When the real world is more rational than the model

February 1, 2011 § Leave a comment

Those of you who stop by regularly have probably noticed that I rarely write about papers that I don’t think are particularly good.  This may be partly a lingering result of early training (“If you can’t say anything nice, don’t say anything at all”), but is mostly because better papers are more interesting to write about.  But a recent paper caught my eye because of the discrepancy between its title — Erratic Flu Vaccination Emerges From Short-Sighted Behavior in Contact Networks — and its actual finding, which might have been summarized as Erratic Flu Vaccination Would Emerge From Short-Sighted Behavior Under Certain Assumptions About The Way People Understand Risk But In Fact This Doesn’t Reflect Real-World Data So Something Else Must Be Going On.

Let’s face it, this is not an area I know much about: my interest is far more personal than professional.  I’m sure this paper makes a perfectly reasonable contribution to its field. And I’m sure that my alternative title would have been frowned upon by the journal, so it’s not entirely the authors’ fault that I found their title misleading. Nevertheless, having been fooled into reading the paper, I found myself disagreeing with the underlying assumptions enough to want to tell you about it and see what you think.  Modeling is all about forcing you to be clear about your assumptions and finding out where that set of assumptions leads you; but that doesn’t mean you have to publish every such exploration.

This is a theoretical paper that aims to address the important question of what determines vaccination rates in a population.  If the vaccine isn’t mandated by your government, then the vaccination rate depends on individual decisions, which may be influenced by individual perceptions of costs/risks and benefits.  The “correct” decision for an individual (defined as maximizing benefit, minimizing cost) may not be the same as the “correct” decision for a population; if individuals think that enough of their friends are being vaccinated that the risk of an infection in their circle is very small, the theory goes, they may choose not to get vaccinated and avoid the costs and risks, while gaining the benefits.   This is the kind of calculation that many parents in the UK apparently went through in deciding to avoid giving their children the MMR vaccine (measles, mumps and rubella) after the perceived risks of the vaccine were sharply increased by the scare engineered by Andrew Wakefield, who has now been comprehensively proven to be a self-interested fraud (if you haven’t read all of the BMJ articles by Brian Deer, do; they’re amazingly detailed and well documented).  As a result of the drop in MMR vaccination rates in the UK, measles is back with a vengeance.  Similar things have happened with whooping cough vaccine, polio vaccine, and many others.

In this paper, the authors focus on the choice to get a flu shot.  They argue that the probability that a rational individual will choose to be vaccinated is determined partly by their perceived risk of infection, which is based on two main factors: the structure of the social network and the virulence of the disease. Social network structure comes into play because individuals who have lots of daily contacts — a politician on the campaign trail, perhaps — would be expected to be more likely to get vaccinated, while those who are determinedly antisocial might be less likely to do so.  The perception of virulence of disease is assumed to correlate with an individual’s memory of previous flu season(s); you are supposed to guess how bad this season will be based on how bad the last season was.

This is my first point of disagreement.  I consider myself a rational individual and yet neither of these factors enters my own calculation of whether to get a flu shot.  I suppose if I were alone on a desert island, I might think that getting a flu shot was unnecessary, but on the other hand if a shot were available I might get one anyway.  You never know when you’re going to be rescued by a flu-infested cruise ship.  I long ago reached the conclusion that getting a flu shot is extremely sensible, and as a result the only factor that affects my likelihood of being vaccinated is how easy it is to get a shot.

I know that it’s dangerous to argue from personal experience, especially when most of the people you know and talk to are scientists. Nevertheless, my guess is that a significant fraction of the population has similarly made what amounts to a policy decision — the flu vaccine is good, the flu vaccine is bad — based on their own analysis, habit, or on what their doctor tells them. (The role of marketing, by doctors and others, seems to me to be seriously underplayed in this paper.)  If you’re in the “flu shot good” camp, your chance of being vaccinated probably depends mostly on convenience, the number of reminders you get, and affordability, modulated only slightly by fear.  Fear certainly comes into play when you have a media event like the recent scare about swine flu, which serves both as a reminder writ large for the “flu shot good” community and a way of getting the attention of the people in the middle, who don’t think much about flu shots at all.

