No, medical error is NOT the third leading cause of death, and no, Emergency Department misdiagnoses are NOT killing 250,000 people a year in the U.S. As an emergency physician, the widely publicized AHRQ report is particularly painful because it has numerous flaws, and like the Institute of Medicine /BMJ  study, is guilty of completely unwarranted extrapolations.  The authors, for instance, looked at a Canadian study on 503 patients discharged from EDs, one of who died within 14 days of the ED visit (it’s not clear whether this actually represented a diagnostic error; the study was looking at outcomes after the visit, not misdiagnoses).  The AHRQ study then took this single death from a single study to establish a 0.2% (1/503) death rate due to ED diagnosis and multiplied it by the 130 million total annual ED visits to get the purported death numbers.  They went on to concoct arbitrary confidence intervals for this extrapolation:

“The rate of misdiagnosis-related deaths in the one high-quality, prospective study (0.2 percent, n=1 of 503) is 217-fold higher than the weighted mean from the three retrospective studies (0.0009 percent). Although the rate of 0.2 percent is based on just a single death (so is imprecise, with a wide 95% CI 0.005 to 1.1), the value is the best estimate from this study and matches data from other sources. However, the confidence interval from the Calder study alone is implausibly wide. Based on data from other sources, we have assigned a +/- 2-fold plausible range to the 0.2 percent estimate (0.1% to 0.4%).”

This is not good science.  For more, see: