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The phrase "already shown to be sensitive" is correct and usable in written English.
It can be used when referring to something that has previously been demonstrated or established as being sensitive in nature or context.
Example: "The data has already shown to be sensitive, requiring special handling and confidentiality measures."
Alternatives: "previously demonstrated to be sensitive" or "already established as sensitive".
Exact(1)
This task is very similar to that already shown to be sensitive to 5-HT manipulations in humans (Murphy et al. 2002) and rodents (Bari et al. 2010).
Similar(59)
We used a recognition task that has already been shown to be sensitive to the influence of Oxytocin nasal spray (Unkelbach et al., 2008).
The 16S-rRNA PCR primers have already been shown to be sensitive (5 IFU) and specific [ 25].
MRS has been shown to be sensitive to these changes.
Similarly, the Fay and Wu neutrality test [49] has already been shown to be highly sensitive to homoplasies [59] which may contribute to the significantly negative value South of the Alps (see related point in the discussion).
CEUS already was shown to be more sensitive than PDUS in the detection of intraarticular synovial vascularity and therefore better differentiation between active and inactive synovial thickening [ 15].
The importance of the proteolytic activity of cells has been already considered in the design of biomaterials by incorporating MMP sensitive sequences, which have shown to be mandatory in tissue regeneration in 3D, including cell proliferation, migration and angiogenesis [62] [65].
One has to be sensitive.
"You have to be sensitive.
One wants to be sensitive.
We need to be sensitive".
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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