Diff of two Doctrine_Collection instances

I have a collection of users who completed a certain test and a list of users who got an invite for that test. Now I'd like to fetch all the users who did not complete the test. I thought it'd be simple to diff the two collections (like arrays), but only Doctrine_Collection::merge() is possible.

My datamodel (much left out for clarity):

Invite:
  columns:
    id: integer (10)
  relations:
    users:
      foreignAlias: invites
      class: User
      refClass: UserInvite

UserInvite:
  columns:
    user_id: integer (10)
    invite_id: integer (10)
  r开发者_如何学Celations:
    user:
      class: User
      foreignAlias: userInvite
    invite:
      class: Invite
      foreignAlias: userInvite

Test:
  columns:
    id: integer (10)
    user_id: integer (10)
    invite_id: integer (10)
  relations:
    user:
      class: User
      foreignAlias: tests
    invite:
      class: Invite
      foreignAlias: tests

Now these two collections are available to me:

$invite = new Invite;
$invite = $invite->users; // All the users who got an invite
$invite = $invite->tests; // All the tests performed for this invite

What's the best method to get all the users? I can perform an SQL query, but I't like to do this in OOP php or else a DQL query. In SQL, I can do something like this:

SELECT u.name, u.id
FROM user u
    LEFT JOIN userinvite i
        ON i.user_id = u.id
    LEFT JOIN test t
        ON t.user_id = u.id
WHERE i.id IS NOT NULL
AND t.id IS NULL

Okay, I now know I had to approach this problem via the User model itself. This DQL query fetches all the users who miss their test from a specific invite:

$user  = new User;
$users = $user->getTable()
              ->getQueryObject()
              ->leftJoin('User.userInvite i')
              ->leftJoin('User.tests t')
              ->where('i.invite_id = ?', $invite->id)
              ->andWhere('i.user_id IS NOT NULL')
              ->andWhere('t.user_id IS NULL')
              ->execute();