Lice and good health and other spurious correlations

This has been a week for spurious correlations in the news.

Computer databases have made generating spurious correlations great sport, but no matter how real the correlations are, that doesn’t mean the variables actually affect each other. But spinning tall tales to explain correlations as causations — like ice cream sales and drownings — has become such fun, the winners of Purdue University’s Spurious Correlations Contest continue to entertain us with their creativity. This week’s spurious correlations could have been contenders.

Fun and scares with correlations

We might intellectually know that correlations don't equal causations, but it's often hard to see in practice. As Darrell Huff explained spurious correlations in How to Lie with Statistics:

Perhaps the trickiest of them all is the very common instance in which neither of the variables has any effect at all on the other, yet there is a real correlation. A good deal of dirty work has been done with this one. The poor grades among cigarette smokers is in this category, as are all too many medical statistics that are quoted without the qualification that although the relationship has been shown to be real, the cause-and-effect nature of it is only a matter of speculation.

As an instance of the nonsense or spurious correlation that is a real statistical fact, someone has gleefully pointed to this: There is a close relationship between the salaries of Presbyterian ministers in Massachusetts and the price of rum in Havana.

Permitting statistical treatment and the hypnotic presence of numbers and decimal points to befog causal relationships is little better than superstition. And it is often more seriously misleading. It is rather like the conviction among the people of the New Hebrides that body lice produce good health. Observation over the centuries had taught them that people in good health usually had lice and sick people very often did not. The observation itself was accurate and sound, as observations made informally over the years surprisingly often are. Not so much can be said for the conclusion to which these primitive people came from their evidence: Lice make a man healthy. Everybody should have them.

Readers may be old enough to remember when, with great alarm, milk was linked to certain cancers, based on a correlation between higher cancers in New England, Wisconsin, Minnesota and Switzerland, where a lot of milk was produced and consumed, compared to Ceylon, where milk was scarce. As Mr. Huff explained, to add to the panic, it was pointed out that milk-drinking English women had 18 times the risk of certain cancers compared to Japanese women at the time, who seldom drank milk. Yikes, milk must be very bad for you, indeed. It turned out, of course, that at that time in history, the highest milk drinking regions also happened to be the longest lived, and cancers are primarily diseases that strike with age.

This trick is used all the time by those looking to support fears that modern diets and lifestyles are unhealthy, compared to less developed, rural regions of the world or to the “good old days” when everyone ate home-grown foods; forgetting that life expectancies were nearly half of what our’s are today. He went on to say:

When you find somebody — usually an interested party — making a fuss about a correlation, look first of all to see if it is not one of this type, produced by a stream of events, the trend of the times. In our time, it is easy to show a positive correlation between any pair of things like these: number of students in college, number of inmates in mental institutions, consumption of cigarettes, incidence of heart disease, use of X-ray machines, production of false teeth, salaries of California school teachers, profits of Nevada gambling halls. To call some of these the cause of some others is manifestly silly. But it is done every day...

[S]cantier evidence than this — treated in the statistical mill until common sense could no longer penetrate to it—has made many a medical fortune and many a medical article in magazines, including professional ones.

Most of the most popularly celebrated relationships are spurious correlations, but it’s easier to be convinced into believing that they are scientific — and hence, have some important causal relationship — when they come from a computer and a medical journal has cited them as statistically significant.

When Michael T. Brett, Ph.D., of the Dept. of Civil and Environmental Engineering at the University of Washington, Seattle, examined four common types of statistical analyses of non-independent variables in the scientific literature, however, he found the chances of deriving spurious correlations was very large. And, “counter-intuitively, sample size [the bigger the study population] did not have a substantial impact on the average magnitude of spurious correlations,” he found. Nor were most spurious correlations the result of measurement errors.

For some reason, he concluded, the rationale behind, and the risks associated with, regression analyses [computer modeling used to identify correlations] have failed to resonate with the epidemiological community. Warnings against pseudo-replication is accepted, but not spurious correlations, even though the dangers of drawing incorrect inferences are exactly the same. “In many cases the expected spurious correlation may be so large that it will be very difficult to discern the actual magnitude of any true correlations,” he concluded.

The magnitude of a correlation is no presumption of its causation, either. Whenever we’re tempted to fall for impressive numbers, it always pays to remember that bras are associated with a 12,500 percent higher risk for breast cancer.

So, this week, we heard:

Clumsiness in childhood and obesity

Children with “body control problems” and clumsiness has been reported in the news as being associated with adult obesity. The explanation for this cruel-sounding correlation was that uncoordinated kids probably participate in less sports and are more sedentary, leading to later obesity.

People with BMIs in the obese category at age 33 were reported as being associated with a “57% higher odds ratio of having poor hand control at age seven, twice as likely to have suffered poor co-ordination and almost four times as likely to have been clumsy.”

Well, not exactly. While these spurious correlations may even appear intuitively correct, there’s more behind this story that didn’t make the news. It goes beyond the fact that just because fat kids might be associated with less sports participation, does not mean that nonsports-related activities caused their obesity.

In this case, the spurious correlations, themselves, were misinterpreted measurements. For this paper, published in this week’s online edition of the British Medical Journal, the authors used the database of the National child development study in Great Britain, which had enrolled about 17,000 babies born between March 3 and March 9, 1958. Attrition over the years left BMI data on 11,042 adults at age 33, but among these there were only childhood assessments at age 7 on 7,990 and at age 11 on 6,875 people.

