In scary news today: Stroke Patients Getting Younger, Stroke Rising Among Young People, and so on.

Apparently some researchers reported that some number went up recently, and the number that went up had something to do with stroke and something to do with 15-44 year-olds.

Sounds like a good excuse for a rousing chorus or two of Fire in the Theater! Obesity! Diet Soda! You’re Gonna Die!, no?


The number reported to have gone up recently is not the total number of strokes among 15-44 year-olds, nor is it the rate (per 10,000 people, for example) of strokes among people that age.

The number that went up recently is the rate of strokes in 15-44 year-olds as a fraction of all hospitalizations for that age group. Not an easy quantity to conceptualize. But when a quantity is hard to conceptualize, you aren’t automatically allowed to grab a “you may pretend it’s something else.” pass and lie with impunity. (Do these same journalists give up and write “Boxer” if they can’t spell “Feinstein”?)

Maybe the stroke rate among 15-44 year-olds is not going up.

It could be that hospitalizations of 15-44 year-olds for reasons other than stroke are going down. Maybe hospitals are more and more likely to list multiple reasons for hospitalization than in the past. Maybe many former headaches are now deemed strokes (thanks to the proliferation of imaging tests). Either of these trends would make the numerical rate of stroke diagnoses per 10,000 hospitalizations go up without reflecting an increase in stroke.

Maybe a lot of things. Maybe the rate of stroke is going up among young people. Which might be scary. Or not. It’s possible more and more diagnoses of stroke are insignificant — no worse than a bad headache. Just because “stroke” sounds scary doesn’t mean there can’t be innocuous kinds of stroke.

Unfortunately we don’t know from today’s irresponsible scramble to turn numbers into fear.

One Response to “Hey, Let’s Scare People with Numbers!”

  1. Steve Kass » Diseases, and Numbers, and Bears! Oh, My! Says:

    […] stroke news was an unjustified scare about stroke and younger […]

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Internet news aggregator robots never leave me alone. Internet news aggregator robots, never leave me alone.

Every day or more, one of the news aggregator robots gets both my attention and my goat. Here’s one of today’s missiles: “CDC: Most Teens Choose to Abstain,” at The first paragraph:

A recent study shows that most teenagers are virgins, contradicting claims from family planning groups that most young people do not abstain from sex and more sex ed should be taught in schools.

YoungCoupleEmbracing-20070508Image by Kelley Boone, some rights reserved (CC-BY-SA 2.0)

This kind of blabbery drives me nuts. They might has well have said, “A recent study shows that the earth is flat, contradicting claims from Unitarians that the planets revolve around the sun and astronomy should be taught in schools instead of the Bible,” when in fact a recent study showed no such thing, and even if it had, it wouldn’t contradict what the Unitarians supposedly said. Maybe if I’d been on the debate team I’d know how to respond more effectively.

If I were a fundamentalist Christian who wanted to justify abstinence education, I wouldn’t quote or misquote studies, nor would I attempt to use logic. I’d be honest: “According to my church, the world is flat, most young people abstain from sex, and abstinence should be taught in schools right after study hall and before creationism. That’s what I believe, because faith in the church is my guiding light.”

Studies be damned, science be damned, the church is the ultimate authority. I might have more respect if they put it that way more often. (I would still object if it got to the point of the Constitution be damned and laws be damned.) Why should fundamentalists care a whit about the fact that science is consistent, well-founded, and predictive? Why should they care about evidence from studies and measurements, if faith, not intelligence, is their life’s compass? I can disagree, disapprove, and be dismayed, but I have no appeal. We live on different planets; we grew up in different universes.

Anyway, for readers who might appreciate facts and figures, let me explain the CBN’s vulpigeration.

