The phrase "a main criterion for" is correct and usable in written English.
It can be used when discussing a primary standard or principle that is used to evaluate or judge something.
Example: "The quality of the materials used is a main criterion for selecting the best supplier."
Alternatives: "a key factor for" or "a primary standard for".
A main criterion for the decision on how many cases to include was empirical saturation.
Among them, 2689 (91%) started antiretroviral therapy soon after their single off-treatment CD4 determination, which presumably often represented a main criterion for treatment decision.
As pointed out before, a low systolic blood pressure is now considered a main criterion for the indication to inotropic therapy.
Hypercapnia is a main criterion for the use of NIV [ 3], which suggests that NIV could be used more often in the Netherlands.
A main criterion for the selection of the word items was that the words could be used in the orthographic spelling condition in either a "yes" or a "no" trial.
Faced with a new warning by a prominent religious conservative against selecting a running mate who supports a right to abortion, Gov. George W. Bush today called himself "a pretty independent thinker" whose main criterion for a vice-presidential nominee was an ability to assume the presidency.
We recognised each other from one of the city's least exclusive clubs, a place where the main criterion for belonging is wanting to.
Overall, 21.8 percent of recruiters surveyed said that the university attended by an applicant was the main criterion for selection, while another 45.1 percent cited it as an important factor.
Rather than making a fetish out of passports, a better approach would be to use residence (especially tax residence) as the main criterion for an individual's rights and responsibilities.
At the time, Bush said that his main criterion for a running mate was "somebody who's not going to hurt you".
In Schumpeter's view, the main criterion for a democracy was the competition for political leadership.
