There are no arrows leading into X, therefore no back-door paths. We don’t need to control for anything. Nevertheless, some researchers would consider B a confounder. It is associated with X because of the chain X → A → B. It is associated with Y among individuals with X = 0 because there is an open path B ← A → Y that does not pass through X. And B is not on the causal path X → A → Y. It therefore passes the three-step “classical epidemiological definition” for confounding, but it does not pass the back-door criterion and will lead to disaster if controlled for.
