Appositives are noun phrases that rename nouns or pronouns. A pronoun used as an appositive has the same function (usually subject or object) as the word(s) it renames.

The appositive Dr. Bell and I renames the subject, managers. Test: I could not agree (not me could not agree).

The appositive the bicyclist and me renames the direct object, witnesses. Test: found me (not found I).