially higher bar than simply comparing the distribution of individual variables between treatment arms.
In Figure 2b, we investigate the effect of the dedifferentiation rate, γ, on the probability of resistance, R t), finding that larger values of γ lead to a substantially higher risk of developing resistance.
Or a substantially higher fine for littering.
Natives experience a substantially higher employment status persistence than immigrants.
Fifty percent were responded to -- a substantially higher rate than I'd ever experienced.
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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