I am looking at the http://www.nejm.org/doi/full/10.1056/NEJMoa021134 paper and don't understand how they made their conclusions.
According to the data in Table 1 they analyzed 440655 vaccinated children and 96648 unvaccinated children.
As of vaccinated childred 269 got Autism, 352 got other ASD, total 621, giving 6.1, 8.0 and 14.1 total cases per 10000 vaccinated children.
As of unvaccinated childred 47 got Autism, 70 got other ASD, total 117, giving 4.9, 7.2 and 12.1 total cases per 10000 unvaccinated children.
So, in conrast to their conslusion I can see vaccinated chilren got higher autism & ASD rate and the question is level of confidence.
Using http://www.quantpsy.org/chisq/chisq.htm calculator I calculate three p-values (Autism vs Other, ASD vs Other, Total vs Other) using two Conditions: Vaccinated and Unvaccinated and get this numbers:
Test | Chi-square | p-value | Autism vs Other | 2.079 | 0.14933798 | ASD vs Other | 0.561 | 0.45385761 | Total vs Other | 2.281 | 0.13096741 |
As far as I understand, this means that there is some, but low confidence ( p-value < 0.15 ) for the Autism and Total cases.
Also there is a second table, talking about person-years, total 2129864 years total, 482360 unvaccinated, 1647504 vaccinated.
For vaccinated it's 263 Autism cases and 345 other ASD cases, 608 total, giving 1.6 and 2.1, 3.7 total cases per 10000 person-years.
For unvaccinated it's 53 Autism cases and 77 other ASD cases, 130 total, giving 1.1 and 1.6, 2.7 total cases per 10000 person-years.
The difference is event more visible and here is Chi-square and p-value data (same calculator):
Test | Chi-square | p-value | Autism vs Other | 6.228 | 0.01257457 | ASD vs Other | 4.667 | 0.03074759 | Total vs Other | 12.215 | 0.00047407 |
So, here the confidence is strong enough for all 3 cases ( p < 0.05). For total case it's very strong ( p < 0.0005 ). Yet I am not sure if Chi-square analysis is applicable for person-years case.
And at the same time paper concludes that there is no dependency between the vaccination and Autism / ASD.
Am I missing something in the analysis?