What is “sex,” anyway? For its study, the CDC defined “sex” to be heterosexual vaginal sexual intercourse¹ only (though the boy need not stay on top). Many English speakers would call a bunch of other things people do naked with others sex, but the CDC’s restrictive definition should suit the Christian Broadcasting Network in two ways. First, this definition doesn’t infringe on the way CBN might define another word, “sodomy.” They might prefer it for that bunch of other things people do naked with each other. Second, it yields higher virgin percentages. As far as the CDC and are concerned, you’re a virgin if you haven’t been part of any penis-in-vagina hanky-panky, even if you’ve gotten plenty naked and nasty with one or more hims or hers.

Fact: Most young people do not abstain from sex. (Or “sex.”) Not during their entire youth, which is what suggested. According to the CDC study, most (65% of) boys aged 18-19 and most (60% of) girls in the same age group have had heterosexual vaginal sexual intercourse. The CDC numbers suggest that most young people do abstain from sex “sex” until about age 17 or 18, but abstaining until you stop abstaining is not the same thing as abstaining. Using the logic, you could say that all people abstain from sex, ’cuz they all do — until they stop, and most stop, as we know from all the babies being born and abortions being performed. Few babies (or aborted fetuses) are incarnate nowadays.

¹ Additional information available on the internet.

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Advanced Global Personality Test Results

Extraversion |||||| 23%
Stability |||||||||| 36%
Orderliness || 10%
Accommodation |||||||||||||||| 70%
Intellectual |||||||||||||||||||| 90%
Interdependence || 10%
Mystical || 10%
Materialism |||| 20%
Narcissism |||||||||||||||| 70%
Adventurousness |||||| 30%
Work ethic |||||||||| 40%
Conflict seeking |||||||||||| 50%
Need to dominate || 10%
Romantic |||||||||||| 50%
Avoidant ||||||||||||||||||||  90%
Anti-authority |||||||||||||||||||| 90%
Wealth |||||| 30%
Dependency |||| 20%
Change averse |||||||||| 40%
Cautiousness |||||||||||||| 60%
Individuality |||||||||||| 50%
Sexuality |||||||||||| 50%
Peter Pan complex || 10%
Histrionic |||||||||| 40%
Vanity |||||||||||| 50%
Artistic |||||||||||| 50%
Hedonism ||||||||||||||||        70%
Physical Fitness || 10%
Religious || 10%
Paranoia |||||| 30%
Hypersensitivity |||||||||| 36%
Indie || 10%
Not that I’d choose to be elsewhere, but, honestly, I’m less than thrilled with the pummeling “trait snapshot” Similar Minds appended: messy, depressed, introverted, feels invisible, does not make friends easily, nihilistic, reveals little about self, fragile, dark, bizarre, feels undesirable, dislikes leadership, reclusive, weird, irritable, frequently second guesses self, unassertive, unsympathetic, low self control, observer, worrying, phobic, suspicious, unproductive, avoidant, negative, bad at saving money, emotionally sensitive, does not like to stand out, dislikes large parties, submissive, daydreamer.

For the record, I’m not particularly fond of small parties, either.

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On Monday, CBS News leapt (or leaped, if you wish) onto the alarm bandwagon, writing (emphasis mine):

So far, the biggest outbreak has taken place on Vancouver Island in British Columbia, but the fungus has since spread past the order [sic] into Oregon where it’s become a "a major source of illness in the region," according to the online journal PLoS Pathogens.

Not to be snarky (translation: Imma snark (translation: sarcasm coming)), but besides misspelling “border,” the CBS News writer failed to read either my previous post here (highly forgivable) or my comment on the PLoS Pathogen article’s discussion page (less forgivable, being that there are only two comments on the article).

It’s interesting to think about where in the scientific peer review process a clinker like “major source of illness” should have been caught. (I’ll think to myself.)

For the record, a publications assistant at PLoS Pathogens who handled my comment deserves thanks. He offered helpful feedback on a first draft of my comment, and he followed up to suggest that PLoS Pathogens cares when their articles are misinterpreted.

