QAD is a medical abbreviation, of the sort used by doctors on patient's medical notes for their private use, and not intended to be seen by the patient. In this case, QAD means 'quaque altera die' which is Latin for 'every other day.'
Other medical abbreviations using Latin include:
h.s. - hora somni - at bedtime
q.2.h. - quaque secunda hora - every two hours
o.d. - omne in die - every day
q.s. - quantum sufficit - as much as suffices
p.r.n - pro re nata - as much as is needed
a.c. - ante cibum - before meals
Abbreviations can often be used more mischievously by doctors. One time in the East of England, a doctor was found to have written 'SNEFS' on a patient's records. When pressed to explain, the doctor admitted 'SNEFS' wasn't a technical term, but meant 'Sub-Normal, Even for Suffolk'! Needless to say, this sort of thing is frowned upon, if only it can cause confusion when notes are referred to in treating the patient.
Here's some genuine abbreviations from a nursing school graduate and YouTube user:
