How can I do a character analysis for We Need To Talk About Kevin by Lionel Shriver?

We Need to Talk about Kevin is a disturbing novel with many disturbing characters.  A character analysis most definitely should focus on one of the three main characters--Kevin, his mother Eva, or his father Franklin.  Any of these three would make a fascinating character, or even psychological, study.  
Kevin is introduced as a hopeless psychopath.  From the time he is an infant, he is different and unsettling.  He won't nurse, he destroys his mother's projects, he refuses to talk.  Even his nanny, who has much experience with children, finds him uncontrollable.  As the novel progresses, we see Kevin's psychopathic tendencies worsen.  He is cruel to other children at school, but he is especially vicious to his little sister Cecilia when he convinces her to wash her eye out with Draino.  Despite others' attempt to befriend him--his English teacher, who tries to bring out Kevin's potential in writing; his father, who believes in him and defends him; and even his mother who sees Kevin for what he is and tries to manage him--Kevin cannot be helped and is the perpetrator of a cruel, senseless mass murder at school.  Any character analysis of Kevin would have to involve his detachment from his mother, his contempt of his father, and his rejection of all those who try to help him and are deceived by him.  Shriver seems to show us that some people are born this way and how easy it is for others to misjudge them because it's difficult to believe that a son, student, friend, or child can be evil.  If you were to focus on Kevin, you might look at his relationship with his mother and how that develops throughout the novel, his relationship with his father, and how his actions become more and more savage, devious, and manipulative.  His victims seem to be those who seem to see him as normal or good.  The focus should be not really on why Kevin acts as he does--there may be no real explanation for why some people are how they are--but on the way others treat Kevin or refuse to see the truth.