Please note the difference between 'causal' and 'casual'. See a dictionary if required. Demonstrating causality might be difficult because there is limited information about the vaccinated population. Perhaps one can contend that the vaccinated population is equivalent to the general population with the exception of being known to have received the vaccine. From there one would need to compare the incidence rate of each of the diseases listed for both populations and identify any trends that are uncovered.

Please note the difference between 'causal' and 'casual'. See a dictionary if required.