Millions of Medicare Advantage customers are fast approaching a deadline for a task they’d rather avoid: Researching and then settling on coverage plans for 2015.

The annual enrollment window for the privately run versions of the government’s Medicare program for the elderly and disabled people closes on Sunday. This is the main opportunity most customers have each year to adjust their health coverage, and it may be worth paying extra attention to the details.

Insurers frequently tweak their coverage plans from year to year, but brokers and other industry insiders say they’re seeing more changes over the past few years as companies weed out lower-quality coverage and adjust to government funding cuts.

About 4 percent of Medicare Advantage enrollees, or 480,000 people, will have to find new coverage for 2015 because their current plan won’t exist, according the nonprofit Kaiser Family Foundation. Last year, 500,000 people faced that choice.

Customers who lose their old plans may be eligible to pick coverage in a special election period that runs through the end of February.

Other customers with discontinued plans are being automatically enrolled in another option offered by the same insurer. Companies generally try to limit the coverage changes in these cases, but the plans may not be identical, especially when comparing premiums.

“It really pays to shop around,” said Dwane McFerrin, a vice president with Senior Market Sales Inc.

However, sitting down to figure out coverage changes or whether there’s a better option can trigger headaches. Customers need to make sure their new plan covers all their doctors and prescriptions and leaves them with manageable bills if a major health problem hits.

Plus, they have to make sure the price or premium is right.

Almost 16 million people are covered by Medicare Advantage plans, nearly twice the total covered just seven years ago, according to Kaiser. The foundation’s researchers have found that people have, on average, 18 plans to choose from, but they generally prefer to stick with what they have and find it daunting to review all those options.

Insurers say those choices are changing more than in the past because years of funding cuts have forced them to trim the plans they offer or adjust their benefits. Deductibles, premiums and other costs can vary with these plans, and many also come with extra benefits like dental and vision coverage or gym memberships that might be pared.

The government has paid insurers who run Medicare Advantage plans more per enrollee than the cost of care for people with traditional Medicare coverage. But that is being scaled back in part to help fund the health care overhaul.

Overall, the Medicare Advantage program is “stronger than ever,” said Aaron Albright, a spokesman for the federal Centers for Medicare and Medicaid Services. He noted that enrollment has climbed since the overhaul was enacted in 2010, and customers still have access to an array of “high value” options for next year.

The government started a quality rating system a couple of years ago that provides extra funding for plans with higher ratings. Next year, only plans with four or five stars will be eligible for the bonus payments.

Most of the plans leaving the market after this year have lower quality ratings, according to Kaiser.

That means, in some cases, plans with weaker coverage are being be eliminated, which can make it easier for customers to sort through options, said Ross Blair, a senior vice president for eHealthMedicare.com, a division of the insurance broker eHealth Inc.