A custodian has been asked to release counts of people with a particular disease. For example, in the year 2008 4 people had that particular disease in Ontario. Since the count is less than five, is there a re-identification risk in disclosing this information ? To make the example concrete, let's say it is a rare disease, like botulism. Note that the custodian has not broken down the numbers by age group, gender, or other demographic - these are simple counts.
When analyzing a situation like that we have to: (a) determine what are the plausible intruder scenarios, (b) decide if the intruder will identify an individual, and (c) whether such an identification would allow the intruder to discover something new about the patient. Based on such an analysis one can determine whether a plausible re-identification risk exists.
To make the intruder scenario concrete, let's assume that the intruder is Bob and he is trying to re-identify Alice. The only way that Bob would know that Alice is in the database is if he already knew that she had botulism. Therefore, Bob would not gain any additional information by knowing that she is one of these four cases.
In such a situation, disclosing counts, even if they are for rare diseases and if the counts are below 5, does not necessarily represent a plausible disclosure risk.
If we extend the example and say that the geography is not the whole of Ontario but a small town, and that everyone in town knew that a certain four people fell ill after eating at a restaurant because their names were posted in the local newspaper. But no one knew what was wrong with them. Then if, say, a public health agency reports that four people had botulism in that town, then that would be problematic. The reason is that an intruder only needs to know that Alice was one of the people affected by a food borne illness at that restaurant, and the disclosed number lets the intruder find out something new about Alice - that she has botulism.
Therefore, the disclosure of small counts (i.e., less than 5) does not necessarily indicate a disclosure risk. But, as the above example illustrates, the specifics of the case may change that general conclusion.
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