At age 7, school teachers were asked to classify children with poor hand control, coordination and overall clumsiness, using rudimentary scorings of: “certainly, somewhat, no or unsure.” The correlations reported in the news were the unadjusted odds ratios. After adjusting for mental retardation, epilepsy, physical disability and other central nervous system conditions, social class, gender, maternal age, birthweight, ethnicity, smoking, and BMI at age 7, there were no tenable correlations. The teachers were most likely to (subjectively) view the fat kids as clumsy and the greatest drop in correlations occurred when BMI at age 7 was adjusted for.

At age 11, the children’s physical control scores were assessed by medical professionals. “The first test involved copying a simple design... The second test involved marking squares on paper within one minute... The third test recorded the time in seconds that it took to pick up 20 matches.” The assessments done during medical examinations showed no correlation between physical control scores in childhood and adult obesity, with adjusted odds ratios of 0.88, 0.82 and 1.09, respectively. In other words, the odds ratios all clung to either side of null (1.00). Adult obesity was associated with a 12% lower odds for poor copying design skills in childhood, 18% lower odds for poor marking squares skills in childhood, and 9% higher odds for poor skills in picking up matches in childhood — all untenable correlations. The authors noted that “body mass does not seem to directly influence physical control and coordination.”

This spurious correlation in the news turned out to not even exist.

Playground safety and fat kids

There was no study behind this second spurious correlation in this week's news. The source was a Wall Street Journal commentator who noted that reported childhood obesity rates correlated with safety warnings on playground equipment. Therefore, he concluded: “safety makes kids fat.”

The explanation he weaved went like this: today’s parents were more afraid to let their kids play in unsafe playgrounds and this risk aversion meant kids weren’t being allowed unstructured play like they were in past generations, making them fat. Of course, this spurious correlation is only believable to those who’ve fallen for the myth that children today are more slothful.

Childhood ear infections linked to obesity

This last spurious association gets the creativity prize for weaving the tallest tale, when its authors attempted to explain how an ear infection during childhood could make you fat as an adult.

This news story was another bird cage story. It came from a press release reporting on presentations at a meeting, meaning it was science by press release and there is no scientific data published in peer-reviewed journals for readers to even examine or evaluate. At the American Psychological Association’s annual convention, professors from the college of dentistry at the University of Florida presented preliminary and surprising findings of a correlation between a history of childhood middle ear infections and a 62% higher risk ratio of having a BMI in the obese category later in life. [JFS readers know that this percentage isn’t even a tenable correlation for an epidemiological data dredge, falling within random error or chance.]

The data used was almost laughably questionable: questionnaires from 6,584 attendees at some lecture, asking them to remember if they’d had ear infections as children, what foods they liked and what they weighed today. It’s doubtful such a study would even be published in a reputable medical journal, although anything’s possible anymore. Others looked at NHANES data from 1960 and purportedly found a correlation between tonsillectomies and adult overweight, and preschoolers with severe history of ear infections were reported as tending to be heavier.

Where did these researchers even get the idea for such a correlation of higher BMIs and ear infections? Perhaps, from a news story last year that had been reported as finding “childhood obesity causes ear infections.” A closer look at the study behind the news had found the authors had compared the fatter BMIs of children being seen in their ear nose and throat department to sick children in a Korean hospital!

According to New Scientist, the explanation for a causation from this week’s spurious correlation presented at the meeting was:

[I]infections damage the chorda tympani taste nerve, which is stimulated at the front of the tongue and passes through the middle ear to the brain... stimulations transmitted by the nerve may inhibit the thick, creamy tactile sensations associated with fatty foods; reduced transmission caused by nerve damage would remove this inhibition, making foods seem creamier and more pleasurable. Reduced taste sensation may also make the smell more noticeable...

Two doctors speaking for the American Academy of Otolaryngology - Head and Neck Surgery weren’t even falling for this one. Dr. John W. House, M.D., of the House Ear Institute in Los Angeles told WebMD: “We see thousands of children and adults with chronic ear infections at our clinic every year. If this association were real we would see it in our patients, but we don't.” And Dr. Barry Hirsch, M.D., FACS, of the University of PIttsburgh said the studies presented at the meeting fall short of proving a link. “It’s a big leap of faith to say from this type of research [epidemiological] that ear problems cause obesity,” he said.

But the urban legend has been born and it will likely be repeated and believed by the public for years to come. Just like the headlines today, claiming “Obesity could be caused by ear infections,” few will read the fine print or realize they’ve just heard another spurious correlation.

© 2008 Sandy Szwarc

Confirmation bias. We’re most likely to jump to conclusions from spurious correlations if they support what we’ve come to believe true. What can seem common sense logic can be quite illogical when it’s based on myths. If we believe the earth is flat, we could foolishly explain the correlation of ships lost at sea and sailing out of visible view, has having fallen off the horizon. Likewise, the damaged taste bud explanation will be most likely to be believed for the correlation between ear infections and obesity by those who mistakenly think that eating too much fattening food causes obesity and explains the natural diversity of sizes. Finally, those last two correlations only fly with those who believe the myth that children today, namely the fat ones, are more slothful.