According to a recent report,

70.3% of adults with medical debt said that all of it was accrued during periods with insurance:

• 9.2% reported medical debt incurred during periods with insurance from services that were not covered by their health plan
• 14.5% reported medical debt from cost sharing under their health plan
• 11.0% reported medical debt from co-payments and coinsurance
• 11.1% reported medical debt from a deductible

Source: "Most Adults with Medical Debt Had Health Insurance at the Time the Debt Was Incurred," The Urban Institute, May 21, 2015, http://hrms.urban.org/briefs/Most-Adults-with-Medical-Debt-Had-Health-Insurance-at-the-Time-the-Debt-Was-Incurred.html