This wasn’t a subsample; it was the entire country. There was a numeric difference, no p value involved in reporting observed results - for an entire country over more than a decade.
Projecting to other places & time periods? Then a p value matters, as do other aspects of observational study design
Their analysis used adjusted hazard ratios and CIs to account for confounding factors like healthcare access or parental education, which can bias who receives vaccines. This isn't a simple comparison of one population vs. another without sampling.
BTW, when they used a stricter endpoint (2 autism diagnoses), the AHR was 0.99 (0.88–1.11). Table 3 looks at other sources of residual bias, even with a fully adjusted model. While p-values aren’t strictly needed here, the confidence intervals show the precision of estimates.
And there, across populations or times, the expectation (from this study and many, many others) is of no difference - ie that MMR vaccine has no impact on autism rates; on that we agree.
As mentioned, I am somewhat familiar with the literature on autism and we are totally aligned on this. I was simply trying to make sure that a non-expert reader didn't walk away with the impression that MMR vaccines might protect against autism, however slightly.
The slight non-significant reduction in autism is likely an artifact of confounding variables (as the more stringent endpoint seemed to show). In any case, it is no more than a hypothesis that would require substantial testing, likely in a(n) (unethical) logistically challenging randomized study.
I agree with you and was not trying to imply that it protected (I haven't seen this claim anywhere so wasn't too worried about leaving that impression); I do think the direction of the trend makes the posterior prob that there is opposite effect of the observed trend less likely, hence the mention.
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Projecting to other places & time periods? Then a p value matters, as do other aspects of observational study design