I am certainly no expert on the subject and have only been keeping bees since 2009 so please keep that in mind. However, I have not used any chemical treatments (unless you consider HBH and essential oils to be "chemical treatments"). I have used thyme oil (added it to the HBH most of last season) and I have begun making my own version of HBH with a formula I received from a local commercial beekeeper. His claim after using his process and formula is a negligible problem with mites. Thyme oil as he has explained to me, kills mites on contact. So in addition to putting thyme oil in the feed, he also sprays down the bees with the 1:1 feed (which contains spearmint, lemongrass and thyme oils), frame by frame on a warm day. Again, I'm no expert, just going on the advice of someone in my area with far more experience. I have not done an alcohol wash or mite drop count to figure out what my mite situation is, but I do know I've not lost a hive due to mites.
I hope this helps.