NADPs are based on a law passed by the Spanish government (the link is in Spanish):
BOE.es - Documento BOE-A-2011-12611
There is further legislation that regulates this matter in depth.
Apparently a commission is created by LEMD (Madrid airport) and the Infrastructure Ministry (Ministerio de Fomento, which is responsible for airport operation). The commission discusses the areas affected by noise and then decides the noise abatament measures to take.
Many departures from MAD fly over certain areas that are inhabited and have complained about noise for years. These areas are not densely populated and I dont know if the houses where there before or after the SIDs that fly over them were approved. What I know is that the neighbours were exposed to very high levels of noise day and night and they made a lot of noise about it too, to be heard by the Ministry.