The good news is that the original data are available here - have fun 
Unfortunatly you can't remove asociation between vaccine inoculation and bad health so easily, perhaps not at all. For example here, if you have a bad health historial, hospitals were sending nurses to vaccinate you in your house. Everybody with bad health is vaccinated.
(Take note Hutch: you can escape from hospitals, but not from nurses

)
If there is more detailed information of individuals it's possible a better picture, but that will take time to process, and you can't expect to much anyway.
Lack of reliable information about some specific questions is fertile field for all kind of charlatans, just is that way. Old ladies, Val and Siekmanski have a lot of fun with speculations
