From what I know, your ST-4500 shifters should work with the 9 speed cassette and Alivio RD-M4000 RD. However, if the RD is marked Dyna-Sys (what Shimano went to on the 10 speed MTB RDs), then it wont work; cable pull was changed for the 10 speed Dyna-Sys MTB shiftes/RDs. Also, Shimano changes the cable pull in the 10 speed Tigras shifter (ST-4700) so they wont work with older 10 speed road RDs, Did you take this opportunity to install new housing and cables? Dirty cables can really cause problems. Best of luck.