Medicare processed 906 billion outpatient insurance claims in 2010 – and refused to pay 10 percent of them. But if you’re a senior on Medicare with a denied claim, your odds of turning that around are surprisingly good if you appeal.

In 2010, 40 percent of Part A appeals and 53 percent of Part B appeals were granted, according to the Centers for Medicare & Medicaid Services, which administers Medicare (CMS). Even in the case of big ticket durable medical equipment appeals, 44 percent of appeals were successful. More than half of appeals to Medicare Advantage and prescription drug plans are successful, too.

Appeals make the most sense in cases where a service is denied and your doctor thinks you’re entitled to it. Other strong cases involve denials where you suspect administrative error, such as incorrect coding done for a service. “If a denial was generated but the explanation of benefits doesn’t look right to you, consider an appeal,” says Douglas Goggin-Callahan, director of education at the Medicare Rights Center, a non-profit advocacy and consumer group.

My column at Reuters Money this week offers tips from Medicare consumer advocates on how to file an appeal. Also see this handy visual guide to the appeals process from the Medicare Rights Center [pdf file].