I know you can not refuse a drug test but can you to your family doctor?
You have a right to refuse any test that you don't want to take at any time from any health care provider. But, why would you do that? If you refuse to take a drug test, that gives us a pretty good idea you are hiding something.
Drug screening isn't done to catch the user and punish them. Drug screens are a health indicator and your health provider needs to know. I'd say go for it.