Bang and Tsiatis - t-test after?

I have a treatment group and a control group (as a result of a matched cohort). I am comparing 12 month costs for a program but since not everyone made it to 12 months I used Bang and Tsiatis to estimate costs for people who fell short of the 12 month time period based on those who were in the program longer.

My question is what kinds of analyses can I do after this? I was told (by a Ph.D in stats) that I cannot really do a paired t-test with these Bang and Tsiatis estimted values but am curious if anyone else has other suggestions or ideas?

Mostly I stop pulling costs after a certain period (because of certain issues I won't get into detail here...not related to the program). So people may not have the opportunity to be followed for 12 months, which is I was using B&T estimator to estimate the 12 month cost for those members.