Steve Kass

News this week of an Adderall shortage, and this report, which draws into question the widely-held belief that methamphetamines cause brain damage and cognitive impairment, prompt me to rescue an old statistical parody I wrote (and posted on my now-moribund Drew web page) in 2003, a few years before I had this soapbox. The news links above are also well worth visiting.

Cocaine’s brain effects might be long term [“news”]

Insulin’s metabolic effects might be long term [parody]

BOSTON, March 10, 2003 (UPI) — Cocaine and amphetamines
might cause slight mental impairments in abusers that
persist for at least one year after discontinuing the
drugs, research released Monday reveals.

MADISON (NJ), March 16, 2003 — Insulin might cause metabolic
disorders in abusers that persist for at least one year after
discontinuing the drug, research released Monday reveals.

However, experts outside the study said the findings were inconclusive
and pointed out although cocaine has been widely abused for decades,
impaired cognitive function is not seen routinely or even known to exist in
former abusers.

"Overall, the abusers were impaired compared to non-abusers on the function of attention and motor skills," Rosemary Toomey, a psychologist at Harvard
Medical School and the study’s lead investigator, told United Press International.

“Overall, the abusers were impaired compared to non-abusers
on tests of sugar metabolism,” Rosemary Toomey, a psychologist
at Harvard Medical School and the study’s lead investigator,
told United Press International.

Previous studies have yielded inconsistent findings on whether
cocaine abuse led to long-term mental deficits. Some studies found
deficits in attention, concentration, learning and memory six months
after quitting. But a study of former abusers who were now in prison
and had abstained from cocaine for three years found no deficit.

Few studies have looked at the long term effects of insulin
abuse, although doctors and scientists generally believe
the drug is harmful. One study of former abusers who
were now in prison and had abstained from insulin for
three years found a higher than normal death rate.

To help clarify these seemingly conflicting results, Toomey’s team,
in a study funded by the National Institute on Drug Abuse, identified
50 sets of male twins, in which only one had abused cocaine or
amphetamines for at least one year. Amphetamine abusers were
included because the drug is similar to cocaine and could have the
same long-term effects on the body.

To address the lack of careful studies, Toomey’s team, funded by
the National Institute on Drug Abuse, identified 50 sets of male
twins, in which only one had abused insulin for at least one year.

Most of the pairs were identical twins, meaning they share the exact
same genetic pattern. This helps minimize the role biological
differences could play in the findings and gives stronger support to the
mental impairments being due to drug abuse.

Most of the pairs were identical twins, meaning they
share the exact same genetic pattern. This helps minimize
the role genetic differences could play in the findings and gives
stronger support to the impairments being due to insulin abuse.

The abusers, who averaged age 46 and had not used drugs for at least
one year, scored significantly worse on tests of motor skills and
attention, Toomey’s team reports in the March issue of The Archives
of General Psychiatry.

The abusers, who averaged age 46 and had not used
insulin for at least one year, scored significantly worse
on tests of sugar metabolism, Toomey’s team reports in
the March issue of The Archives of General Metabolism.

The tests all were timed, which indicates the abusers have
"a motor slowing, which is consistent with what other investigators
have found in other studies," Toomey said.

The tests all were performed after fasting, which indicates the abusers
have “an impaired metabolism unrelated to diet, which is consistent
with the consensus in the medical community,” Toomey said.

Still, the abusers’ scores were within normal limits and they actually
performed better on one cognitive test, called visual vigilance, which
is an indication of the ability to sustain attention over time. This
indicates the mental impairment is minor, Toomey said. "In real life,
it wouldn’t be a big impact on (the abusers’) day-to-day functioning
but there is a difference between them and their brothers," she said.

The finding is significant, she added, because given that the study subjects
are twins and share the same biological make-up, they would be expected
to have about the same mental status. This implicates the drug abuse
as the cause of the mental impairment.

The finding is significant, she added, because given that the study
subjects are twins and share the same biological make-up, they would
be expected to have about the same metabolic status. This
implicates the drug abuse as the cause of the impairment.

Among the abusers, the mental test scores largely did not vary in
relation to the amount of cocaine or amphetamine used. However,
on a few tests the abusers did score better with more stimulant use.

Among the abusers, poorer test scores were consistently associated
with increased levels of insulin abuse. Among the heaviest abusers,
not one scored better than his non-abusing twin.

"The results seem to me to be inconclusive," Greg Thompson,
a pharmacist at the University of Southern California’s
School of Pharmacy in Los Angeles, told UPI.