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Spores of C. immitis Yesterday, I wrote about the emerging public alarm over the fungus Cryptococcus gattii. Alarm continues to emerge, though some welcome voices of moderation are also appearing. (Time magazine’s writer Alice Park, for example, insightfully explored both the fungus and the alarm in “The ‘Killer Fungus’: Should We Be Scared?”)

Today’s topic is another fungus, a fungus of my childhood.

Like every nerdy kid in the 1960s, I could say and spell the words “antidisestablishmentarianism” and “pneumonoultramicroscopicsilicovolcanoconiosis.” But unlike most nerdy kids outside the desert Southwest, I could also say and spell “coccidioidomycosis.” When I read about C. gattii yesterday, I couldn’t help but think about it — coccidioidomycosis, or Valley Fever. Like the killer disease du jour, Valley Fever infects humans and animals who inhale fungus spores. In the case of Valley Fever, the fungus is Coccidioides immitis, which resides in the local soil around Phoenix and other parts of the Southwest. After a dry spell, rain and wind dislodge the spores and carry them into the air, where they float, free for the breathing.

I breathed in my share. Whenever a dust storm rolled in, my brother and I would don our swim masks, run outside, and play in the carport until rain and lightning arrived, if it did. Driving through the desert on dirt roads or off-road probably kicks up spores, too, and Dad took us on more than a few dirt-road and off-road trips in the Wagoneer.

Like C. immitis, C. gattii, according to some sources, usually causes no symptoms or minor ones.’s Robert F. Service writes that “most of [Vancouver Island’s] 750,000 residents have been exposed to C. gattii multiple times with no symptoms.” That’s not to say these fungal infections are innocuous; serious infections have occurred particularly in the immunocompromised, such as transplant recipients or (especially before HAART) persons with AIDS.

One Response to “Another Fungus Story”

  1. Janice Arenofsky Says:

    Hi Steve,
    Ditto to your comments on Valley Fever. As executive director of the Valley Fever Alliance in Phoenix, I know how dangerous this particular fungal disease is. And it’s getting worse every day, killing hundreds if not thousands of dogs and zoo animals and threatening the lives of Arizona residents and visitors.

    The Valley Fever Center for Excellence is testing the possibly curative experimental drug nikkomycin Z on dogs, so soon we may see if we have a cure. If it’s a go, it still won’t be in anyone’s medicine cabinet until another few years. Unfortunately, this is thanks to the State of Arizona for dragging its heels for 40+ plus years and not funding a medication or vaccine but instead inviting tourists to come and sample our five-star hotels, gourmet food and spore-filled air.

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The popular press is beginning to report on an article that appeared in PLoS Pathogens today, and you can bet public alarm will spread incomparably faster than the “highly virulent fungus” discussed in the article.

The Los Angeles Times was one of the first to pick up on the scare. They interviewed the article’s lead author, Edmond J. Byrnes, III for their report. In PLoS Pathogens, Byrnes and his coauthors described an “increasingly fatal fungal outbreak” in their discussion, without providing statistical support or an inline reference. The Times knows what readers will glom onto, however, and they devoted a couple of paragraphs to this “more lethal” angle.

The spread is also a concern because the strain of the fungus that moved into the United States in 2004 has mutated to become more lethal than the original strain that invaded British Columbia in 1999.

Five of the 21 people who contracted the fungus in the United States have died (about 25%), compared with 8.7% of the 218 infected people in Canada. The fungus has also infected many different species of mammals.

These details aren’t in today’s PLoS Pathogens article. Today’s article focuses on the molecular biology of C. gattii, not its epidemiology. My admittedly cursory search for the source of the Times’s numbers turned up one mention of an “over 25%” U.S. fatality rate. That was in a previous article of Byrnes’s, where he referenced the figure as the “unpublished observations” of two other scientists. But let’s give Byrnes and the Times the benefit of the doubt and suppose the numbers are reliable.

