pronoun case after than / as
Than I versus than me.
After than or as, use the case the full clause would take. She is taller than I am, so taller than I. The news surprised her more than it surprised me, so more than me. The object form is common. Keep the case of the implied clause.
Examples
Use She files faster than I.
Use The delay cost her more than me. (Than it cost me.)
Avoid She files faster than me. (If you mean than I do.)