“The results seem to me to be conclusive,” Greg Thompson,
a pharmacist at the University of Southern California’s
School of Pharmacy in Los Angeles, told UPI.

This is "because both twins are within a normal range
(and) sometimes the cocaine-abusing twin did better than the
non-abusing twin and sometimes not," Thompson said.

This is “because almost without exception, only the non-abusing
twin is within a normal range (and) the insulin-abusing twin did
worse than the non-abusing twin,” Thompson said.

In addition, cocaine has been abused by millions of people, going
back as far as the 1930s and before, he said. "You’d think you’d be
seeing this as a significant clinical problem and we are not," he said.

In addition, insulin has been abused by millions of people,
and poor sugar metabolism among former insulin abusers
has been reported by physicians going back as far as the 1930s
and before, he said. “This is a significant clinical problem,” he said.

Of more concern to Thompson is the effect stimulants such as Ritalin,
which are used to treat attention deficit disorder, are having on
children. "This would be a much bigger problem I would think if
it’s true stimulants impair cognitive function," he said.

Of more concern to Thompson is the effect daily insulin injections
are having on children. Insulin is commonly prescribed to control
diabetes (frequent urination, weight gain, and fatigue syndrome).
“Many of these children will become former insulin abusers, and
poor sugar metabolism will be a major healthcare issue for
them in the years to come,” he said.

"Before I’d worry about the 46 year-old abuser, I’d want to know about the
3 year old being treated for ADD (attention-deficit disorder)," Thompson said.

“Before I’d worry about the 46 year-old abuser, I’d want to
know about the 3 year old being treated for diabetes,” Thompson said.

NASA’s Solar Dynamics Observatory captured last week’s X1.4-class solar flare on camera. Higher resolution video and more information here.

The possible existence of heteroscedasticity is a major concern in the application of regression analysis, including the analysis of variance, because the presence of heteroscedasticity can invalidate statistical tests of significance that assume the effect and residual (error) variances are uncorrelated and normally distributed. —Wikipedia

Perhaps I’m overeager to use one of my favorite words, but the more I look at Figure 11 of The Neutrino Preprint, the more I think I see a hint of heteroscedasticity in the residuals. If present, it would support the possibility that the model used for the best fit analysis (a one-parameter family of time-shifted scaled copies of the summed proton waveform) was not appropriate. See my previous post for some background.

The figure above (which is the bottom half of Figure 11) shows the best fit of the complete summed proton waveform (red) vs. the observed neutrino counts (black), summarized using 150 nanosecond bins. For both extractions (left and right), the residuals of the fit (the distances from the red curve to each black dot) appear possibly heteroscedastic in two ways.

First, they seem to be slightly (negatively) correlated with the time scale — positive residuals are more likely towards the beginning of the pulse, negative residuals towards the end. Second, there may be a slight negative correlation of the variance of the residuals with the time scale as well. The residuals seem to become more consistent — vary less in either direction from zero — from left to right. [I didn’t pull out a ruler and calculate any real statistics.]

To be fair, there is little evidence of heteroscedastic residuals in Figure 12 (below), which shows a zoomed-in detail of the beginning and end of each extraction, summarized into 50 nanosecond bins. In all, only about a sixth of the waveform is shown at this resolution. (A data point appears to have been omitted from this figure; between the first two displayed bins in the the second extraction, there should probably be a black point to indicate that zero neutrinos were observed in that 50 ns interval.)

The authors report some tests of robustness; for example, they analyzed daytime and nighttime data separately and found no discrepancy. They also calculated and report a reduced chi-square statistic that indicates a good model fit. They may also have measured the heteroscedasticity of the residuals, but they don’t mention it.

They do say a fair bit about how they obtained the summed proton waveform (the red line) used for the fit, but so far I don’t see any indication that they considered the possibility of a systematic process occurring over the length of each proton pulse that caused the ratio of protons to observed neutrinos to vary.

Then again, I don’t understand every sentence in the paper that might be relevant, such as this one: “The way the PDF [the probability density functions for the proton waveform] are built automatically accounts for the beam conditions corresponding to the neutrino interactions detected by OPERA.” And I’m not a physicist or a statistician.

[I’ve posted a follow-up here: Heteroscedasticity in the Residuals?]

When applying statistics to find a “best fit” between your observation and reality, always ask yourself “best among what?”

The CERN result about faster-than-light neutrinos is based on a best fit. If the authors were too restrictive in their meaning of “among what,” they might have missed figuring out what really happened. And what might have really happened was that the neutrinos they detected had not traveled faster than light.

