An ongoing measles outbreak in Zimbabwe begs for the use of Bayes' rule, but first some background.
In September 2009, the first few cases of measles were discovered in Zimbabwe. The most recent update, data from mid-July, has 8,708 suspected cases and 517 deaths. In a world where a safe and cost-effective vaccine is available and in a country where National Immunization Days reached 92% coverage in the most susceptible population (children aged nine months to five years) in June 2009, how does an outbreak like this begin?
Initial data indicate that the measles cases all occurred in individuals who, unsurprisingly, were unvaccinated and - as significantly – that the vast majority of these were in children whose parents belong to particular Apostolic faith sects. Anecdotally, officials observe that these parents refuse immunization for their children, although finding direct data to support this claim is onerous.
In the World Health Organization Zimbabwe bulletin of 25 Oct 2009, a figure is presented that provides estimates of the probability of being in five different religious faiths if your child was not vaccinated during the 2009 N Immunization Days. The specifics are that in 8% of the sample the unvaccinated children's parents are Catholic, 13% Protestant, 23% Pentecostal, and 45% Apostolic, and 11% Other. It should be clear that these numbers depend implicitly on the percentages in the population that fall into each category. On one hand, if 50% of the population in Zimbabwe is Apostolic, then it is unsurprising that the Apostolic category also leads in unvaccinated children. On the other hand, if only 1% is Apostolic, then most likely these results are due to Apostolic parent's not vaccinating their children.
The method used to convert the previous percentages into the probability of not being vaccinated is known as Bayes' rule. In this case, we find the probability of not being vaccinated if your parents are members of a particular religious category by multiplying the probability of being in that category if your child is not vaccinated by the overall unvaccinated rate and divide by the percentage of the population that is in that particular category. Finding data on the percentage of the population in each religion in Zimbabwe is also hard, but reports from the U.S. Department of State suggest that around 75% of the population is
Debate is ongoing in Zimbabwe about whether to require vaccination for children. It would be helpful if good statistics were available for both the percentage of the population in each religious category and the probability of vaccinating your children if you are in a particular category. These statistics would help inform the public health debate about the best course of action for Zimbabwe's future. In the meantime, we can make use of the statistics we do have.