Many Medicare Advantage health plans routinely overbill the government for treating elderly patients — and have done it for years, a federal study shows. Department of Health and Human Services researchers found that many plans exaggerate how sick their patients are and how much they cost to treat. Medicare expects to pay the privately run plans — an alternative to traditional Medicare —$160 billion this year. The HHS study does not accuse any specific insurers of wrongdoing or name the plans that were scrutinized. But the researchers offer the most comprehensive evidence to date that suspect billing practices have been common across much of the Medicare Advantage industry and are likely to get worse unless officials crack down.