I applied to the Ph.D. in Economics of Education (SHIPS) program and I have been trying to find an answer regarding the interview procedures. Here is a post from Stanford SHIPS page back in 2014. I also remember them saying that there is no formal interview process when I called them before the application deadline; however, it seems that the majority of the people that were admitted had some sort of an interview/conversation with their POIs.
In short, it seems to me that not getting an interview does not qualify as an implied rejection; however, it is not good news either.
@jose_lr please let us know if you find further information regarding this question.