Prescriptions as an Extension of the Doctor-Patient Relationship

A woman has been taking "The Pill" for three years under her doctor's prescription although she has not seen her doctor in ten months. A professor has a renewable prescription for his heart condition, but has not seen that physician for more than a year. A stroke victim has been taking a prescription pain killer for seven months beyond the time when he was last examined by his physician. Does the doctor-patient relationship exist in situations such as these?