Sample bias

by Henry Farrell on December 15, 2003

I’ve been meaning to blog this ever since I read about it a few days ago on “Marginal Revolution”:; it’s one of the neatest ideas that I’ve seen in a while. Given endemic shortages in the availability of some vaccines (viz. flu shots this year), how should one allocate shots so as to prevent the spread of the disease in the general population? Tyler Cowen points to an “article”: by Reuven Cohen, Shlomo Havlin, and Daniel ben-Avraham that suggests how best to do this. It’s fairly well established that some individuals are a lot more likely to spread viruses than others; these ‘super spreaders’ are exceptionally gregarious people, who have a wide and varied circle of friends with whom they share time, conversation, and unpleasant infections. This means that virus diffusion can be “modelled nicely”: using scale free networks with power law distributions of linkages. Some individuals are much more ‘connected’ than others, and these highly connected individuals are much more likely to be the vectors of contagion. If you can vaccinate these individuals, who are the ‘hubs’ of the network, you can do an awful lot to limit the spread of the disease. The problem is that it’s often hard to figure out who the hubs are. Cohen, Havlin and ben-Avraham have figured out a very clever way of doing this. You randomly sample the population, and ask each person who you sample to nominate one of their acquaintances. You then vaccinate _not_ the initial person who has been sampled, but instead their acquaintance. Because ‘super spreaders’ are likely to know far more people than the average member of the population, they will be heavily over-represented among the ‘acquaintances’ – and thus will be far more likely to be vaccinated. According to Cohen, Havlin and ben-Avraham’s model, you may be able completely to halt the spread of the disease by sampling some 20% of the population, and then vaccinating their acquaintances. This is very clever indeed – insights into the topology of social networks can be used to stop the spread of viruses. It goes to show that the study of power-law distributions may have more uses than securing your bragging rights in the blogosphere.



Brett Bellmore 12.15.03 at 4:33 pm

Assuming the “superspreaders” agree to be vaccinated, and that people are willing to respond to such surveys. At least the current model of vaccination effectively exploits perceived self interest.


ogged 12.15.03 at 5:00 pm

This is a neat idea, but I’d like to know if the researchers have accounted for the possibility that social “hubs” may be less likely to be closely connected to any one person and therefore less likely to be named.


Keith M Ellis 12.15.03 at 5:26 pm

I have the strong impression (not terribly informed and definitely a layperson’s) that epidemiology is a moribund field in need of some shaking up.

First and foremost, I have been dismayed to read coverage of the flu epidemic that discusses past flu pandemics, particularly the 1918 pandemic, with no mention of Paul Ewald’s work. In spite of his work, the unquestioned assumption is still that all pathogens quickly evolve toward benignity and that, thus, virulent pathogens are always cross-species contagions.

Additionally, Ewald makes the case that some of the modern increase in virulency is the result of pallative medication that encourages people to be mobile contagion vectors while ill. The general public needs to understand that staying home when ill is essential both to limit the spread of contagion and to decrease virulency.

Health care workers are implicated in this, as well. They act as independent vectors that encourage increased virulency and it is absolutely crucial that they be innoculated and follow sanitary procedures. It’s my understanding that in the US, only about a third of the health care professionals are being vaccinated for the flu each year.


Barry 12.15.03 at 5:52 pm

Keith, you might want to check out he epid literature, before you make judgements on the field. Judging it from newspaper reports is sort of like judging eonomics from usenet posters and bloggers.


Ross 12.15.03 at 6:00 pm

There are some fairly significant human rights and legal issues underlying this approach (e.g., could you mandate vaccination of these acquaintences based on the report of another? what if the acquaintence has personal objections to vaccination?), and there are certainly significant cost concerns as well (I’d venture contact tracing + immunization is far more expensive than setting up a clinic), but it’s an interesting article worth strong consideration.


Keith M Ellis 12.15.03 at 6:04 pm

Barry, that’s why I carefully qualified my comment. :)


schnauze 12.15.03 at 6:05 pm


I can’t wait for the first sociologist/epidemiologist to call me up and ask which of my friends I would nominate to go to the doctor for some shots!

