Health insurers process more than five billion payment claims annually, federal figures show. About 850 million are denied, according to health-policy nonprofit KFF. Less than 1% of patients appeal. Few people realize how worthwhile those labors can be: Up to three-quarters of claim appeals are granted, studies show. Patients who fight denied claims must marshal evidence from medical studies, navigate dense paperwork and spend hours on the phone during what is often one of the most difficult times of their lives.