A real meta-analysis of Africa and India
RFK is almost certainly describing a 2016 meta-analysis funded by the Danish government and showing "that DTP was associated with increased child mortality in rural Guinea-Bissau", with even higher death rates in Senegal, and similar death rates in India and Bangladesh. Some other Guinea-Bissau studies showed that unvaccinated children had a higher death rate, but they were in a minority.
The most extreme study, named as Guinea-Bissau III, showed a likely ratio of 7 times more deaths for vaccinated girls, with a 95% confidence ratio between 1.5 and 33. The meta-estimate of all studies was 2.5 times as many deaths. Kennedy is exaggerating with his claim of "10 times", but he's not making up the meta-analysis.
"Nonspecific effects"
Sometimes vaccines decrease or increase mortality in diseases unrelated to the one for which they were prepared. The reason for this is unknown:
We still need to find out exactly how the vaccines induce nonspecific effects and why the live vaccines: BCG, measles vaccine, and Vaccinia are associated with benefits, whereas the opposite is seen for DTP. It is also imperative to understand why these effects are only seen as long as a vaccine is the most recent vaccine; the effect can be reversed with a new vaccine. Also, we need to understand why these effects seem more pronounced in females. The most striking observation so far is the parallel between the epidemiological observation that BCG given to LBW neonates reduces neonatal mortality from all causes by 48%. (Benn et al. 2013)
As you can see, the most common "side effect" of vaccines is an unexpected boost to the immune system. DTP may have unexpected, deadly side effects when given to girls at specific early stages. This has nothing to do with with the diseases being vaccinated against.
Danish study recommended continuing DTP
The authors of the Danish study did not suggest discontinuing DTP, because the side effects in girls are appearing in the context of societies which are now able to protect infants against the DTP viruses: diphtheria, tetanus, and pertussis. For instance, pertussis (whooping cough) is a terrifying and deadly disease. This is why DTP is so widely administered in the first place.
Instead, they wrote:
It is now imperative to vigorously examine the link between DTP and susceptibility to infection. Is a new vaccine needed, can the damage be minimized by co-administering DTP with other vaccines or by providing a live vaccine shortly after DTP?
In fact, DTP (DTP3, DTwP) is no longer common in the West; DTaP is administered instead.
Consensus against the WHO?
The Danish meta-analysis contradicts an earlier meta-analysis was done by the WHO, and the Danish article critiques the WHO's methodology. A second meta-analysis published in BMJ confirmed the Danish results. While it said that the studies analyzed were at risk of bias, it also acknowledged that the high death rate was a cause for concern.
However, more recent studies have had contradictory results.
New contradictory studies
A 2022 study found that DTP decreased mortality in girls, and accused prior studies of being full of methodological and statistical errors.
Another 2022 study said that DTP only increased mortality when it was administered long after another vaccine called BCG; when BCG and DTP were administered jointly, mortality decreased. Furthermore, the authors pointed out that the Danish and BMJ study draw on data from the 1980s through 2000s. Their own data, as well as the data of the other 2022 study, is based on vaccinations administered after 2010, when the negative nonspecific effects of DTP became widely known to doctors. They suggest that African and Asian vaccination programs have already changed the way they handle DTP.
There has not yet been a meta-analysis of these studies, but it would be nice for RFK to get on top of these new scientific developments.