But are the complications from the intervention or from the reason-the-doctor-is-worried-and-intervening? You're implicitly comparing P(complication|intervene)

But are the complications from the intervention or from the reason-the-doctor-is-worried-and-intervening? You're implicitly comparing P(complication|intervene) with P(complication|not intervene) but you should probably be comparing P(complication|intervene and want_to_intervene) to P(complication|not intervene and want_to_intervene).