updates to the 'autism and vaccines' infographic

Every so often this infographic makes the rounds. Overall it's a good infographic (definitely better than anything I could come up with) but there's several parts that really irked me. So without any authorization or demand for it whatsoever I decided to make an updated version of it.

(image opens in a new window)

The following changes were made:

1. Removed text: "the science facts about"

I won't go into it here but I try to avoid using 'science' except in certain circumstances.

2. Added text: "updated Dec 24th, 2014"

Makes it clear it's not the original and adds a date to give people a point of reference.

3. Changed the portrait of Andrew Wakefield

As much as I like the original infographic I really didn't like most of the images and this one I could do something about.

4. Added text: "a study of 12 children"

Helps to put the later numbers in context.

5. Changed the image of the study

Initially changed to make room for the additional text but also changed it so it's clear the the "link" was dubious.

6. Changed text from "Lancet published a paper by Dr. Andrew Wakefield, a dramatic study that found a connection between autism and vaccines" to "Lancet published a paper by Dr. Andrew Wakefield, a study which made dramatic claims of a connection between autism and vaccines."

Being cautious about the way the information is portrayed to ensure it doesn't accidentally leave people with the idea that there was a link.

7. Changed text from "2005 A review of 31 studies covering more than 10,000,000 children also found no connection" to "2005 A review of 6 studies covering more than 1,100,000 children also found no connection"

This refers to the 2005 Cochrane review 'Vaccines for measles, mumps and rubella in children', numbers were corrected to reflect the part of the review concerned with autism.

Honestly I still think it's a bit dodgy including it at all instead of just the updated version but then it messes up the layout a bit too much: http://i.imgur.com/uCsXHqB.png

8. Changed text from "2012 A review of 27 cohort studies, 17 case control studies, 6 self-controlled case series studies, 5 time series trials, 2 ecological studies, 1 case cross-over trial covering over 14,700,000 children" to "2012 A review of 3 cohort studies, 3 case control studies, 1 self-controlled case series studies, 2 time series trials and 1 case-only study covering over 1,150,000 children"

Refers to the 2012 Cochrane review 'Vaccines for measles, mumps and rubella in children' which is an update to the 2005 review. Numbers were corrected to reflect the part of the review concerned with autism.

9. Changed text from "Recently an anti-vaccine..." to "In 2013 an anti-vaccine..."

Adding a specific year will help the infographic age better.

10. Changed text from "Although declared eradicated in 2000..." to "Although eliminated in the USA in 2000..."

This was downright misleading, especially in the context of the cases in the UK & France.

Eradicated means the disease has been wiped out whereas eliminated from a region means that the disease is no longer endemic to that region (i.e. it needs to be imported).

In 2000, measles was declared eliminated in the USA.

11. Changed text from "Before widespread vaccinations of babies" to "Before worldwide vaccinations of babies"

Just wanted to clarify that the figures are global.

12. Changed the pertussis cases image

The graph was bizarre to say the least with numbers given for only the 1960s, 1970s, 1980s, 2004 & 2012 which made it seem cherry picked.

The numbers also didn't seem to match up with the CDC figures (I think 1959 may have been added to the 1960s).

13. Changed text from "a new study concluded that vaccine refusals were largely to blame for a 2010 outbreak of whooping cough in California" to "A 2013 study conclude that vaccine refusals contributed to the 2010 outbreak of whooping cough in California."

Changing 'new' to '2013' helps the infographic age better.

The study states, "Our data suggest clustering of NMEs may have been 1 of several factors in the 2010 California pertussis resurgence." which is very different from saying non-medical exemptions are "largely to blame".

Nonsense: "Estimates suggest that 30% to 45% of all prescription drugs are nothing more than placebos."

According to Payam Saljoughian & Manouchehr Saljoughian, "Many believe that some of the most widely used drugs in modern medicine are completely inert, and estimates suggest that 30% to 45% of all prescription drugs are nothing more than placebos." Which is quite astounding and also quite baseless. For a start it doesn't even match up with their source:

Some estimates suggest that placebos comprise of 30-45 per cent of all prescriptions.

Prescription drugs vary in how often they're used so the percent of prescriptions is not the same as the percent of prescription drugs. Further it's possible to use an effective medication as a placebo (e.g. antibiotics for a viral infection).

