Measles arithmetic

I’d been worrying about this, so it’s an excuse to do some arithmetic in a news setting.

Hannah Martin at Stuff has a story about the current measles outbreak

Of the 516 cases across the country, 299 had not been vaccinated at all.

A further 154 people who contracted measles this year did not know their vaccination status, ESR data showed.

I thought that implied a surprisingly high number of cases in vaccinated people.  Here’s the ESR report. Let’s compare fully-vaccinated and unvaccinated people, and restrict to those over 4 where ‘fully vaccinated’ means two doses of vaccine, not just ‘on schedule so far’.

There were 30 cases in fully vaccinated people, and about 150 in unvaccinated people.  What sort of ratio would we expect?  Roughly 90% of people have been vaccinated, so if the vaccine had no effect and exposure was uncorrelated with vaccination we’d be expecting about a 10:1 ratio in favour of vaccinated cases. We get a 1:5 ratio the other way.  This very crude comparison suggests about a 50-fold reduction in risk from full vaccination, which is about what’s expected.

It’s a bit more complicated than that. Firstly, the vaccination coverage figures don’t count immigrants.  People who immigrated as kids from somewhere that needs a visa would typically have been vaccinated.  It’s less clear for adults — I had one dose of measles vaccine as a baby  and one when I started my PhD [edit: and another one when I applied for US residency], but no-one asked when I moved here. If immigrants are less likely to be vaccinated, the 10:1 population ratio is smaller and we’d expect more unvaccinated cases.

Second, people who aren’t vaccinated are more likely to be exposed to measles, because of the way vaccination is distributed in the population.  That’s true both for ‘vaccine hesistant’ groups and (as Kirsty Johnston and Chris Knox report) because of poverty and access limitations. If you aren’t vaccinated, it’s more likely that your friends and neighbours aren’t.  Again, this would give us more unvaccinated cases.

Putting these together, the proportion of unvaccinated cases might be a bit lower than we might expect, but not seriously lower.  If there is a discrepancy, it could be due to trusting self-report of vaccination status — adults who know they got all the vaccines that were on offer as kids might well assume they were fully vaccinated against measles if they didn’t have the paperwork to check.

If you’ve only had one dose of the measles vaccine, or if you aren’t sure, you need another one.  Check with your doctor about the current recommendations — and if they’re short of vaccine now, make a note to check again in a few months.  We eradicated the ancestor of measles in 2011, the cattle disease rinderpest, but we’re not close to eradicating measles.