Robin Miller, a 62-year-old oncologist in Atlanta with bladder cancer, was scheduled to receive a potentially lifesaving drug in December. But her doctor’s office called shortly before the appointment to say: “Sorry, we don’t have any. We can’t give it to you,” according to Dr. Miller.

The disruption was due to a global shortage of the drug, BCG, which arose after manufacturing problems at two of the few global suppliers. Without the drug, Dr. Miller feared her cancer would come back and she would have to have her bladder...