Hashing identity solves this. All of the data can be anonymized while retaining the linkage of measurements and procedures performed on the same subject.

e.g. We don't know who this guy is, but we do know that every measurement of him was linked to this same enormous random string.

Only if your data is very limited in depth.

When doing data linking I can usually identify one person in a dataset of almost 1 million from three innocent seeming pieces of data. Pseudonimisation doesn't really work.