The ideal way to protect the public from hazardous medical devices, the Food and Drug Administration says, is a brand-specific identification number on devices like implanted heart defibrillators and artificial hips.

If one goes haywire, the thinking goes, doctors can quickly tap large insurance databases to find out whether the malfunction was rare—or part of a broader public-health threat. Further implants would be stopped before the faulty device is widely used.

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