When Charlotte Alger, 25, was working at Home Depot in Boston last year, she said, she earned $10.75 an hour working on the sales floor in the woodworking department. She chose one of the more comprehensive health insurance plans offered, but it came with a whopping $3,000 deductible.

Paying for such a large share of her costs upfront was burdensome, particularly because Alger, who recently went back to college, regularly sees a psychologist for depression and anxiety. "I felt sort of ripped off," she said, adding that none of her previous doctors were included in the plan’s network. "I see a mental health care professional, and it’s not the kind of doctor you want to switch."

She ultimately decided to switch employers, largely in an effort to find better benefits. She recently started working as an accounting clerk with a more affordable plan.

Although the rise in premiums has slowed since passage of the Affordable Care Act, workers who receive health insurance through their employers are shouldering more health care expenses at a time when wages are stagnant, according to a new report from the Commonwealth Fund that analyzed costs across the states.

These costs are particularly high — relative to median income — for workers in the South and South Central States, where income is below the national average, the report found, even though the growth of premiums had slowed in several states in those regions.

"Without growth in income, rising out-of-pocket costs means less affordable care," said Cathy Schoen, executive director of the Commonwealth Fund’s Council of Economic Advisors.

Insurance premiums have risen faster than median incomes for workers under 65 in all states in the decade from 2003 to 2013. Average annual premiums — including what both employers and employees contribute — represent 20 percent or more of the median income in 37 states. That was the case in only two states in 2003.

While employers are trying various strategies to contain health care costs, shifting more expenses to employees is one of the main tools. "Increasing cost-sharing is the tried and true way to keep their premiums down," said Drew Altman, president of Kaiser Family Foundation. "We’re seeing a steady, slow increase in cost-sharing every year."

According to Commonwealth, out-of-pocket costs — including workers’ premium contributions and deductibles — accounted for 9.6 percent of median household income in 2013, on average, up from 5.3 percent in 2003.

That is the case even though the growth of overall premium increases has slowed.

In the three years after the passage of the Affordable Care Act in 2010, premiums rose about 4.1 percent annually, down from a national average of about 5.1 percent from 2003 to 2010, according to the report.

In 31 states and the District of Columbia, premiums increased more slowly from 2010 to 2013 than in previous years, particularly in several Southern and Western states. But in 10 other states, annual premium growth rates remained high during the same period, at least 6 percent on average.

The average premium for a family was $16,000 in 2013 — including the portions paid by both employer and employee — and ranged from $13,477 to $14,382 in the states with the lowest costs, which include Alabama, Arkansas, Idaho, Mississippi and Hawaii. In the most expensive states — New Jersey, Massachusetts, New York and Alaska — premiums were more than $17,000 to nearly $21,000.

"The steady increase in premium growth means health insurance is expensive no matter where you live," Schoen said.

The burden of out-of-pocket costs causes Elizabeth Price, a 40-year-old administrative assistant with a rare genetic disorder, to avoid the emergency room, which costs $175 each visit. "High copays that do not count towards my out-of-pocket maximum definitely make me think twice before going," said Price, who works for a small college in Chicago. "And that’s just the copay — once I’m in the hospital, there are more costs, and I can never be sure that all the treatment I’m receiving is ‘in network’ and preapproved, so it might not be covered."

At less than $80 a month, her premiums are reasonable, she said. But since she is prone to kidney stones, she said, she could expect to visit an emergency room two to four times a year. She said she had to weigh the pain level and possible complications from delaying treatment.

Given her health condition, Price said, her job choices had been limited; she needs to work for an employer that offers policies with reasonable out-of-pocket maximums because she knows she will reach them.

To contain costs, many large corporate employers are offering high-deductible plans, also known as consumer-directed plans. At about one-third of large companies, it is the only option available, according to the National Business Group on Health. The plans require employees to pay for a greater share of their medical costs upfront, before the plan starts making payments. The goal is to make employees comparison shop for medical services, something not always easy to do, particularly in emergency situations.

"It’s quite shocking when you see the range of costs for the same services in a market," said Brian Marcotte, president and chief executive of the National Business Group on Health. "But employers are also trying to get employees to play a greater role in managing their care."

In 2013, 81 percent of workers were enrolled in a health plan with a deductible, according to Commonwealth Fund, compared with 52 percent in 2003. The average per-person deductible has more than doubled over that period, rising 146 percent on average. In 2013, the average per-person deductible exceeded $1,000 in most states, and exceeded $1,500, on average, in seven states.

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