Following the chain back further, it turns out that the lower-end of the figure comes from 1952 and the higher end of the estimate comes from 1906:

Dunlap, Henderson, and Inch (1952) analyzed over 17,000 prescriptions of physicians from representative areas in Great Britain for a one month period. Approximately one third were considered to be in the placebo category. The British Medical Journal (1952) editorialized that, "...a bottle of medicine is given as a placebo in about 40 per cent" of the patients seen in the general practice, a figure that is close to Cabot's (1906) estimate of 44 per cent of the prescriptions filled by Boston Bac Bay drug stores.

Sometimes following the source of the information really feels like witnessing a game of broken telephone.

a few thoughts on the anti-vaccine body count

The anti-vaccine body count is a website that keeps a tally of all of the vaccine preventable deaths that have occurred in the USA since mid-2007. I really appreciate the effort that's been put in setting up the site and maintaining it (it's done by a single person) but there are a few things I think I would do differently.

I'll just quickly note at this point I've written this post with only the body count in mind and I'm not sure how much applies to the cases.

Starting with something minor I think I'd probably call it the 'unvaccinated body count' rather than the 'anti-vaccine body count'. Anti-vaccine is a fairly nebulous term (e.g. should it apply to people not getting a flu shot?) and isn't something people self-identify as. By keeping to the broader 'unvaccinated' phrasing it avoids potential arguments as to what is and isn't an anti-vaxxer (e.g. should the influenza associated deaths be included in an "anti-vaccine" body count).

Secondly, an unnecessarily large number of sources are used for the tallies (which also creates a few minor inaccuracies as the figures used are preliminary). Take 2014 for example, on the anti-vaccine body count there are 31 reports listed to get the figures. It looks impressive. It's also completely unnecessary as you can get the cumulative total for the year from the final report (and for the five previous years as well). By listing only the necessary reports it would make the numbers easier to verify and thus make them stronger.

Thirdly, there's no real breakdown on the cause of death and for most of the reports listed on the source page it doesn't mention the cause (generally influenza-associated infant mortality). I think it'd be nice to have that information readily available (in a chart or a table).

Figure 1: The cause of deaths in the anti-vaccine body count

Finally, as a number of the deaths would still have occurred in the absence of unvaccinated people I think it's unfortunate that all vaccine preventable deaths were given and no attempt was made to refine the number. While I think it would be extremely difficult to do accurately I think the following formula could be used to work out the lower limit of the body count:

body count = VE×( (1-VC) / (1-VC)+VC×VE )

Where VE is 'vaccine effectiveness' and VC is 'vaccination coverage'. The formula doesn't take into account different mortality with the disease in vaccinated and unvaccinated people and it doesn't take into account the fact that a lot of vaccinated people who were exposed wouldn't have been had there been no unvaccinated population. I'm unsure if there's a way these things factors could be incorporated but until then the formula should provide a lower limit to the body count.

After writing this post I might set up a page on this blog for the 'unvaccinated body count' to be a compliment tally that can be used alongside the 'anti-vaccine body count'.

UPDATE: Put together some rough figures and made the unvaccinated body count.

Vaccine Effectiveness

Vaccine Effectiveness is the approximate measure of the percentage of cases that a vaccine prevents in an outbreak. It is calculated using the following formula:

VE = (ARU - ARV)/ARU [x100%]

Where VE is the vaccine effectiveness, ARU is the attack rate in the unvaccinated and ARV is the attack rate in the vaccinated. The attack rate is the proportion of the given population (unvaccinated or vaccinated) that are infected with the disease.

Figure 1: ARU 0.3, ARV 0.06

In Figure 1 it's easy to visualize how the formula works. The shaded area is the unvaccinated attack rate applied to the vaccinated population. The people within the shaded area would have been infected had there been no vaccinations. All of the healthy people in the grey area represents an infection that the vaccine prevented, this can be calculated using (ARU - ARV). Then to get the proportion of cases prevented as a proportion of the cases that would have occurred the full formula is used: (ARU - ARV)/ARU.

In the above example the ARU is 0.3 (3 out of 10) and the ARV is 0.06 (6 out of 100) so the proportion of cases prevented (ARU - ARV) is 0.3 - 0.06 = 0.24 which means the vaccine effectiveness is 0.24/0.3 = 0.8 or 80% (the vaccine prevented 24 out of 30 cases that would have occurred in an unvaccinated population).

Another thing to notice is that even with an effective vaccine, when there is a high vaccination rate it is expected that there will be more cases in the vaccinated population than the unvaccinated population. Only if the ARV was equal to the ARU would the vaccine be ineffective.

