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The phrase "any such relationship" is correct and usable in written English.
It can be used when referring to a specific type of relationship that has been previously mentioned or is understood in context.
Example: "The study aims to explore any such relationship between diet and mental health."
Alternatives: "any similar relationship" or "any corresponding relationship".
Exact(31)
But in the room, any such relationship seemed forgotten.
And there are two sides (at least) to any such relationship.
If Mr Krugman knows of any such relationship, I'm sure Mr Brooks is all ears.
"There were people who felt the university was morally culpable for not saying no to any such relationship.
But a number of Alliance officials in Brussels said yesterday that they were unaware of any such relationship.
Mr. Einhorn does not appear to have had any such relationship with Punch, and so absent a fiduciary duty there would be no basis to charge insider trading in the United States.
Similar(29)
Those who can claim to have any such relationships are exempt from the order.
What effect, if any, such relationships have on the outcome of clinical studies is difficult to evaluate, said Dr. Mildred Cho, a bioethicist at Stanford University who has studied conflict-of-interest policies at the 100 largest research institutions in the country.
However, when interest lies in investigating whether patient characteristics are related to treatment, IPD analysis will generally be necessary to discover any such relationships.
This study investigates the relationships between benthic macrofauna and biogeochemical properties of sediments within and among different habitats in multiple mangrove forests in a temperate estuary, in order to address the generality of any such relationships.
Although the interaction effects must be tended to in valuation studies, it is not self-evident that there are any such relationships between mean utilities from two countries.
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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