Vayne is weak.

Vayne is currently the only "late-game" adc that has a trash early game and takes some brain-power to use.

Her team-fighting is terrible, her laning is terrible, the only thing she is good at is 1v1's IF she's ahead of the enemy.

There is no point in the game where Vayne is good in the current meta. Her range is too short, her tumble is trash, her E is too buggy, and her ult has too long of a cooldown and not enough of an ad steroid.

The only Marksmen that you shouldn't pick over Vayne are possibly Sivir and Ashe (Not counting Urgot or Teemo as marksmen.) And even those two have something that makes them unique or good in teamfights.

With the meta being centered around teamfights and Vayne literally being the only adc that cannot teamfight well, she has no way of being viable. Yes, I acknowledge there are streamers like hiimgosu, Doublelift, and more that are able to play her well. But even they will tell you she is weak compared to everyone else in the game.

From my own personal experinces, I'm only able to win as Vayne if my opponents are terrible or if my team is hard-carrying me. Even when I hardcore win my lane, I feel weak and useless compared to other ads.

TL;DR: Vayne is weak and needs to be looked into for a rework/buffs.

Edit: When you give the argument that she can go invisible, a well placed pinkward or upgraded red trinket will solve that problem easily. She also cannot build the two best first items (IE and TF) or she will have even less damage because she relies on auto attacks to proc her W.