I know this is the type of study many here have been waiting for and asking for, though not perfect since its looking back but better than a lot of what we have:
In their study, the authors compare the occurrence of infections and allergies in vaccinated and unvaccinated children and adolescents. These include bronchitis, eczema, colds, and gastrointestinal infections.
The evaluation showed that unvaccinated children and adolescents differ from their vaccinated peers merely in terms of the frequency of vaccine preventable diseases. These include pertussis, mumps, or measles. As expected, the risk of contracting these diseases is substantially lower in vaccinated children and adolescents.
the paper is here with the methods outlines: