I just found a blog called Photon In The Darkness, and plan to add it to my feed. The author has some great articles up, and I think that there will be plenty more. I would like to highlight one of them as an inaugural article from there. This is one of those cases where, as repeatedly stated, humans are very poor at assessing risk.

Let’s run the vaccine risk/benefit numbers!

March 12th, 2010

While reading another ‘blog, I found - in the comments - one of the worst examples of “bad epidemiology” I have ever seen. I won’t embarrass the commenter by name or by quoting, but the gist of their “argument” was that (in the US) the risk of vaccination exceeds the risk of the vaccine-preventable disease.

I think we’ve all heard that before.

There were many problems with their math, not the least of which was being too lazy to look up the actual numbers, but I realized that this was the tip of a much larger iceberg of innumeracy, especially as it pertains to understanding prevalence and risk.

So, to begin at the beginning, let us start with fractions.

Most of the time, risk or prevalence is expressed as a fraction, although it may not always look like a fraction (e.g. 1 in 100 is the same as the fraction 1/100). And - harkening back to our elementary school days - the two components of a fraction are the numerator (the top number) and the denominator (bottom number).

I bring up these apparently irrelevant mathematical issues because, in the world of risk and prevalence, there are two major types of errors: numerator errors and denominator errors (although, sometimes, there are errors of both).

In the example I mentioned above (the ‘blog comment), the risk of contracting a certain vaccine-preventable disease was calculated (wrongly, I must add) by dividing the number of people in the US who contracted that disease in a year by the population of the US. This was then stated - indirectly - to be the risk of an unvaccinated person contracting the disease.

Perhaps you’ve already noticed the error - it’s a denominator error. Since most people in the US are already immune to this disease (mostly by vaccination), the proper denominator would have been the number of unvaccinated people in the US. Let’s see how this changes the numbers:

If we use measles as an example, there were 140 cases of measles reported in 2008 (still compiling and verifying 2009 reports). At the end of 2008, according to the US Census Bureau, there were 300,459,786 people in the US. If we use the incorrect method from the example, that would give a “risk” of contracting measles of 0.47 per million per year (1 in 2,146,141 per year).

That seems a pretty low risk, doesn’t it? It’s a bit higher than your “risk” of winning the Powerball lottery, but still quite low.

But is it accurate? [Hint: No]

The correct way to calculate your risk of contracting measles is to divide the number of reported cases in the US by the number of vulnerable people in the US. By “vulnerable”, I mean those people who haven’t been vaccinated and haven’t had measles. That is a bit harder number to find.

The CDC’s NIS shows that, in 2008, 92.1% of children ages 19-35 months had received at least one MMR vaccination. Going back as far as 1994, that number seems fairly steady - about 90 - 92%. By the age of school entry, that percentage (in the 2007 - 2008 school year) was up to 94.9%. Even if we assume that this percentage doesn’t change, it would mean that - at most - 5% of the population is vulnerable to measles.

But even that isn’t an accurate number, because people born before the measles vaccine was available (1963) - and even the years immediately after the vaccine was introduced - would have gotten the disease if they weren’t vaccinated (it is highly contagious).

By 1968, the incidence of measles had dropped low enough to assume that anyone born after 1968 who was not vaccinated is not immune. So, that means that 5% of the US population age 41 or less is vulnerable to measles. This estimate compares with the value found by Hutchins et al (2004) for measles immunity in 1999, which supports the estimate.

According to the US Census Bureau, there are about 172 million people in the US age 41 years or less, so that gives us - at most - 8.6 million vulnerable people. Now the risk of contracting measles is 140 divided by 8.6 million or 16.3 per million per year (1 in 61,428).

After calculating the risk of contracting measles, we need to calculate the risk of death or serious complications. Measles has a case-fatality rate of 2 per thousand, so the risk of contracting measles and dying of it is about 0.03 per million per year - in the current situation, where 95% of the population is immune.

