Should parents be held responsible for their children's behaviour ?

So I should be held responsible for the behavior of my child if, for instance, my child has some sort of disorder that makes it difficult or impossible or at the least MUCH harder to affect their behavior. Let's say that a child has depression. There are kids who have committed suicide by 9, and others who have tried as early as 2-3. These children almost always have some sort of imbalance that drove them to it. Should I be held responsible for that?