Hi joylk! All the interferons: Avonex, Rebif, and Betaseron can potentially cause problems with you liver. That is why it is very important to get blood work done every three months to monitor your liver enzymes. Good for you for staying on top of it! As far as I know, the only therapy that does not affect liver function is Copaxone. In their info guide, the manufacturer states that it is not necessary to have periodic blood work done while on Copaxone.
Have you recently started taking any other meds which may have affected your blood test? I would discuss it with your neuro, since the Avonex can cause the same liver panel elevation as the Rebif. Best of luck

- Sharon Grace