Math time. If you know only a handful of small numbers about a disease, drawing any epidemiological conclusions — especially alarmist ones that might be misconstrued — is risky, but mathematics can still help us evaluate the numbers. There will be lots of ifs, but that’s to be expected when you have limited data. The standard way to proceed is to ask the following question: If in fact nothing scary is happening (meaning that the infections in the U.S. are not more deadly than they are in Canada), might we really see as many as five deaths in 21 cases?

Under the probabilistic assumptions of this kind of analysis, getting infected with C. gattii is treated like a crap shoot as to whether you die or not; you die with probability 8.7%, the Canadian fatality rate. If 21 people get infected and for each one God rolls the dice to see who dies, what’s the likelihood at least five of them will succumb? Well, it’s around 3%. To put that in context, imagine that tomorrow’s traffic is terrible, like once-a-month terrible. Would you chalk it up to bad luck or a real change in traffic congestion? I’d chalk it up to bad luck and assume a real change only if traffic was similarly terrible again tomorrow or maybe next week. (Even then I would probably look for other explanations, like an announced construction project or a visiting dignitary.)

Other factors should be considered when comparing fatality rates to test the hypothesis of increasing deadliness, particularly with such small numbers of cases. Were the U.S. persons infected by C. gattii diagnosed as promptly (or not) as the Canadians and given identical treatments? If not, the higher U.S. fatality rate could be due to late diagnosis or ineffective treatment. Were the U.S. persons infected or killed similar to the Canadians in age, general health, and other factors known to be independent predictors of mortality from disease? If not, the higher U.S. mortality might not be due to greater virulence.

PLoS Pathogens is a peer-reviewed journal, and that provides some assurance that the scientific conclusions were based on accepted scientific practices. Unfortunately, published science has the potential to affect society and policy via the popular press, and reviewers need to think about how a publication might be construed by a journalist.

To Byrnes’s credit and the Times’s, readers who ventured a few paragraphs past the alarming headline will read this more moderate assessment of the situation: “Overall, I don’t think it is a large threat at this time. But the fact that it is continuing to spread geographically and the number of cases is rising makes it a concern.”

Whether or not Byrnes et al. were more justified than I can tell in calling this a “increasingly fatal fungal outbreak,” sure, this could be the next black plague. So could any number of currently very rare or unknown pathogens. But based on the science I’ve seen, you shouldn’t be any more worried about C. gattii today than you were last week, when I’m guessing you’d never heard of it.


Updated at 2010-04-22 at 23:28. I added the words Deadly and Fungus to the post title hoping to get more play. A list of headlines on this story follows.

One rebuttal of the alarm: Ore. DHS questions article statements about deadly fungus
(DHS is Department of Human Services, not Homeland Security)

Alarm and alarm in all the other headlines, though.

  • Airborne fungus claiming lives
  • New strain of virulent airborne fungi, unique to Oregon, is set to spread
  • New Deadly Fungus Found in US, Has Already Killed Six
  • Potentially Lethal Airborne Fungus May Spread to California
  • Deadly Oregon fungus may spread on West Coast
  • Deadly airborne fungus in Oregon set to spread
  • Killer fungus seen in Pacific Northwest
  • Potentially deadly fungus spreading in US and Canada
  • Deadly Oregon fungus may spread on West Coast
  • Deadly Fungus In Oregon: New Strain Of Fungus Killed 6 in Oregon
  • Fungus Cryptococcus gatti Threat to Healthy People
  • New Likely Deadly Fungus Invading US & Canada – Signs & Symptoms
  • Emerging Northwest fungal disease develops virulent Oregon strain
  • Oregon Fungus Spreading South
  • Toxic Airborne Fungus From Oregon Spreading Across West Coast
  • New Concerns About Deadly Fungus Found in Oregon
  • Deadly strain of airborne fungus spreading among healthy people and animals
  • Life threatening tropical fungus seen in Pacific Northwest
  • Fungus Spreading Throughout US, Canada
  • Killer Fungus Migrates To The US
  • Killer Lung Fungus Hits Northwest
  • ‘Highly Virulent’ Strain of Killer Fungus Found in Ore

