Take a look to see if there are any corresponding changes in rate of autism? Here's a nice chance to run a natural experiment--the non-vaccinated become the test group...
There wasn't.
This would have became apparent relatively quickly; this measles outbreak may be 15 years after the fact, but the autism rates would have been affected within the first few years if there was anything in this. They weren't.
The research that linked autism with this vaccination was soundly debunked within a few years of being released. The original paper was fully retracted in 2004, and the researcher found guilty of misconduct and fraud.
The full sorry story is documented on Wikipedia and many other places.
The really sad part is that even a decade after the story was retracted, there are still some people who are convinced that they shouldn't immunise their kids.
The trouble is that we live in a world where these diseases don't scare us any more because we don't see them. They ought to. If you want to know what happens to populations without immunity that are exposed to measles, try reading up on what happened when the Conquistadors introduced it to South America.