I'm looking to vaccinate my son with Hexacima in less than two months. I've been going through studies looking at the long term efficacy and/or adverse effects for EU infant vaccines (Hexacima and Infanrix Hexa in particular) and, as expected, the number of adverse effects reported is quite low. What I haven't been able to find, however, are long term studies looking at more subjective attributes like intelligence, attention, personality, etc. How are these more subjective attributes studied? Where can I find these studies?
The main problem you are going to run into, if you are limiting yourself to that particular multivalent vaccine formulation, is that it hasn't been on the market long enough (2013) for something specific to that 6-in-1 formulation. However, note that in the US at least, all vaccine preparations are continually monitored for safety (I believe in the EU as well, I just didn't find a direct source on that).
However, there have been substantial studies on the effects of the of the individual components, and when they have been given at the same time, just not out of the same syringe. This is a very common questions pediatricians face, and should be quite able to walk you through your concerns. I highly recommend going over the CDC's "Multiple Vaccines and the Immune System" which is written for the public.
Subjective attributes are monitored from parent feedback, and large meta-studies, specifically retrospective cohort studies are common. A good study on the subject looks at DTP or DT vaccination and the following behavioral issues:
general developmental disorders, language or speech delay, tics, attention-deficit disorder, autism, unspecified developmental delays, behavior problems, encopresis, and enuresis
Only found that may have been a weak correlation with tics, and that observation was likely an artifact of how the group was made.
The biggest concern you should have coming into vaccinating your children is if the child is immunocompromised (HIV infection, genetic disorder, etc) or if the biological parents have relevant allergies, particularly to previous vaccines or heavy metals (normally you don't make it to adulthood in the West without finding out).