The removal of any individually identifiable data that may allow someone to connect the data in question with a specific person. 

The Office of Civil Rights gives this clarification:

There are no restrictions on the use or disclosure of de-identified health information. De-identified health information neither identifies nor provides a reasonable basis to identify an individual. There are two ways to de-identify information; either: 

a formal determination by a qualified statistician; or

the removal of specified identifiers of the individual and of the individual’s relatives, household members, and employers is required, and is adequate only if the covered entity has no actual knowledge that the remaining information could be used to identify the individual

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