The data for this experiment was, as usual, a bunch of numbers. These numbers were precisely-measured (by portable atomic clocks and other very cool techniques) arrival times of neutrinos at a detector. The neutrinos were created by shooting a beam of protons into a long tube of graphite. This produced neutrinos, some of which were subsequently observed by a detector hundreds of miles away.

Over the course of a few years, the folks at CERN shot a total of about 100,000,000,000,000,000,000 protons into the tube; they observed about 15,000 neutrinos. The protons were fired in pulses, each pulse lasting about 10 microseconds.

A careful statistical analysis of the data, the authors report, indicates that the neutrinos traveled about 0.0025% faster than the speed of light. Whooooooosh! Furthermore, because the experiment looked at a lot of neutrinos and the results were consistent, the experiment indicates that in all likelihood the true speed of neutrinos was very close to 0.0025% faster than the speed of light, and it was almost without doubt at least faster.

If the experimental design and statistical analysis are correct (and the authors are aware they might not be, though they worked hard to make them correct), this is one of the great experiments of all time.

So far, I haven’t read much scrutiny of the statistical analysis pertaining to the question of “among what?” But Jon Butterworth of The Guardian raised one issue, and I have a similar one.

Look at the graph below, from the preprint.

The statistical analysis of the data was designed to measure how far to slide the red curve (the summed photon waveform) left or right so that the black data points (the neutron observation data) fit it most closely.

The experiment didn’t detect individual neutrinos at the beginning of the trip. The neutrons were produced by 10-microsecond proton bursts, and neutrinos were expected to appear in 10-microsecond bursts at the other end. The time between the bursts, then, should indicate how fast the individual neutrinos traveled.

To get the time between the bursts, slide the graphs back and forth until they align as closely as they can, and then compare the (atomic) clock times at the beginnings and ends of the bursts.

For this to give the right travel time, and more importantly, to be able to evaluate the statistical uncertainty, the researchers appear to have assumed that the shape of the proton burst upstream of the graphite rod exactly matched the shape of the neutrino burst at the detector (once adjusted for the fact that the detector sees about one neutrino for each 10 million billion or so protons in the initial burst).

Why should the shapes match exactly? If God jiggled the detector right when the neutrinos arrived, for example, the shapes might not match. More scientifically plausibly, though, at least to this somewhat-naïve-about-particle-physics mathematician, what if the protons at the beginning of the burst were more likely to create detectable neutrinos than those at the end of the burst? Maybe the graphite changes properties slightly during the burst. [Update: It does, but whether that might affect the result, I don’t know.] Or maybe the protons are less energetic at the end of the bursts because there’s more proton traffic.

The authors don’t tell us why they assume the shapes match exactly. There might be good theory and previous experimental results to support the assumption, but if so, it’s not mentioned in the paper. The authors do remark that a given “neutrino detected by OPERA” might have been produced by “any proton in the 10.5 microsecond extraction time.” But they don’t say “equally likely by any proton.”

If protons generated early in the burst were slightly more likely to yield detectable neutrinos, then the data points at the left of the figure should be scaled down and those at the left scaled up, if the observational data is expected to indicate the actual proton count across the burst.

If that’s the case, then the adjusted data might not have to be shifted quite so far to best match the red curve. And the calculated speed would be different.

Whether this would make enough of a difference to bring the speed below light-speed, I don’t know and can’t guess from what’s in the preprint. And of course, there may be good reasons for same-shape bursts to be a sound assumption.

[Disclaimer: I’m a mathematician, not a statistician or a physicist.]

Ten years have passed since 9/11. The New York Times put the passage of time into days, and hours, and minutes, and seconds in today’s paper. [A Day That Stands Alone]

Three-thousand six-hundred fifty-two days have now passed. At 8:46 a.m. — the time when the first plane slammed into the north tower of the World Trade Center — 87,648 hours had gone by. Another [*]  5,258,880 minutes. Another [†] 315,532,800 seconds.

For the record, 315,532,802 seconds passed between 8:46 a.m. on September 11, 2001, and 8:46 a.m. today, September 11, 2011. The missing seconds were inserted into our collective timeline by the authority of the International Earth Rotation and Reference Systems Service. One of them passed (largely unnoticed, no doubt) at 6:59:60 p.m. on December 31, 2005 (in New York City), and the other occurred at the end of 2008.

As decades go, this one was as short as they come for us, even with its two leap seconds. Many decades include not two, but three occurrences of February 29^th, and all decades beginning between 1972 and 1997 have contained more than two leap seconds in addition to the minimum‡ number of two leap year days per decade.

