.. I find this thread a tad disturbing ... if you are flying a SID AEO, then you MUST have a gameplan to cover the very much inferior OEI climb performance .. whether that involves continuing on the SID, or heading off along some escape path ..
.. some here appear to be separating the two .. as if you have an option as to when you will, or won't, have a failure .. ?
The question of AEO climb is covered by the presumption that the aircraft will be flown in a manner which will cause it to be above the OEI flight path along the same track .. but if you haven't done the OEI sums up front, then don't have a failure half way down the takeoff path ..