Who can explain the different use of "Like", "As", "Similar"

Similar to rising interest rates, consumer and producer prices have been rising.

A

B Consumer and producer prices have been rising, as have interest rates.

C As interest rates are rising, so have consumer and producer prices.

D Consumer and producer prices have been rising, like interest rates do.

E Consumer and producer prices, as interest rates, have been rising.

Who can explain the different use of "Like", "As", "Similar" in this situation? Thanks!