The math behind estimating seasonal flu deaths.

Health and medicine explained.
May 14 2009 12:20 PM

Influenza Body Count

The math behind estimating seasonal flu deaths.

Students with masks. Click image to expand.
Students with masks in Mexico City

By now, the swine flu panic has started to recede. Kids in Mexico are back at school; President Obama worked a flu joke into his White House Correspondents' Dinner routine; drugstore face mask displays have been demoted from the impulse-purchase bin to the medical aisle. And in the media, the swine flu backlash has begun. According to the CDC, 36,000 Americans die of ordinary strains of flu every year—so why, the new narrative goes, did we get so agitated over a bug whose victims worldwide, as of this writing, number just 65?

The problem is, we can't compare those numbers. The official swine flu deaths are from patients who were confirmed by lab tests to have been infected with the H1N1 strain. The 36,000 figure, by contrast, isn't a count of people whose death certificate lists "flu" as cause of death; in 2005, the total number of those was just 1,812. But people who die of flu are often no longer infected when they die. Instead, they succumb to pneumonia or heart disease or emphysema—ailments they would have survived if they hadn't been weakened by the flu. That's why the 2,000 or so certified flu deaths represent an underestimate of the flu's real cost.

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How does the CDC come up with 34,000 more flu victims? The number comes from a 2003 study led by William W. Thompson. All winter, about 80 labs across the United States continually test patients for flu virus, so we have a pretty good estimate for the number of Americans infected with flu in any given week of the last 20 years. We also know how many Americans total died each week.

Suppose 52,000 people died in the first week of February 2004; 55,000 in the same week in 2005; 51,000 in 2006; and 54,000 in 2007. Suppose furthermore that the number of influenza specimens confirmed by labs was 1,000, 2,500, 500, and 2,000 in the four weeks in question. Then it certainly looks like the flu is killing people (whether directly or by opening the door to another lethal illness) at a rate of about two deaths per confirmed specimen; in a world without influenza, the death rate would be constant at 50,000 per week.

In real life, though, the numbers aren't that clean—they never are. Lots of nonflu factors push the death rate around from week to week and year to year. But a statistical technique called regression allows us to find the value of X such that the formula

[Total deaths] = [Deaths if there were no such thing as flu] + X*[number of confirmed flu cases]

matches the data as closely as possible. The rightmost term, X*[number of confirmed flu cases], is then our estimate for the number of deaths you can attribute to flu. In the example above, you'd choose [Deaths without flu] to be 50,000 and X to be 2. And if 18,000 specimens test positive for flu over the course of a year, you'd blame 36,000 deaths on the flu.

Not everybody's comfortable with a body count that consists of statistically inferred victims instead of, well, bodies. And there are potential glitches—for example, if a snowy winter causes both more flu (people spend more time indoors) and more car accidents (slippery roads), the model is going to blame the flu for a lot of traffic deaths. For this reason, some versions of the model, including Thompson's, exclude causes of death, like car crashes, that don't seem plausibly related to flu.

But what's the alternative to the estimate? Counting only the 1,812 people who died with the flu still in their lungs? That would be like recording the cause of death as "car accident" only for victims who died in the car and filing everyone who bled out in the ambulance under "anemia." Or like restricting your account of the lives lost to the Iraq war to documented violent deaths, like those in the Iraq Body Count, instead of making a statistical best estimate as the Lancet study did. (While the specific methodology used in the Lancet study has drawn some criticism, the use of statistical techniques to estimate excess deaths is standard.) That 36,000 estimate is far from an exact figure—tweaking the technique can easily knock it up or down by 10,000 or so—but it's a "least bad" estimate; the 1,812 number is very precise but also very incorrect.

The true death toll from the swine flu, as the virus continues to spread and as estimates for flu-induced respiratory deaths start to roll in, is going to end up greater than 65—a lot greater. How much greater we don't know, and won't for a while—estimates of the total deaths from this season's flu might not be available for a few years, according to David Shay of the CDC. Still, the last pandemic influenza virus, the "Hong Kong" H3N2 strain of 1968-69, killed only 34,000 Americans—fewer than the 36,000 who die from flu in a nonpandemic year.

Given that, can we calm down about swine flu  now that the initial fear of an ultralethal "1918 event" has died down? Not quite. "How many people died?" is only the first question a statistician might ask of the flu data. The second question is "Which people?" In Mexico, the swine flu has struck down young, healthy people, not the elderly and immuno-compromised who typically succumb. That effect hasn't shown itself yet in the United States. But it might, if the new flu goes pandemic. A 1998 paper by Lone Simonson, et al., shows that each of the three pandemic influenzas of the 20th century has killed far more than its share of the young. According to that paper, the Hong Kong flu killed between 6,000 and 8,000 Americans under the age of 65; in the years following, the H3N2 strain grew less and less deadly to younger people, and by 1982 it was killing fewer than 500 under-65s a year, even as it kept its overall death count high by victimizing the ever-growing elderly population.

If you're over 65 and have chronic respiratory problems, your risk of getting knocked off by the flu isn't that much greater than it was last year. Otherwise? If you want to keep that face mask close at hand a few months longer, you've got my mathematical blessing.

Jordan Ellenberg is a professor of mathematics at the University of Wisconsin and the author of How Not to Be Wrong. He blogs at Quomodocumque.

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