3 Responses to “Deadly Oregon Fungus: We’re All Gonna Die!”

  1. Steve Kass » Soy como soy Says:

    […] with CNN” thing. For example, in today’s Time, Alice Park insightfully explored both the fungus I wrote about yesterday and the alarm surrounding it in “The ‘Killer Fungus’: Should We Be […]

  2. Steve Kass » Another Fungus Story Says:

    […] I wrote about the emerging public alarm over the fungus Cryptococcus gattii. Alarm continues to emerge, […]

  3. Steve Kass » Fungus Follow-up Says:

    […] but besides misspelling “border,” the CBS News writer failed to read either my previous post here (highly forgivable) or my comment on the PLoS Pathogen article’s discussion page (less […]

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Today’s eLetter from the folks at Fine Cooking began “Baked Pasta 259,200 Ways. We did the math.” As you can imagine, I did the Baked Pasta Recipe Maker math, too. I figure it’s 16,128,000 ways, or about 60 times the number Fine Cooking found when they did the math. Here’s the calculation. The recipe maker walked me through the following steps:

  • Choose one or two of four Flavor Bases
  • Chose one of three Sauces
  • Choose two or three of nine Sauce Enhancers
  • Choose one of eight Pastas
  • Choose zero, one, or two of five Vegetables
  • Choose two or three of six Cheeses

Assuming no choice combinations are forbidden (the recipe maker doesn’t appear to prevent you from adding olives and sherry vinegar to sausage and chicken in pink sauce, for example), you find total number of different ways to make a choice at every step by multiplying together the numbers of choices at each step.

It’s easy to count the number of ways to “choose this many of those Things.” If this many is k, and those Things are n in number, the number of ways to choose k of the n things is “n choose k,” sometimes written as C(n,k). These numbers can all be found in Pascal’s triangle. As it’s shown here, C(n,k) is in the row labeled with the n value, under the column labeled with the k value. Here’s how to use the triangle to find the value of C(9,3):Pascal

  • To choose one or two of the four Flavor Bases, there are C(4,1) = 4 ways to choose one plus C(4,2) = 6 ways to choose two, for a total of 10 ways to choose this item.
  • To choose one of the three Sauces, there are C(3,1) = 3 ways.
  • To choose two or three of the nine Sauce Enhancers, there are C(9,2) = 36 ways to choose two plus C(9,3) = 84 ways to choose three, for a total of 120 ways.
  • There are C(8,1) = 8 ways to choose a pasta.
  • There are C(5,0) + C(5,1) + C(5,2) ways to choose up to two vegetables, or 1 + 5 + 10 = 16 ways.
  • There are C(6,2) + C(6,3) to choose the Cheeses, or 15 + 20 = 35 ways

Multiplying these numbers of choices for each step yields 10·3·120·8·16·35 = 16,128,000 ways, about 60 times as many as Fine Cooking found when they did the math. Counting ways isn’t standard recipe math, and I’d like to note that Fine Cooking’s math is generally fine when it comes to ounces, grams, cups, servings, and calories.

2 Responses to “Cooking Fine, Counting Not So Much”

  1. Sarah Breckenridge Says:

    Hi Steve,
    Thanks for checking our math–and you’re correct in your calculation of the absolute maximum number of combinations for this recipe maker.

    We ran the permutation two different ways: on the lower numbers of the spectrum as well as on the higher number. We decided to go with the lower number in our headline, since, well, 259,200 is more pasta than I’ll ever get to in my lifetime (don’t know about you!).

    4 Flavor Bases (1 choice)

    3 Sauces (1 choice)

    9 Sauce Enhancers (2 choices)

    8 Pasta (1 choice)

    5 Vegetables (1 choice)

    6 Cheese (2 choices)

    4 x 3 x ((9 x 8)/2) x 8 x 5 x ((6 x 5)/2) = 259,200

    Now maybe you can help us grapple with an even trickier question: how many of these combinations do you think are actually tasty? :-)

  2. Steve Kass Says:

    Thanks for stopping by and resolving the mystery of the pasta number, Sarah.

