Vayne is a REALLY weak ADC early on in the game. If you just matchup numbers, she should lose in power against most every other ADC in the game early on if they can land their abilities. Her real strength is in her late game power, her strong dueling ability, and her outplay potential.
She has no wave clearing ability, which makes it so she can get pushed into tower very easily. Early in the game, minions do a significant amount of damage, so you having no/less minions then your lane opponent means that if you fight, you should end up taking more overall damage then them if they play correctly.
Her range is fairly short for an ADC, making it so champions like
can hit her before she has any chance of touching them. That is also just their AA. Most other champions have abilities that outrange their AA range which they can use to harass Vayne down before she can even touch them.