I am a liver patient and have not had any alcohol since December of 2014 my peth test from August 2015 showed a minor trace per the peth test. Why?

Maybe because while you didn't drink what you thought of as Booze... you didn't abstain from using other products that contain it. Which is as simple as reading the labels.. and buying and using alcohol free formulations. Mouthwash, and cough medicine are two of the most common (but far from the only)....and alcohol free formulations do exist

Hand sanitizer is another one. Remember that cooking doesn't clear off all alcohol, like a white wine sauce or a bourbon BBQ sauce, and some recipes don't deal with the alcohol whatsoever, like rum balls. You need to be extra vigilant.