In fact, anything that is punitive towards gregarious people, I’m all for! (Note that this would also be especially punitive towards gregarious people (“gregarians”) who mix not just with other gregarians, but also with all those random losers lost out there amidst the general population) Maybe we could also wipe out AIDS through random chemical castrations performed on “your last sexual partner!”



Brian Weatherson 12.15.03 at 6:32 pm

I hardly think providing people (presumably for free) with a flu shot is ‘punitive’.

Disease control is really a very tricky area for balancing out important freedoms with social responsibilities. We don’t want to move to a situation of mandated immunisations for everything that comes up. But it is worth watching for whether we’ve crossed the point that walking around un-immunised poses an unacceptable risk to one’s neighbours. I don’t know where that point is, or whether we are anywhere near it, but some people seem to assume that it could never be crossed, and this just seems false.


Keith M Ellis 12.15.03 at 6:53 pm

I don’t know where that point is, or whether we are anywhere near it, but some people seem to assume that it could never be crossed, and this just seems false.“—Brian Weatherson

I think it’s commonly crossed. It took me a little while to find this, but your comment reminded me of a New York Times article from last year that discussed a Washington (state) community that is suffering because of lessened “herd immunity” that results from a high percentage of parents opting their children out of vaccination.


Keith M Ellis 12.15.03 at 6:55 pm

(/me is pleased with my recall. Senility isn’t hitting me too badly now that I’m about to turn 40. :) )


dsquared 12.15.03 at 7:05 pm

If you’re asked to nominate an acquaintance to receive a flu shot, do you nominate:

1) Granny, sitting at home in her hourse, who doesn’t get out much


2) Jim Bob, the loudmouthed joker from down the pub who everybody knows?

I haven’t read the paper, but I’d bet quids that its engine is an assumption that people asked to name an acquaintance select one at random. This might be a dangerous assumption; plenty of buildings have burnt down because everyone assumed that someone else would “obviously” have called the fire brigade.


Keith M Ellis 12.15.03 at 7:17 pm

I’d bet quids that its engine is an assumption that people asked to name an acquaintance select one at random.”—Daniel

Damn. I can’t get PRL online via the Austin Public Library. (They offer access for patrons to many databases of journals.)

Well, they could ask for, say, ten names and select one at random.


patrick 12.15.03 at 7:35 pm

Collect 10 names from each interviewee, put them all in a database, and vaccinate the top ‘vote getters’.


Keith M Ellis 12.15.03 at 7:51 pm

Yeah, I was going to suggest that, too, or more: why not just determine the social network in more detail? But I suspect the authors were attempting to avoid anything that would unduly aggravate privacy fears, i.e., compiling such a database.


Ross 12.15.03 at 8:18 pm

Keith: On your last point, I respectfully disagree. I think they were working purely in the mathmatical and statistical realms, and while willing to speculate on the potential uses for their formula, they weren’t trying to write the policy article on how to practically implement such a thing.

That’s my job. :)

P.S. The place in Washington they discussed in the NY Times article was Vashon Island. A similar phenomenon is occurring in the greater Boulder, CO area. In both cases, the scientist on the scene doing research on the statistical impact of philosophical exemptors is Daniel Salmon of Johns Hopkins University.


Keith M Ellis 12.15.03 at 8:32 pm

Ross: Ah. Not having access to the paper, I was speculating on why they didn’t just go whole hog. That seemed a reasonable possibility.

If one puts such considerations aside, I suppose the main practical problem with actually determining the social network would be that it would take time that one doesn’t have in an epidemic. I assume that the whole point of their paper is that a randomly selected aquaintence of each sampled individual will (with a large enough sample) cumulatively approach the same result, while the latency of actually applying the vaccines would be as short as possible.

Danial’s objection is a very good one, in any case. They simply must use some method that avoids the problem that Daniel describes. But wouldn’t my suggestion work? Ask each person for ten (or more) names of people they know. Then select one of those names at random, discarding the rest. The more names you ask for, the less the results will be skewed toward isolated old aunts.

