I have a database storing various information about fictional people. There is a table person with general information, such as name, adress etc and some more specific table
Depends on your SQL engine. Newer SQL systems that have reasonable query optimizers will most likely rewrite both IN and JOIN queries to the same plan. Typically, a sub-query (IN Clause) is rewritten using a join.
In simple SQL engines that may not have great query optimizers, the join should be faster because they may run sub-queries into a temporary in-memory table before running the outer query.
In some SQL engines that have limited memory footprint, however, the sub-query may be faster because it doesn't require joining -- which produces more data.
I think I understand what you're trying to do. There is more than one way to skin a cat, but may I suggest splitting your query into two separate queries, and then replacing the complicated WHERE clause with a couple inner joins? So, something like this:
/* Find connections based on health care */
SELECT p2.p_id as id, p2.fname, p2.lname, p2.image
FROM person p
JOIN health_case hc on hc.patient = p.p_id
JOIN health_case hc2 on hc2.doctor = hc.doctor and hc2.healthcenter = hc.healthcenter and hc.start <= hc2.end and hc.end >= hc2.start and hc2.patient <> hc.patient
JOIN person p2 on p2.p_id = hc2.patient and p2.p_id <> p.p_id
WHERE p.p_id = :id
Then, create a separate query to get connections based on education:
/* Find connections based on education */
SELECT p2.p_id as id, p2.fname, p2.lname, p2.image
FROM person p
JOIN education e on e.pupil = p.p_id
JOIN education e2 on e2.school = e.school and e2.start <= e.end AND e2.end >= e.start and e.pupil <> e2.pupil
JOIN person p2 on p2.p_id = e2.pupil and p2.p_id <> p.p_id
WHERE p.p_id = :id
If you really want the data results to be combined, you can use UNION
since both queries return the same columns from the person table.