    As for how many of these pasta combinations are tasty? That’s an easy one for me calculate: lots and lots and lots! No mystery at all. :)

    Steve (happy subscriber of Fine Cooking since 1995)

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Breast The Journal of the National Cancer Institute just published the results of a large study evaluating the survival benefit of contralateral prophylactic mastectomy in the surgical treatment of breast cancer. In some mastectomy patients, breast cancer will reoccur in the remaining breast, and that risk can be reduced (but not eliminated) by removing the non-cancerous breast .

Contralateral prophylactic mastectomy lowers post-mastectomy five-year death rate by 30%

The five-year death rate after mastectomy was 11.5% for women who had both breasts removed. It was 16.3% for those who only had the cancerous breast removed. Adding a contralateral prophylactic mastectomy to the original surgery therefore reduced the five-year death rate from 16.3% to 11.5%. Almost a third fewer mastectomy patients died within 5 years when the had chosen to remove the second (healthy) breast, compared to mastectomy patients who had not chosen to remove the second breast. The bilateral mastectomy decreased the 5-year death rate by 29.4%.

This strikes me as a significant benefit. Suppose I have breast cancer and need a mastectomy. I can choose a single mastectomy and have a one-in-6 chance of dying in five years, or I can choose a double mastectomy and have a one-in-9 chance of dying in five years. One-in-9 sounds quite a bit better to me. If 100,000 women with unilateral cancer need mastectomies, performing 100,000 double mastectomies instead of 100,000 unilateral mastectomies will reduce the number of deaths in the first five years from 16,300 to 11,500. About 4,800 fewer women will die within five years.

Contralateral prophylactic mastectomy benefits only 5% of mastectomy patients.

The reporting of this study takes a very different viewpoint. It compares the survival rate, not the death rate, and notes that the bilateral prophylactic mastectomy increases the survival rate from 83.7% to 88.5%, “a difference of less than 5%.” Five percent sounds like a small number, but 5,000 lives saved sounds like a large number.

Point of view

Both statements (lowers by 30%; benefits only 5%) are the same. Only the intent to communicate is different. Whether prophylactic mastectomy is good practice depends not only on the change in five-year survival rate, and I don’t have more information.. For example, how does a double mastectomy (which for 95,000 of the women will not change the five-year death rate outcome) affect a woman’s well-being and general health over time? What is the cost to save these 5,000 lives, and how will the disparity of death rates change more than five years after surgery?


Good news

There is a good piece of news in the study: The study data identified a subgroup of women for whom double mastectomy had an even greater benefit: women 50 and younger with early stage estrogen receptor negative cancer. Removing the second breast had no benefit for women 60 and older, and the benefit for women in their 50s was uncertain, presumably because of the small number of bilateral mastectomies in the sample.

The journalists writing about this study generally downplayed the benefits. It would have been better for them to downplay the benefits on most of the women, but hype the discovery that there is a subgroup of women who might get a substantial benefit from this procedure. If you read the study, or find better summaries of it, you may find that this study can help patients and doctors make wise treatment choices (contralateral mastectomy sometimes among them). With luck and more studies like this, prophylactic mastectomies might in the future go only to those women whom they might help. With even more luck, we’ll improve our diagnosis and prevention of breast cancer and the number of mastectomies will go down.

One Response to “The reports say “Double Mastectomy Only Slightly Increases Breast Cancer Survival Rate”; The Numbers Say “Double Mastectomy Significantly Lowers Five-Year Death Rate.”

  1. Feminist Peace Network » Blog Archive » Breast Cancer Statistics–Understanding The Difference Between Death Rates and Survival Rates Says:

    […] can get hugely confusing to understand the various statistics in favor of one treatment or another. Steve Kass, an old high-school buddy who now happens to be a professor of mathematics has some thoughtful […]

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