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"by causing" is correct and usable in written English.
It is a phrase used to explain the result of an action. For example, "The storm uprooted the tree by causing strong winds."
Exact(60)
This affects customers by causing service interruptions and slow speeds.
Hard times often expose wrongdoing by causing scams to collapse.
Decongestants reduce secretions by causing vasoconstriction of the nasopharyngeal mucosa.
By causing illness and premature death, [it] reduces the quality of life.
The first operation that came into use for severe obesity worked by causing "malabsorption".
She accused her daughter of breaking up the family by causing trouble.
(Stay classy, Ms Ciccone!) Both singers' efforts did the job by causing a media flurry.
Originally, they thought L.S.D. would terrify alcoholics by causing symptoms akin to delirium tremens.
Opponents say they end up punishing the poor by causing layoffs of some low-paid workers.
"Motorola now seeks to absolve itself of liability by causing the debtors to release these claims".
But some scientists suspect that angiotensin may work some of its damage by causing inflammation.
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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