Well, if the truncated data are more than 80%, the whole analysis is meaningless. The main stream way to do the truncated data and censored data are quite stupid, actually. Either they throw away those nondetect data, or use the averange number of the interval instead of the truncated data. Also you could write a macro yourself and run it into SAS. So far, there are a few procedures like LIFEREG, RELIABILITY in SAS are dealing with nondetect data. I think there are a few packages work in R as well too. But because the difficulties of how to treat the trunceted data are so huge, most statisticians in the U.S. would choose the main stream ways which is pretty sad.