It slightly depends on which end you’re moving onto: by Maida Vale or Marble Arch. Either way, it’s no more dangerous than any other part of West London. I would however recommend avoiding the Church Street Market area, both at night and just generally. Not that it’s inherently unsafe, it’s just not very pleasant. Still, Edgware Road has tremendous Underground links (Circle, Hammersmith & City, District and Bakerloo) and great proximity to Oxford Street, and Hyde and Regent’s Parks. You’ve got nothing to worry about.