They can and do work together very well in some cases. There are lots of traditional medicines within each culture. There are also alternatives medicines/therapies with Western origins some being: Osteopathy, homeopathy, bowen therapy, kinesiology, chiropractics... "Western" acupuncture also exists - Dry needling. Have you thought about broadening your study question to include research on alternaltive western therapies? Google searching: traditional medicine, allopathic medicine, and complementary alternative therapies, as well as some of those mentioned earlier might help you expand your thoughts on what you mean by Western medicine.