If it is an American novel that you read, it is unlikely that the
title is "The Absence." That name has already been copyrighted:
Elizabeth Spencer, Fiction, “The Absence,” The New Yorker, September 10, 1966, p. 53
Also, the plot isn't similar to the one you're trying to find. If you'd care to
see the plot of "The Absence," it's at the link below:
Fiction: The Absence: The New Yorker