Here is a very quick and over simplified explanation about why some of the cases of measles are fully vaccinated (epidemiologists look away!).
The vaccine is not 100% protective. One dose is around 92% and two doses around 98%. Generally, things look like this pie chart, assuming the vaccine is potent and the patients relatively healthy. Most cases occur in the unvaccinated with a few in the vaccinated.
A common pitfall is to look at the number of cases by vaccine status, for example when I looked today at the recent measles report it shows that among 10-19-year-olds 17 cases are fully vaccinated and 96 are not vaccinated. A natural inclination is to go OMG! the vaccine is only 85% protective. The problem with doing this is that most people are vaccinated, you need the denominator.
The correct way to do it is to consider the attack rate among the vaccinated and the attack rate in the unvaccinated. The attack rate is the proportion of cases in the population at risk divided by the number of persons in that population. Of course, I have totally over-simplified things here, if I was going to do this in a robust manner it would be through a cohort study using data-linkage and would adjust for confounders, a bit like we did for our gonorrhea cohort study, which has quite cool methodology. Also, the formula for effectiveness uses odds ratios, but I only wish to illustrate a point here so please bear with my over simplistic explanation.
The formula for vaccine efficacy is (ARU-ARV)/ARU x 100%. ARU means attack rate in unvaccinated and ARV means attack rate in vaccinated.
We need some additional information for our calculation other than the vaccine status of the cases. We need to know how many of our population are vaccinated and how many are unvaccinated. For this 10-19-year age group, based of the number of individuals born in the years 2000-2009 I get around 480,000 vaccinated and around 108,000 unvaccinated (remember this is crude!).
Plugging the information into the basic formula I get around 96%. There are many more unknowns for this age group, for example for 75 cases the vaccine status was unknown. However, if I perform the same exercise for the 5-9-year old’s (where vaccine status is known for all but 4 cases), I get 97%.
Another exercise is to imagine that 98 in every 100 people at the raging party in a downstairs nightclub are vaccinated and measles is invited. The two unvaccinated party goers get measles. Also, two or three of the fully vaccinated people get measles. OMG! half the cases were vaccinated.
Hopefully you can see that if one wants to avoid measles it is much better to be in the vaccinated group! Also, remember that most people are in this vaccinated group. I have likely underestimated this in my assumptions.