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  <title>health | Two 〈Foo〉s Walk into a 〈Bar〉</title>
  
  <updated>2011-05-08T19:50:00-05:00</updated>
  <author>
    <name>Chris Povirk</name>
    <email>beigetangerine@gmail.com</email>
    <uri>http://twofoos.org/</uri>
  </author>
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  <rights>Copyright © 2003–2015 Chris Povirk.  All Rights Reserved.</rights>
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<entry>
    <updated>2011-05-08T19:50:00-05:00</updated>
    <summary>
            New: If corn had no calories, how much could you eat per day before it made you sick?  How much are you eating now?</summary>
    <title type="xhtml">
      <div xmlns="http://www.w3.org/1999/xhtml">Too Much Corn</div>
    </title>
    <link rel="alternate" type="application/xhtml+xml" href="http://twofoos.org/content/too-much-corn/#update_2011-05-08T19:50:00-05:00"/>
    <id>http://twofoos.org/content/too-much-corn/#update_2011-05-08T19:50:00-05:00</id>
    <category term="health"/>
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      <div xmlns="http://www.w3.org/1999/xhtml">
        <strong>initial posting</strong>
        <div>

    <xhtml:h3>How much is too much?</xhtml:h3>
    <div>

    <p>
    I'm not fully convinced that it's possible to eat "too much" of certain foods (barring forced overfeeding), but it's clearly true of many foods, even some very healthy ones.  One staple food that was sometimes overconsumed was corn.  Setting aside the question of whether corn is "very healthy" on net, we can say that eating too much (at least, without traditional preparation methods) can cause <a href="http://en.wikipedia.org/wiki/Pellagra">pellagra</a>.  With modern, niacin‐fortified diets, we can eat corn without fear of pellagra, but presumably the level of safe consumption still has <em>some</em> upper bound.
    </p>

    <p>
    In a trivial sense, you're eating "too much corn" if you eat so much that there's no room for other foods needed to supply nutrients lacked by corn.  But let's suppose that corn had no calories so that you could eat as much other food as you needed to avoid basic deficiencies.  Still, I propose that it's probably possible to eat too much corn.  Maybe it has trace amounts of poisons (like mercury in fish?).  How much would you need to eat before they (or some other constituents) cause problems?
    </p>

    <p>
    We'll suppose that you eat corn every day.  How many ears sounds like too many? ten a day? twenty? thirty, day in and day out, every day of your life?  Let's go with thirty and see where that leads us.
    </p>

    <p>
    <a href="http://nutritiondata.self.com/facts/vegetables-and-vegetable-products/2424/2">One ear of corn contains 213 mg of omega‐6 fatty acids and 2.3 g of sugar.</a>  It contains a lot of other things, but let's focus on those two because they are frequently demonized.  That demonization is partly on the basis that both are regarded as "empty calories" added to many foods, but we're discounting calories, so we'll focus on the idea that the substances themselves are blamed for various ills (inflammation, tooth decay, etc.).  Perhaps some of our assumed negative effects would be produced by these two substances.
    </p>

    <p>
    Luckily, none of us eat thirty ears of corn per day.  Probably none of us have eaten thirty ears of corn in a single day even once.  So we're out of the woods.
    </p>

    </div>

    <xhtml:h3>Thirty ears of corn</xhtml:h3>

    <div>

    <p>
    ...unless we eat anything with corn in it.  But even if we count the chicken‐corn soup from lunch, we're nowhere near thirty ears.  If we want to hit our "goal," we're going to need to refine the corn.
    </p>

    <p>
    <a href="http://nutritiondata.self.com/facts/fats-and-oils/580/2">1 T of corn oil contains 7224 mg of omega‐6 fatty acids.</a>  1 T isn't that much in the context of a meal:  It's about 120 calories.  Using corn oil in your daily cooking could easily get you many times that, not even counting what's added to prepared foods you purchase.
    </p>

    <p>
    <a href="http://nutritiondata.self.com/facts/foods-from-mcdonalds/6298/2">A 32‐oz Coke contains 85.4 g of sugar.</a>  Not everyone drinks a 32‐oz Coke every day, but the average amount of added sugar in the US diet is usually estimated in this range, so most of us are getting that amount in some form (plus, of course, whatever sugar we get in whole foods).
    </p>

    <p>
    Now for the math: Let's assume that we can extract every bit of sugar and fat from an ear of corn.  (<a href="http://www.corn.org/wp-content/uploads/2009/12/CornOil.pdf">Modern extractors use hexane to harvest about 95 percent of the oil.</a>  I couldn't find numbers for <a href="http://www.sweetsurprise.com/learning-center/hfcs-vs-sugar/manufacturing">the sugar extraction process</a>, but the linked page quotes a 90% number for beet molasses, so it's at least plausible that the percentage is similarly high for corn.)  How many ears of corn had to die for my tablespoon of oil and my large Coke?
    </p>

    <ul>
    <li>Omega‐6: 7224 ÷ 213 = 33.9 ears of corn</li>
    <li>Sugar: 85.4 ÷ 2.3 = 37.1 ears of corn</li>
    </ul>

    <p>
    That's over thirty ears of corn for either of the two.  In the case of the Coke, this comes out to more than one ear of corn per ounce.
    </p>

    </div>

    <xhtml:h3>Conclusion</xhtml:h3>
    <div>

    <p>
    We can only guess what part of our thirty ears of corn a day would kill us.  Omega‐6 and sugar sound like decent guesses, and it would't help if we stripped out most of the vitamins and minerals (oil retains some but only a small amount), converted some of the fat to <i>trans</i> fat, and oxidized the oil by heating it during cooking.
    </p>

    <p>
    Fortunately, nobody eats thirty ears of corn a day, much less under those conditions....
    </p>

    </div>

  </div>
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    </content>
  </entry><entry>
    <updated>2011-05-07T15:45:00-05:00</updated>
    <summary>
            New: "Overweight was associated with a slight reduction in mortality (−86 094 deaths; 95% CI, −161 223 to −10 966) relative to the normal weight category."  Really?  (I have no idea, but here are some numbers.)</summary>
    <title type="xhtml">
      <div xmlns="http://www.w3.org/1999/xhtml">BMI vs. Mortality</div>
    </title>
    <link rel="alternate" type="application/xhtml+xml" href="http://twofoos.org/content/bmi-mortality/#update_2011-05-07T15:45:00-05:00"/>
    <id>http://twofoos.org/content/bmi-mortality/#update_2011-05-07T15:45:00-05:00</id>
    <category term="health"/>
    <content type="xhtml" xml:base="http://twofoos.org/">
      <div xmlns="http://www.w3.org/1999/xhtml">
        <strong>initial posting</strong>
        <div>

    <xhtml:h3>Introduction</xhtml:h3>
    <div>

    <p>
    The paper <a href="http://americandreamcoalition-org.adcblog.org/safety/JAMA_flegal.pdf">"Excess deaths associated with underweight, overweight, and obesity"</a> examines the association between body mass index and total mortality.  It, like some other studies, finds that a BMI in the "overweight" range associates with fairly low mortality.  In fact, "overweight was associated with a slight reduction in mortality (−86 094 deaths; 95% CI, −161 223 to −10 966) relative to the normal weight category."  This contrasts with statements like <a href="http://apps.who.int/bmi/index.jsp">"the increasing prevalence of overweight and obesity is associated with many diet‐related chronic diseases including diabetes mellitus, cardiovascular disease, stroke, hypertension and certain cancers."</a>  To put the debate in oversimplified terms, we have "becoming overweight is healthy" versus "becoming overweight is unhealthy."  We could look at ways to resolve these claims:
    </p>

    <ul>
      <li>The formula for BMI, which takes into account only height and weight, may not measure "fatness" as well as other measurements, like waist circumference or waist‐to‐hip ratio.</li>
      <li>Even ignoring that, the cutoffs between the BMI categories may be misaligned:  Maybe "fatness" doesn't appear until a BMI of 27, rather than 25.</li>
      <li>Maybe people in the overweight category suffer from more non‐fatal health problems than those in the normal category.</li>
      <li>Maybe the overweight would suffer more deaths, too, if not for medical treatment, which they may be more likely to seek out or which doctors may be more likely to recommend.</li>
      <li>The people used in this study might not be representative of you or of the world at large.</li>
      <li>The BMI measurements in this study were done only at the beginning of the study.  People's BMIs surely changed as time went by.</li>
      <li>And, of course: correlation is not causation.</li>
    </ul>

    <p>
    At the moment, I'm not interested in any of that.  What I am interested in is how the numbers were arrived at.  One challenge in this kind of study is adjusting for confounding factors.  Do people gain weight as they age?  If so, if an old, overweight person dies, is it because of his age, his weight, or some interaction between them that neither would produce on its own?  Do men weigh more than women?  Does smoking reduce weight?  To adjust for some of these factors, the model in the "Excess deaths..." paper includes BMI, sex, smoking status, race, and alcohol consumption.
    </p>

    <p>
    Knowing this, we have to be careful in interpreting the results.  Such a model could show, hypothetically, that, while overweight men die more often than those of normal weight, many of the overweight are alcoholics, and the likely cause of their deaths is alcohol, not weight.  This doesn't change the fact that, given two men of the same age and BMI, the one with the higher BMI is more likely to die.  And the model doesn't contradict that.  Indeed, there's nothing wrong with such a model; the question is how we interpret it.
    </p>

    <p>
    My questions was, without these adjustments, do the results come out the same?  Is overweight really associated with a longer life, or does that association hold only for (roughly speaking) "overweight resulting from causes other than alcohol?"  (To be fair, on the other side, some people avoid being overweight partially due to smoking.)  I downloaded some of the same data used by the "Excess deaths..." study to find out.
    </p>

    <p>
    This left me with a decision: What factors <em>do</em> I adjust for?  I ended up leaving in two factors, sex and age, on the theory that weight may affect the sexes differently and that low weight may be more hazardous among the old.  You could also rationalize this choice by saying that these two factors, unlike smoking and alcohol use, aren't under the subject's control.  This justification would argue for including race as a factor, but I did not, largely because I didn't want to attempt too complex an analysis and, compared to sex and age, I assumed that the effects of weight changes were least likely to vary by race.  (I have no evidence for this assumption.)
    </p>

