Despite relatively slow average growth in annual employer-based family premiums, employees are shouldering more and more of the burden of health insurance costs, according to a survey released Wednesday.

Though employer-based premium growth increased by 3 percent over the past year, remaining consistent with minor increases over recent years, employers have steepened deductibles over the same period, according to the Kaiser Family Foundation/Health Research and Education Trust 2014 Employer Health Benefits Survey.

“These findings are positive and reflect a general slowing of health care costs overall,” said Maulik Joshi, president of the Health Research and Education Trust and senior research vice president at the American Hospital Association, in a release.

“As we work to improve health care, making sure it remains affordable to Americans is critically important to ensure greatest access by all,” he said.

The 3 percent increase is consistent with the yearly wage and general inflation increases, the release said.

But 80 percent of covered employees have a general annual deductible, compared to 63 percent in 2009. The average deductible is more than $1,200, the study showed.

“Today, 4 in 10 covered workers face at least a $1,000 deductible, nearly double the share from just five years ago,” said Gary Claxton, a Kaiser Family Foundation vice president and lead author of the study.

Family premium increases have slowed over the past five years. They have increased 26 percent over that period, in contrast with a 34 percent rise from 2004 to 2009. But family premiums have still more than doubled since 2002, according to the new survey. On average, annual family premiums in 2014 cost around $16,800 and employees contributed around $4,800.

The cost of co-payments used for physician office visits and prescription drugs remains about the same as in 2013.

The study also suggests that most employers with at least 100 full-time employees provide health benefits for their workers. In 2015 under the Affordable Care Act, the 6 percent of employers the study shows do not currently offer health benefits could face penalties if they do not change their policies.

The implications will be greater in 2016, when employees with at least 50 workers could face penalties if they do not provide health benefits. Only about half of employers with fewer than 50 workers currently provide health benefits, according to the study.