I remember the game of Liverpool against Newcastle when they were playing away and they were even with 10 men yet they managed to equalize from 2-0 to 2-2 at that game where Newcastle was at top performance at that time.Based on this no matter that Liverpool is playing against Manchester City I would not write them off from a big,huge surprise if they are able to win at Etihad stadium,statistics are good to be shown but I don't think we should rely to much on them because the teams are not the same as they were years before.I think a draw would be the most likely result during this game.
Newcastle this season is not the best example, because their game is not as stable as it was before and perhaps you are confusing something, because in the match with Newcastle Van Dijk get red card, and Liverpool was able to win this match 1-2 despite the fact that they I had to play most of the match with ten men.
It will be difficult for Liverpool at the Etihad, perhaps more difficult than any other team, but they have a chance to take points from City. Liverpool is a team of mood, you need to watch how they start the match.