Assuming that you're unsure as to whether it's a complement or an adjunct, standard tests can be applied:
(1) Optionality: #The latest research on dieting always warns people about the dangers. (Not possible except when the PP is elided)
Compare: I tied my shoelaces (at noon).
(2) Restrictions on type: *The latest research on dieting always warns people about the dangers at sleeping late. ('Dangers' requires 'of', not 'at')
Compare: I tied my shoelaces in the washroom/at school/during recess.
(3) Restrictions on number: *The latest research on dieting always warns people about the dangers of too much cholesterol of too little sleep. (Can't have more than one complement)
Compare: I tied my shoelaces in the washroom at school during recess.
(4) Restrictions on position: *Of too little sleep, the latest research on dieting always warns people about the dangers.
Compare: At school, I tied my shoelaces.
All these point to the PP being a complement, so it should be the daughter of N' and the sister of N.