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"independently associated" is a grammatically correct and usable phrase in written English
You could use it to describe the relationship between two entities that are not directly connected, but linked in an indirect manner. For example: "The two separate projects were independently associated, but achieved similar results."
Exact(60)
Endodontic lesions are independently associated with coronary artery disease.
Obstructive sleep apnea is independently associated with insulin resistance.
Discordance was independently associated with outcomes.
A person's good health was independently associated with the happiness of his or her spouse.
Hb-levels were independently associated with DAT and age.
Objective: Hyperhomocysteinemia and hypertriglyceridemia are independently associated with atherosclerotic disease.
Calcium-channel blockers were independently associated with AAA.
The −351A/G polymorphism was not independently associated with CHD.
Reutrakul, S. et al. Chronotype is independently associated with glycemic control in type 2 diabetes.
Rights & permissionsfor article Area socioeconomic status is independently associated with esophageal cancer mortality in Shandong, China.
Unless your family members are independently associated with Cornell, we cannot offer them NetIDs.
More suggestions(15)
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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