    </div>

    <xhtml:h3>Disclaimer</xhtml:h3>
    <div>
    <p>
    I am not qualified to perform a good statistical analysis.  I did this because I was curious about possible alcohol‐weight confounding, but it may not address even that issue competently.
    </p>
    </div>

    <xhtml:h3>Results</xhtml:h3>

    <div>
    <p>
    Before we get to the final charts, here's a table that takes only sex and BMI into account, ignoring age:
    </p>

    <table>
      <tr>
        <th>Weight class</th>
        <th>Male death %</th>
        <th>Female death %</th>
      </tr>
      <tr>
        <th>underweight</th>
        <td>34.7</td>
        <td>39.1</td>
      </tr>
      <tr>
        <th>normal</th>
        <td>32.2</td>
        <td>21.8</td>
      </tr>
      <tr>
        <th>overweight</th>
        <td>27.7</td>
        <td>24.5</td>
      </tr>
      <tr>
        <th>obese</th>
        <td>27.3</td>
        <td>22.1</td>
      </tr>
    </table>

    <p>
    On to the charts.  The lines estimate, for each weight class, how much more or less likely a member of that weight class is to have died than average for that sex and age.
    </p>

    <img src="/resources/men-bmi-mortality.png" alt=""/>
    <img src="/resources/women-bmi-mortality.png" alt=""/>

    <p>
    Technical digression: You may notice that the men's chart between 70 and 80 has all negative values.  This is obviously bogus.  It's an artifact of the way I did the analysis, finding a best‐fit line for each of the weight classes individually and then another best‐fit line for their aggregate.  The cutoff points used for the various best‐fit lines are not necessarily the same, so, for example, the age‐71 estimate for all men is an estimate designed for both the 71‐ and 72‐year‐old men in the sample, while the age‐71 estimates for three of the four weight classes are designed only for 71‐year‐olds.  Thus, we can't just combine the four weight classes' estimates for age 71 and <em>sometimes</em> 72 to compute the aggregate estimate for ages 71 and 72 <em>total</em>.  If the negative numbers feel wrong to you, then focus on the <em>differences</em> between the classes at each point.  The highest line is still the weight class with the highest estimated risk at that age.  I could instead have graphed the <em>absolute</em> risk estimates for each class; the result would be that, at each age, all data points would be shifted upward by the average mortality at that age.  In such a chart, however, the large range of values and the constant shifting of the baseline make it difficult to compare among weight classes, so I've chosen the imperfect charts above.
    </p>
    </div>

    <xhtml:h3>Conclusions</xhtml:h3>
    <div>
    <p>
    Mortality among the overweight does appear at least as good as that among those of normal weight, as the more advanced analysis in the paper showed.  My fears that alcohol intake made overweight look less dangerous are allayed.
    </p>

    <p>
    More generally, the associations from the paper (looking exclusively at its NHANES III data, the only data with available publicly mortality information) seem to hold up, with only underweight showing an clear association with mortality.   Even then, the difference in mortality between the lowest‐risk group in an age range and the highest‐risk group (often reflecting changes of 50 or more pounds) maxes out at approximately an extra 0.3% chance of death over the approximately 15‐year range of the study.
    </p>

    <p>
    I refer back to my earlier list of caveats, though, when it comes to drawing conclusions beyond "<i>x</i> is associated with <i>y</i>."
    </p>

    </div>

    <xhtml:h3>Analysis Program</xhtml:h3>

    <div>

    <p>
    I don't expect for anyone to want to try this out himself, but I'm posting the details here in something akin to Linus Torvalds's <a href="http://en.wikiquote.org/wiki/Linus_Torvalds">"real men" backup strategy</a>:
    </p>

    <xhtml:h4>Data and Code</xhtml:h4>

    <div>
    <ul>
      <li><a href="ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/nhanes/nhanes3/1A/adult.dat"><code>adult.dat</code></a> (<a href="ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/nhanes/nhanes3/1A/ADULT-acc.pdf">documentation</a>)</li>
      <li><a href="ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/datalinkage/linked_mortality/nhanes3_mort_public_use_2010.dat"><code>mort.dat</code></a> (<a href="http://www.cdc.gov/nchs/data/datalinkage/nh3_file_layout_public_2010.pdf">documentation</a>)</li>
      <li><a href="/resources/bmiagesex.scripts.tar.gz"><code>bmiagesex.scripts.tar.gz</code></a></li>
    </ul>
    </div>

    <xhtml:h4>Instructions</xhtml:h4>
    <div>
    <p>
    Run <code>excess.sh</code>; you'll need the data files (named as shown above) in <code>../data</code>, a <code>wekaisotonic</code> script to run Weka's <code>weka.classifiers.functions.IsotonicRegression</code> classifier, and various Unix commands.  It will take about a minute to run, and it will generate a bunch of files, culminating in <code>male.excess</code> and <code>female.excess</code>.
    </p>
    </div>

    </div>

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