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The decades-long overdose epidemic in the United States is driven by opioid misuse. Overdoses commonly, although not exclusively, occur in individuals with opioid use disorder (OUD). To allocate adequate resources and develop appropriately scaled public health responses, accurate estimation of the prevalence of OUD is needed. Indirect methods (e.g., a multiplier method) of estimating prevalence of problematic substance-use behavior circumvent some limitations of household surveys and use of administrative data. We used a multiplier method to estimate OUD prevalence among the adult Medicaid population (ages 18–64 years) in 19 Ohio counties that are highly affected by overdose. We used Medicaid claims data and the US National Vital Statistics System overdose death data, which were linked at the person level. A statistical model leveraged opioid-related death rate information from a group with known OUD to estimate prevalence among a group with unknown OUD status given recorded opioid-related deaths in that group. We estimated that 13.6% of the total study population had OUD in 2019. Men (16.7%) had a higher prevalence of OUD than women (11.4%), and persons aged 35–54 had the highest prevalence (16.7%). Our approach to prevalence estimation has important implications for OUD surveillance and treatment in the United States.