Herd Immunity Threshold

When reading an article about vaccines and vaccine preventable diseases it's not uncommon for there to be a statement in the article along the lines of, "With 90% of full immunisation needed for herd immunity..." or, "When the number of people vaccinated drops below 95%, a community loses herd immunity to highly contagious germs like pertussis..." What are these numbers and how are they determined?

The numbers are referring to the 'herd immunity threshold' which is the approximate proportion of the population that's needed to be immunised so that the infectious disease will die out  in that population and it is worked out with the following formula:

threshold = 1 - 1/R₀

The key to understanding this formula is the 'basic reproduction number' (R₀). The basic reproduction number is the average number of additional people that will be infected for each case in a population with no immunity.

Figure 1: A disease with an R₀ of 4

If a disease has a reproduction number greater than 1 then the disease will increase in numbers in the population whereas if the reproduction number is less than 1 then eventually the disease will die out in the population. To create a population in which a disease cannot persist then it is necessary to reduce the reproduction number to less than 1 (or thereabouts).

Figure 2: A disease with an effective reproductive number reduced to 1

So out of all the number of additional people that would be infected from a case (R₀), all of them except one needs to be immunised (R₀-1), or as a proportion this can be written as:

(R₀-1)/R₀

Which can be arranged to arrive at the herd immunity threshold formula:

=> R₀/R₀ - 1/R₀

=> 1 - 1/R₀

The final figure given is an approximate figure and doesn't take into account things like vaccine effectiveness or other public health efforts used to combat infectious diseases. Finally, herd immunity is not all or nothing and even if the vaccination rates aren't as high as the herd immunity threshold it's still possible for unvaccinated people to benefit from the cocooning effect of herd immunity. If you vaccinate you're not only protecting yourself, you're also helping to protect those who can't (or won't) be vaccinated.

Blood Groups and Population Genetics

In the ABO blood group system there are three alleles: A, B & O. The A and B alleles are codominant and the O alleles are recessive which means there are four possible phenotypes: A, B, AB & O.

Figure 1: All possible genotypes (orange) & their respective phenotypes (red)

As such the approximate proportion of the different phenotypes in the population will be as follows:

Blood Group A = a² + 2ao

Blood Group B = b² + 2bo

Blood Group AB = 2ab

Blood Group O = o²

Where 'a' is the proportion of a alleles in the population, 'b' is the proportion of b alleles in the population and 'o' is the proportion of o alleles in the population.

Knowing this we can now take the known phenotypes of a population and begin to work backwards and work out the proportions of the A, B & O alleles in that population.

According to the Irish Blood Transfusion Service the phenotype distribution is O 55%, A 31%, B 11% & AB 3%, which gives us the following equations:

o² = 0.55

a² + 2ao = 0.31

b² + 2bo = 0.11

2ab = 0.03

As such if o² is 0.55 then we can take the square root of 0.55 to determine that the proportion of o alleles in the population is approximately 74% and we can now substitute that value into the rest of the formulas:

o = 0.74

a² + 2a(0.74) = 0.31
=>a² + 1.48a = 0.31

b² + 2b(0.74) = 0.11
=>b² + 1.48b = 0.11

2ab = 0.03

We can then complete the square for the A & B phenotypes to give us:

o = 0.74

(a + 0.74)² - 0.55 = 0.31
=>(a + 0.74)² = 0.86
=>a + 0.74 = 0.93
=>a = 0.19

(b + 0.74)² - 0.55 = 0.11
=>(b + 0.74)² = 0.66

=>b + 0.74 = 0.81

=>b = 0.07

2ab = 0.03

Now we know the proportion of a alleles in the population is approximately 19% and the proportion of b alleles in the population is approximately 7%. If we add all the proportions up (74%, 19% and 7%) we arrive at 100% which is probably pretty lucky considering how imprecise the data is. We can also test this by substituting the values into the formula for the AB phenotype (2 x 0.19 x 0.07) and we also arrive at the same figure (AB phenotype = 3%).

What makes this really wonderful is that the ideas used to determine the formulas and the data that was collected were not connected. The formulas were based on a genetic model and not on the data, the proportions of blood types were counted and not worked out mathematically. Because of this, the proportion of blood types in the population could have been such that the mathematics wouldn't have worked (e.g. A 25%, B 25%, AB 25%, O 25%), the mathematics did work using the data gives credence to those ideas the mathematics was based on.