BOSTON — The overwhelming majority of Bay Staters continue to have health insurance coverage, but a new survey highlights nagging challenges in accessing care and affordability woes exacerbated by high-deductible plans.

The uninsured rate in Massachusetts is 2.1%, compared to the national rate of 8.2%, according to the biennial Massachusetts Health Insurance Survey released Thursday. Nine out of 10 residents also reported continuous insurance coverage for all family members living in their household over the past 12 months.

A 2006 reform law signed by former Gov. Mitt Romney was crafted to facilitate universal insurance coverage.

But health care affordability issues persist, and about 28% of residents said they or a family member in the past 12 months refrained from seeking care due to

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