The second factor the authors consider is the balance between the actual cost of a flu shot and the perceived cost of being infected.  The numbers they use are $27 for the cost of a flu shot, and $73 as the perceived cost of infection to an unvaccinated individual (having looked at the paper from which this latter number is derived, I don’t at all understand where it comes from.  But never mind; that’s the least of my worries.)  The tipping point in the decision of whether to vaccinate or not is then assumed to be the point at which the risk of losing $73, given the number of contacts you have and how likely you think they are to get sick, is equal to the actual cost of vaccination, $27.  I know that much of economics is built on the idea of the rational consumer, but this seems to me to stretch the idea of rational a little far.  Especially since the consequence of the model is that individuals act highly irrationally, deciding not to get vaccinated when the chance of getting sick is actually at its highest, because everyone is making the same calculation: last year was OK, so I don’t need to get vaccinated this year.

[I’m not happy with the simplicity of this cost-benefit calculation anyway. For a significant fraction of the population, $27 is a lot of money.  I suspect that if you’re living at or near the poverty line, the choice between getting vaccinated and buying this week’s groceries may not seem like a choice at all.  If you’re in this category, you may want to get vaccinated and you may even be aware that getting sick would be a financial disaster (or you may be in denial), but you probably still feel that putting food on the table is more important than protecting yourself against an event of uncertain probability.  On the other hand, if you’re rather well-off, then $27 may seem like nothing, and again you may not enter into any kind of financial calculation in deciding whether to get a shot.  So at both ends of the financial scale, cost-benefit analyses may not be very important.]

The authors then put the two sets of assumptions together into a model that simulates the individual decisions that each person makes, and then simulates the spread of a virus through a population given the choices made by each individual.  If the model says that a person with 50 contacts per day is likely to decide to be vaccinated, for example, then that person is assumed to be protected (77% less likely to get sick, in the model) and therefore all the people in contact with them are less likely to be infected as well.  (This is why I send out my annual e-mails to the Department [marketing, see?] suggesting that everyone take advantage of the vaccination clinics at Harvard Medical School.  Herd immunity is a wonderful thing.)  They simulate a flu season, determine how severe it looked to the population, and take that perceived severity into the model for the next season, where it influences the level of fear of flu in the population by increasing the perceived likelihood of infection.  There is a lot of analysis of potential free-rider effects and the Nash equilibrium, and how the structure of the social network might affect the behavior of individuals.

What the authors think is the big result, I assume, is summarized in the title: if you make these assumptions, you get oscillations in the vaccination rate.  Low vaccination rates one year lead to a bad flu season, which increases the level of fear next year, which leads to higher vaccination rates and a less scary level of infection.  And vice versa.  But such oscillations — as the authors point out — are not visible in real-world data; the possibility that they might exist comes straight from the assumption that our level of fear of infection is directly correlated with the severity of the most recent flu season.  If you allow people to remember 2 or 3 seasons back, the oscillations attenuate or disappear.  Perhaps we have longer memories for illness than for politics; or perhaps something else is going on.

Whatever the reason for the lack of oscillations, the more we talk about the reasons for getting vaccinated (did I mention that flu vaccine generally reduces your chance of getting sick by 70–90%?) and the fears and barriers some people face that prevent them from getting vaccinated, the better.  The problem that a vaccine always faces in public perception is that you don’t know whether you, personally, would have been infected without it; so a vaccine that prevents you from getting sick in the first place gets less credit than a drug that may shorten the course of your infection by a day or two.  On the other hand, if you suffer some kind of adverse effect from the vaccine — and vaccines are never completely safe, though they’re usually much safer than even the most benign drugs — you’re furious.  It’s an unfortunate wrinkle of human psychology, and it contributes to the lack of public affection for vaccines that allows someone like Wakefield to attack them without being attacked back.  Prevention is (much) better than cure; but prevention is far less visible than cure.  It’s too bad.

Cornforth DM, Reluga TC, Shim E, Bauch CT, Galvani AP, Meyers LA (2011). Erratic Flu Vaccination Emerges from Short-Sighted Behavior in Contact Networks PLoS Computational Biology, 7 (1) : doi:10.1371/journal.pcbi.1001062

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