Thanks for linking to an actual peer reviewed study. You should immediately see, however, that it was later corrected, and should check out that correction.

In that correction, you'll see that the study was done by two people: one person who belongs to an anti-vaccine group, and one person who used to. The funding for the study was also provided by an anti-vaccine group. And remember: they somehow managed to "forget" to reveal all of this information and these massive conflicts of interest initially, and needed to correct them. That's not how science works: if you're going into a "study" hiding your affiliations and looking to prove a political point for the people who paid you for the study, it's not science, it's just garbage.

With that said, authors being disingenuous, blatantly biased, or even outright liars doesn't entirely discredit statistics or research, just their interpretations. In this example, though, it's incredibly clear how they rigged their numbers: they chose to look at only the United States and countries with a lower IMR than it. The United States is infamous as the only country in the developed world without universal health care: every single other country that was included in the study has free universal health care: all 33. The US also requires a large number of vaccinations, for basic public health reasons, and because the majority of them are developed in the the country. I am very sure that a closer look at the correlation in the authors' study that included the next couple of dozen countries on the list of IMR would make the authors' conclusion fall apart almost instantly.