The central storyline in his book is that a mother doses her kid with benadryl so that she can go out. When the kid accidentally dies, she panics and makes up a story about how a stranger took her kid.
Which, according to People Magazine, seems to be a theory Portugese police are playing with. But these parents are doctors, so presumably they would be more aware of the dangers of giving kids medcine to make them stay asleep. [Full disclosure: Price's book is also about race and poverty, neither of which play a role here.]