Medicare’s top officials said in 2006 that they had reduced the number of fraudulent and improper claims paid by the agency, keeping billions of dollars out of the hands of people trying to game the system.

But according to a confidential draft of a federal inspector general’s report, those claims of success, which earned Medicare wide praise from lawmakers, were misleading.

In calculating the agency’s rate of improper payments, Medicare officials told outside auditors to ignore government policies that would have accurately measured fraud, according to the report. For example, auditors were told not to compare invoices from salespeople against doctors’ records, as required by law, to make sure that medical equipment went to actual patients.

As a result, Medicare did not detect that more than one-third of spending for wheelchairs, oxygen supplies and other medical equipment in its 2006 fiscal year was improper, according to the report. Based on data in other Medicare reports, that would be about $2.8 billion in improper spending.