Zero connection? Really?
A child who never catches measles because he/she was vaccinated is not going to die from measles. A child who is unvaccinated and catches measles has about a 1 in 500 chance of dying, and if they don't die immediately, measles can reemerge several years later and cause a fatal encephalitis in about 1 out of 1,000 survivors. In addition, measles can destroy the immune system, making the affected child susceptible to every disease, even if he/she has been vaccinated against that disease.
And measles is just one infection that killed children. There were also polio, influenza, chicken pox, streptococcus infections, diphtheria, tetanus (I probably missed a few) that also killed children.
There is a direct correlation between the number of vaccines and the decreased childhood death rate. And in this case, correlation actually does relate to causation, since there is a mechanism tying the cause (vaccination) to the effect (increased childhood survival).
I saw a grave once, of a two year old who died in the 1800s. It had this inscription: "Maggie, darling, you have left us. And your troubles are at rest. No one knew you but to love you. But God loved you the best." I'll never know which disease killed little Maggie, but I've never been able to look past the pain of these parents who lost their little girl. And these kinds of losses were common in the 1800s. Better sanitation had only a limited effect. Preventing diseases through vaccination was a much larger factor in the decrease of child deaths.
Bwahaha. You again.
There is a long list of childhood vaccines these days.
Most of them exist only to enrich big pharma and doctors—with highly debatable health benefits.