In general, patients stayed in the same dosage category (low, moderate or large) before and after their overdose, the researchers found. To the extent that dosages changed, they tended to get smaller. Even so, 7 percent of the patients who had already suffered one opioid-related overdose went on to suffer a second overdose while they were still in the study pool.

Most patients wound up leaving the pool because they switched their health plan (including those who enrolled in Medicare). Still, the researchers were able to calculate that 17 percent of patients getting high doses of opioids were likely to have a repeat overdose within two years. So were 15 percent of those getting moderate doses of opioids and 9 percent of those with low doses of the painkillers.

Despite these risks, there could be some legitimate reasons to keep patients on prescription opioids even after an overdose, the study authors wrote. For instance, if a patient didn’t abuse the drug but merely followed instructions from a doctor that turned out to be unsafe, perhaps the best thing to do is modify the prescription. Or a doctor may decide that although the risk of another overdose is bad, letting a patient’s pain go untreated would be even worse—especially if the patient would be tempted to get relief from an illicit painkiller.