ok cait wins before 1st back... she shoves the lane pushes you under turret and can harass with her Q and headshot passive... after 1st back cait's power starts to dip and is usually bad til mid-late game ... so any other adc at this point usually can out trade her and push her back and punish her...
if she is pushing the lane hard and shoving you under turret. don't give free kills. take the cs you can and play the lane into a farm lane til your jungler/mid roams bot and ganks her for being so far forward.
typical match up like this is cait vs vayne...
as vayne all you wanna do is not die and be even in cs and you won the lane... because you will out scale her late game... be more of a threat 1 vs 1... and have potentially more damage output
but as vayne if you die and let her get her IE and HURRICANE early and hit a two item power spike early... then she has control but still kinda falls of mid game if she don't continue to snowball...
so play the lane safe. farm what you can. try not to give kills. and wait for ganks to go ham