See https://arxiv.org/abs/1809.02201 for the main paper from the Census.
If you had access to anonymised health data from my nation, for example, picking me personally out of the records would be extremely trivial, using just two data points:
+ I have an illness that only 1% of people have.
+ I lost my spleen whilst I was in primary school.
Both of those things are actually a matter of public record, thanks to being mentioned in various local newspapers, so it's reasonable to assume someone somewhere has that data.
I believe the general consensus on health data is that you have the age a person was at an incident, and the nature of an incident, you only need to have two or three incidents in your database to de-anonymise their records.
The only way to combat it is to not provide the detail required for the analysis that is exactly what the above organisations wish to do. No profiles, no fine-grained demographics.
And yet, people with rarer illnesses or events than mine will still stand out, so you also need to eliminate them from the dataset, even though they may well be the ones who could benefit most from this sort of widescale analysis.
For example, if they're tracking all instances of various ailments seen by some doctor in some time period. Suppose you are the only person of a given age and gender with that ailment, so that bucket would one entry for anonymous you. Fine. But then suppose the aggregating party begins to buy and correlate against credit card and location records that place you at the doctor's office in that time frame, bingo, they have a match to tie all three data.
I'm not yet convinced it can be done in a way that can't trivially be reversed by anyone combining it with other datasets.
And if it can't be anonymised, then it probably shouldn't be saleable.