Other serious complications of measles include pneumonia (about 6% of cases) and encephalitis (1 per 1000 cases). Adding these to the risk of dying brings the total risk of serious complications to 0.8 per million per year. If we exclude pneumonia as a “serious” complication, the combined risk of contracting measles and having a permanent, life-altering (or life-ending) complication is 0.05 per million per year.

The risk of serious complications (i.e. death or permanent disability) from the MMR vaccine (discounting the as-yet-undemonstrated “autism connection”) is less than 1 per ten million doses (1 per million allergic reaction, less than 10% of which are “life threatening” = less than 1 per ten million), which (because the recommendation is two doses) works out to less than 0.2 per million per lifetime. With an average lifespan of 75 years, that works out to less than 0.003 per million per year, so the risk from the disease is over ten times greater than the risk of the vaccine even with 95% of the population immune.

Oh, and by the way - the MMR vaccine protects against three diseases, not just measles. We’ll just ignore that for right now.

And even this approximation doesn’t show the true risk of forgoing just the measles vaccine (let alone the MMR) because we haven’t considered how having a large immune population prevents spreading and how that has limited the number of measles cases reported.

Measles is transmitted from person-to-person, a single infection provides life-long immunity and it has no non-human reservoir and no known long-term carrier or dormant state. In this respect, it is similar to smallpox, polio, mumps, rubella, and many other vaccine-preventable diseases. If it is not transmitted, the measles virus “dies out”. It doesn’t “hang out” in the environment. That is why measles could be eradicated, just as smallpox was.

Currently (since 2000), measles is not endemic in the US, largely because there aren’t enough susceptible (non-immune) people in close enough contact to keep the virus going. Measles in the US is an imported disease that, until 2008, was rarely transmitted beyond the person importing it and any under-age (i.e. less than 2 years old) or immune-compromised people they came in contact with.

Starting in about 2008, the percentage of immune people in the US had slipped far enough that imported cases were able to spread locally in pockets of non-immune people. The August 22, 2008 edition of Morbidity and Mortality Weekly Report (MMWR) details two outbreaks of measles that occured in the US that year. In both cases, the outbreaks occured within groups that did not vaccinate for religious or philosophical reasons and were home-schooled.

This latter point is worth noting - even though these children did not attend a public or private school, they still contracted measles from one another.

Here is a telling statement from the MMWR report:

The number of measles cases reported during January 1–July 31, 2008, is the highest year-to-date since 1996. This increase was not the result of a greater number of imported cases, but was the result of greater viral transmission after importation into the United States, leading to a greater number of importation-associated cases. These importation-associated cases have occurred largely among school-aged children who were eligible for vaccination but whose parents chose not to have them vaccinated. [emphasis added]

As the percentage of non-immune people in the country rises, imported measles cases will spread to more people, further raising the risk of infection to non-immune people and increasing the already large benefit to risk ratio of vaccines.

What this shows is that those people who choose to not vaccinate should - at the least - take precautions against associating with other people who don’t vaccinate. This would help reduce their risk of infection to the levels I calculated above.

Perhaps they should wear some sort of lapel pin, similar to what many fraternal organisations (e.g. Masons, Rotarians, etc.) have. Except, of course, that instead of stepping forward and embracing when they see a fellow member (with or without secret handshake), they should immediately turn about and walk briskly in opposite directions, to avoid transmitting vaccine-preventable diseases.

As the events of 2008 showed us, there will not be a gradual increase in measles spread as vaccine coverage declines - there will most likely be an abrupt increase as the percentage of non-immune people (and their proximity to one another) crosses a critical threshold.

And it is important to note that non-immune people are not just the children of parents who choose not to have them vaccinated. They include children too young to be vaccinated and people who are immune-suppressed due to disease, cancer or genetic disorders. They include the elderly, whose immune systems are weaker, and those people who - for one reason or another - did not develop an adequate immune response to vaccination.

Those who choose to not vaccinate and think they are letting others take the risks for them are fooling themselves; they are taking the greater risk - even now.

Prometheus

Non-hyperlinked References:

Hutchins SS, Bellini WJ, Coronado V, et al. Population immunity to measles in the United States, 1999. J. Infec. Dis.. 2004; 189(Suppl 1):S91–7