"We applied our composite probability distribution to each patient to calculate the probability that the patient was a member of the 'extreme' group. That is, we multiplied the size of each stratum of patients by its posterior probability of population 3 membership to estimate the total number of probable shoppers in the United States. Summing these probabilities, we estimated that of the 19 million patients in the US who purchased opioids in the first 60 days of 2008, 135,000 (0.7%) were members of this extreme population (Table 2).
"Although only a small fraction of active patients, members of this extreme population obtained an estimated 1.9% (4.3 million) of all 223 million opioid prescriptions dispensed during 2008, and 2.8% of all oxycodone prescriptions (Table 3). They purchased an average of 32 opioid prescriptions that year. When we accounted for the quantity of drugs prescribed, their share of the market was even larger: an estimated 4.0% of the total amounts of these drugs dispensed that year, or about 11.1 million grams. This was equivalent to approximately 5.4 million grams of morphine. This would have provided an average of 109 morphine equivalent milligrams per patient in this extreme group for every day in 2008."

Source

Douglas C. McDonald and Kenneth E. Carlson, "Estimating the Prevalence of Opioid Diversion by 'Doctor Shoppers' in the United States," PLoS One, 2013; 8(7): e69241. Published online 2013 July 17. doi: 10.1371/journal.pone.0069241.
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