Tuesday, August 11, 2009

Herd Immunity and Risk Estimation for vaccine advocacy

Well, I have a friend who seems to be skeptical of the benefits of vaccination and how they outweigh the risks. He's not an autism advocate, but more what some antivax campaigners refer to as "pro-choice". He thinks it's up to the parents to decide whether they want their children to be vaccinated.

I had a discussion with him about vaccines and most of my arguments started out as the ones we hear all the time - children die because they, or other children, aren't vaccinated. Really, that should be enough, but he wanted to hear about the merits of vaccines for their own sake, without the horror stories of 4 week old babies dying. So I've tried to summarize our discussion in blog post form, with some added statistics thanks to the power of the internets.

Here are two reasons I think can be powerful tools to demonstrate the awesomeness of vaccination. The first, you've seen before. The second, I haven't seen before, though maybe you have.

Altruism (or, the herd immunity)
There are people out there who can't be vaccinated, as well as the vaccines themselves having an efficacy of 85-95%1, which means that there are still people who can get these diseases even with perfect level of vaccination. (The people who can't be vaccinated generally suffer from an immune disorder, certain types of cancer, and can include organ transplant recipients.)

However, diseases can still be eradicated by vaccinating enough people so that it can't find someone new to infect too easily. It's believed that most diseases have a threshold - a minimum percentage of people who will need to be vaccinated in order to protect the community at large. According to Wikipedia, at the low end of mumps this is 75%, whilst at the high end of whooping cough and measles it is 94%.2 The most often quoted figure is 95%.

So, by vaccinating your child, you are contributing to the herd immunity in your community. This is a good thing - as much as I don't want to bring up the "kids die, and if you vaccinate them, they won't" angle in this post, well, it's true.

Value for money (it's 50% off!)
Vaccines are expensive - in Australia, a dose of a vaccine generally goes for around $40-$150 depending on the dose, with the doctor's appointment costing maybe another $20-60 after medicare. The vaccine price, keep in mind, is if it isn't subsidised by the government. We're fortunate in that a great many childhood vaccinations are subsidised.3 Of course, you'll still have to pay for the GP visit.

There are 9 lots of vaccines listed before a child is 6; most schools will vaccinate children for free after this age, using the vaccines from the government list. So, let's assume a more expensive doctor with no private health cover - you might find yourself paying $50 for their services per vaccine, leading to a rather hefty $450 for these, spread over 4 years.

Imagine your child gets sick with one of these vaccine preventable diseases. It doesn't have to be something scary like polio or whooping cough - even chicken pox isn't much fun (and take it from someone who somehow managed to catch it twice - the second time at age eighteen). Take into account a 1 in 100,000 chance of dying from chicken pox, and use a little trick for risk estimation I've learned in my software management course.

Risk can be defined as "severity multiplied by probability". That is, if you have a 10% chance of losing 10 days in your software project, you are risking 1 day in total. That is, 1 day is what you can "afford" to add to your project in order to mitigate the effects losing 10 days would have on your time budget.

Take it to the chickenpox example. We know the probability - 0.001% - and the amount you are being asked to spend in order to mitigate this risk - $50, for the visit to the doctor for just the chickenpox vaccine.4 With this, we can work out how 'severe' your child's death would have to be for the $50 to be worth spending. You do the numbers - (50/(1/100000)) - and you have a value of your child's life of $5 million, at least with this metric.

Of course, most people would say their child's life is a priceless miracle, but I have heard some engineering companies will put a price of $10 million on preventing a death in construction. Surely you value your child's life more than they do?

So, by spending $50 on a vaccine, you're getting good value for money - $10 million worth of protection for what you'd expect to pay for $5 million dollars. And that's if you value your child's life the same amount risk analysts value the lives of people they've never met.

NB: This may not be as well-researched as I would like. I'm not a doctor, I have no medical training.

[1] http://www.cdc.gov/vaccines/vac-gen/6mishome.htm
[2] http://en.wikipedia.org/wiki/Herd_immunity
[3] http://www.immunise.health.gov.au/internet/immunise/publishing.nsf/Content/nips2
[4] If you want to say "why didn't you put the $450 in the equation instead of the $50", the answer is because each of those 8 other vaccines prevent diseases that are far more dangerous than chickenpox, so it'd make the value of a child's life even less.

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