Might be OR Might have been [closed]
Both are correct. One indicates a different time frame from the other.
Had the doctor been more careful, my cousin might still be alive.
This sentences describes the PRESENT time. My brother would still be alive NOW.
Had the doctor been more careful, my cousin might still have been alive.
This sentences describes a PAST time. My brother would have still been alive at that moment in the past...
This is really more of a question of the past perfect than the use of the modal verb might.