For accurate information on the efficiency of vaccines, consult the WHO website.
The only way to definitively prove vaccines are both effective and safe would be to take a population living in exactly the same geographic location, with very similar genetic traits, and vaccinate one half of the population while leaving the other half unvaccinated and examining the effects among the vaccinated population. The ethical problems with a study of this nature mean that it would never be permitted to take place. Until a study like this, it is impossible to determine if vaccines are safe or not.
Natural experiments have occurred. For instance, the 2019 Measles epidemic in Samoa: In 2018 two children in Samoa died after receiving a routine vaccine that had been incorrectly reconstituted using a muscle relaxant rather than sterile water. Parents understandably were concerned and the immunisation rates in Samoa subsequently plummeted to 31% compared to 99% in nearby Pacific islands. In 2019 the same measles outbreak that occurred internationally, occurred in Samoa. The combination of low immunisation rates and inadequate hospital facilities for such an outbreak led to over 80 children dying. A subsequent intensive immunisation catch up programme has seen immunisation rise to now offer herd immunity. Other countries - Great Britain, Sweden and Japan - all cut back the use of pertussis (whooping cough) vaccine because of fears about the vaccine. The effect of the dropped immunisation levels was dramatic and immediate. In Great Britain, a drop in pertussis vaccination in 1974 was followed by an epidemic of more than 100,000 cases of pertussis and 36 deaths by 1978. In Japan, around the same time, a drop in vaccination rates from 70% to 20%-40% led to a jump in pertussis from 393 cases and no deaths in 1974 to 13,000 cases and 41 deaths in 1979. In Sweden, the annual incidence rate of pertussis per 100,000 children of 0-6 years of age increased from 700 cases in 1981 to 3,200 in 1985. Comparisons between countries with a robust immunization programme and those without has already given the evidence of the benefits. Weighing the benefits against the harm of vaccination, vaccines provide a substantial reward by saving lives, reducing infection rates and contributing to the eradication of several dangerous diseases. Vaccinations are safe.
[P1] The only way to test if vaccines are safe would be to immunise half a population and leave another unvaccinated and see what the effects are. [P2] This is not ethical and will never happen. [P3] Therefore, we can never know.
Rejecting the premises
[Rejecting P3] We may not know with 100% certainty but we can conclude that they are "safe", relatively speaking.