Also, really unpopular people who are, nevertheless, very social will be selected against. That might be a good thing. :)


Anna 12.15.03 at 9:12 pm

veering somewhat off topic – why is it that social mores, even behind the scenes at large employers, are such that sick people a) still show up for work; b) still use common facilities; c) still cough into their hands before shaking yours, touching doorknobs, etc; and d) don’t wear masks or use hand sanitizer gel? It would seem logical (i.e. cost-effective) for organizations (at least those that don’t need to put up a healthy-looking front for customers) to recognize that sick employees reduce productivity, and try to encourage behaviors that reduce transmission.

p.s., re the original topic – you could improve on the algorithm by asking people to name the [N] _most sociable_ people they know, and give the top votegetters incentives to get shot up. And have a 2-tier(?) system – 1) the clinic for everybody (so you can lure people in for asking) and 2) outreach+incentives for the sociables.


Anthony 12.15.03 at 9:21 pm

Really, the difficult question is in obtaining compliance from the selected super-social. I suppose that offering people who fit the criteria free shots while charging others might help, but I don’t know what else is reasonable.


Keith M Ellis 12.15.03 at 9:35 pm

I suppose that offering people who fit the criteria free shots while charging others might help…“—Anthony

That’s a very good idea, and almost certainly cost-effective, don’t you think?

It would seem logical (i.e. cost-effective) for organizations (at least those that don’t need to put up a healthy-looking front for customers) to recognize that sick employees reduce productivity, and try to encourage behaviors that reduce transmission.”—Anna

This reminds me of when I worked at a catalog sales phone center almost twenty years ago for one of the big catalog retailers. Every year around Christmas time, they’d balloon the staffing up to nearly a thousand part-time people; but, also, every year about that time they’d have a flu/cold mini-epidemic that would affect at least a quarter of the workforce.

I had recently read the results of a study of how colds and flus are commonly transmitted—rarely is it airborne, the route is eye/mouth/nose –> hand –> object –> hand –> eye/mouth/nose. What was obviously happening at this call center was that all these temp workers, who were working perhaps four hour shifts, would share computer keyboards and transmit the pathogens that way. I suggested to the management that wiping down the keyboards between shifts with an antiseptic (either having each individual do it, or have someone wander around doing it) would dramatically decrease the spread of the cold/flu and reduce absenteeism.

They didn’t do it, of course.


Anna 12.15.03 at 10:07 pm

..and there’s also the self-serving delusion that “once I actually have symptoms, I’m not contagious anymore” that lots of people seem to have. Would love to see research bearing on this one.

Question – before this one, the last “blindingly original intuitive simple method discovery” I remember was the “how to get good data on yes/no answers to embarrassing telephone survey questions” thing, where the respondent was to spin the arrow and if it landed on “Yes” answer yes, if on “No” answer no, if on “the truth” answer the truth.

Besides these 2 cases, are there others?


Keith M Ellis 12.15.03 at 11:43 pm

Anna: I hadn’t heard of that method, and it makes me very geekily happy to learn of it. Thanks.


sennoma 12.16.03 at 6:48 am

the self-serving delusion that “once I actually have symptoms, I’m not contagious anymore”

It depends what you have. IIRC, rhinovirus infections are no longer contagious by the onset of symptoms, but influenza and parainfluenza viruses remain infectious right through the symptomatic period and even beyond. I dunno about coronaviruses (rhino-, corona- and parainfluenzavirus infections make up the majority of afflictions we call “colds”). A reasonable rule of thumb is that you are contagious for a weeks after your symptoms start, since that covers the most infectious period of all common viral illnesses.

[googling, googling…]

Here’s the Straight Dope on the question. I forgot adenoviruses, but was mostly about right.


sennoma 12.16.03 at 6:51 am

“a weeks”, gah. Also, I meant “all common viral illnesses that fall under the general heading of ‘colds'”. Also also, I’m not a virologist but the Straight Dope info comes from the CDC, so it’s reliable.


schnauze 12.16.03 at 4:28 pm

of course the wimpy, stay-at-home losers who read this blog don’t think of shots as “punitive,” but as “social responsibility.” that’s why they are losers.

seriously, it is only punitive in the sense that this program would make it worse to be a gregarite than to be a non-gregarite (modification of original terminology). think about once this is actually made social policy and children grow up knowing that being talkative=you get the shots. what are the second-order effects of such knowledge, my technocrat friends? And what about my AIDS prevention idea: chemical castration of “your (second(?)) most recent sexual partner”?

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