Let the People of the Gospel judge by that which Allah hath revealed therein. Whoso judgeth not by that which Allah hath revealed: such are evil-livers.
Times are computed by method; your mosque's timetable governs the adhan. Every text carries its source and grade. Nothing here is a fatwa, a prediction, or a substitute for a doctor: your own scholar decides what is contested, and the tradition itself says the practice is alongside treatment, never instead of it.