The study is trying to determine if there is a statistically significant difference in the autism rate of at risk children due to vaccination. The methodology is not necessarily wrong but so many people overlook the simple implications of the test sample. The abstract states that there were 1,929 high risk kids and 134 of them (6.95%) got Autism with no statistical difference in the Autism rate between the 1,409 vaccinated children and the 520 non-vaccinated children.
At a 6.95% incident rate we would expect 98 vaccinated and 36 non-vaccinated high risk children to become autistic if there is no effect due to vaccination. If the non-vaccinated group had a much lower incidence rate than 6.95% or if the vaccinated group had a much higher incidence rate then we could conclude that vaccinations cause Autism. So the question is simple, How much higher/lower would the rates have to be to say that there is a statistically significant difference?
Since the sample size is so small, the non-vaccinated group incident rate would have to be 59% lower than 6.95% or drop to an incidence rate of 4.06% to be statistically significant at the 99% level of significance. The vaccinated group, which is relatively small but at least larger would have to increase by 25% to 8.70% to conclude that vaccinations cause Autism.
You see, statistics are your friend. Since vaccinations don't increase the rate of Autism by 25% in high risk children big pharma can conclude that vaccinations don't cause Autism. This study is a piece of crap and any idiot that has been using it to make a conclusion regarding the safety of vaccinations is just an imbecile.
85 - without checking your math, you are correct that with a small sample size there is a large margin to be statistically significant.
But the study found that the rate of autism was LOWER for vaccinated kids vs nonvaccinated kids, both in the small at-risk and large non-at-risk groups.
Since vaccinated kids have lower autism rates, the margin for statistical significance only stops the investgators from concluding that vaccines help prevent autism.