IMO training a dog with
PR methods and the time needed to succeed it depends a lot in the particular dog.
For example: With Liza all the negative reinforcement was useless! When I started with
PR she was doing amazing things in a matter of days! She is very attached with me (with a little of Separation Anxiety-my fault!) and when I praise her it is the best for her so I used that drive and in a few days she was able to do whatever I wanted!
It was not the same with the other dogs especially with my Mals. A few corrections and NR was like "necessary" to control them at first. Of course that may have to do with how I like to train my dogs (Until the age of 8-9months only socialize HUMANS:women and men,young adults / adults, elderly people, disabled / infirm,loud, confident people,shy, timid people,joggers,delivery / wearing uniforms
people wearing hats,people with beards,people wearing glasses, CHILDREN:babies,toddlers,juniors,teenagers ANIMALS:adult dogs,puppies,cats, small pets / birds,livestock / horses ENVIRONMENTS: friend's house, shopping centre, park,school / play grounds,day care country walks, party,slippery floor
bus,bridges,tunnels,elevators,stairs,veterinary practice,groomer,boarding kennels. OTHERS:motorbikes,bicycles,breed related stimuli, wheel chairs, traffic...and starting some training and after I am happy with their character I start training at about 1yo or more). Same with NR with the GSDs except my girl

which does better with purely
PR
Again with the rotties purely
PR methods was the quickest way.
I try very hard to use purely
PR methods with all my dogs but from what I've seen with some dogs (maybe breeds????) is faster even from NR and with others is almost inevitable to not use corrections