A new analysis of government data finds that millions of seniors face double-digit hikes in their Medicare prescription premiums next year unless they shop for cheaper coverage.

The analysis of Medicare data comes from a private research firm, Avalere Health.

Premiums will go up an average of 10 percent among the top 10 drug plans that account for about 70 percent of enrollment.

Marketing for next year’s drug plans gets under way Oct. 1. Seniors will see some of the biggest changes since the Medicare prescription benefit became available in 2006. More than 17 million are signed up in private drug plans offered through Medicare.