Nothing is simple.

Steve on the Hoboken waterfront, September 1, 2011.

* Do not be distracted in search of the anaphor. It’s missing, and the issue is not addressed here.

† Another Another is missing its anaphor. Press on, dear reader.

‡ The minimum during our lifetime. The last decade to contain only a single leap year (which was the leap year 1896) ended early in 1904, because 1900 was not a leap year, despite its divisibility by four. The next single-leap-year decade will not begin until the year 2096.

The Soda Police are getting noisier lately, but their concern for public health is a subterfuge. When it comes down to brass tacks (and I doubt brass’s slight lead content is going to kill you when used judiciously in plumbing, by the way), the S.P. don’t care most about the public health or about overweight kids at risk for diabetes and heart disease. They’re hell-bent on demonizing soda, especially soda made by Big Food and sold by the Big Chain Store and Restaurant Corporation.

Demon or not, it probably won’t hurt Americans to drink less soda on average than we do now. It will definitely help the environment if we drink less of anything that comes in individual single-use containers — even water — if there’s an environmentally friendly alternative already in place.

Here’s a simple two-part proposal to bring back running water.

BBRW Part 1. Require public water fountains everywhere.

Schools, parks, subway stations, airports, shopping centers, offices, stores, and more. We already require a lot of things, sensible and otherwise, so the means is in place. Require enough of them so no one has to wait in line. These water fountains (bubblers in Wisconsin and parts of New England) should have good water pressure, and they should be designed so they can fill up a bottle, too — or there should be some faucets for that. Simply making it possible to fill a personal water bottle in an airport — and yes, you can carry one through security so long as it’s empty — will reduce heart disease.

No flow restrictors, either; use spring-loaded knobs to conserve. (I’m not going to say a word about those infrared hand-wavy travesties.) Restrictors belong in kitchens and showers, if anywhere. It doesn’t need to take ten minutes to deliver half a cup of water. ADA compliant, but otherwise basic and solid. Call me nostalgic, but I like porcelain-coated cast iron.

Room-temperature, pure water is already available from every municipal water system. Only a little effort makes it ubiquitous. (If you’re afraid it will give you cancer, carry your own personal PET-free container full of home-purified water.)

BBRW Part 2. Require water to be available everywhere soda is available, for less.

If a restaurant offers a meal that includes soda, require it to offer the same meal with the same size tap water for less money. Less by at least half the restaurant’s own à la carte price for the included soda. Except during water emergencies, require restaurants to offer tap water when patrons are seated.

Stop the endless debates over soda vs. fruit juice, sugar versus high-fructose corn syrup, artificially-sweetened beverages vs. sugary ones, and aspartame vs. stevia extract. Bring back running water.

While I was initially drawn to this 2008 New York Times article by the phrase “Male and female sand dollars,” I’m certain that “fish mucus split” will be what sticks.

Even today, some things are worth repeating. Fish mucus split.

Year after year, thousands of Americans are devastated to discover that their community has been stricken by a disease cluster. Some rare and frightening disease of unknown cause has visited their community like a plague. Residents are afflicted at rates many times the national average.

Despite years of study, billions of dollars, massive lawsuits and at least two Hollywood movies, little progress has been made towards understanding, let alone preventing, disease clusters.

The general public continues to suspect and blame environmental causes, especially chemicals with names that are hard to pronounce. The real reason for most disease clusters is likely something else.

Math.

Yes, math. Look at this map.

This map shows the 2009 rate of aleatorum gravis, an emerging and debilitating disease that currently affects only one American in 5,000. In some communities, however, the disease is rampant. Counties with rates more than five times the national average are shaded in red, and those with more than twice the national rate are shown in the darkest shade of green. [Click on the image or here for the full U.S. map.]

Nebraska.

Clusters of a. gravis are concentrated in the nation’s heartland, especially Nebraska and neighboring states. Why? If you wanted, you could look for and find potential causes alarmingly close to each cluster. A gas pipeline, a chicken farm, a power plant, a landfill. Or you could have a lawyer look for you.

Look as hard as you want, but the fact is that the cause of these disease clusters is mathematics. There is no such thing as a. gravis. The map shows the result of randomly giving each U.S. resident the disease with a 1-in-5,000 chance. (Mathematica notebook and links to population and geographic data files available on request.)

Math, indomitable math, caused these clusters.

Randomness.

Cases of non-communicable disease come in clusters just by chance. So do bags of M&Ms that have more blues than average, but it’s hard to drum up fear about them. Randomness and uniformity are not the same thing.

By chance alone, some counties will end up with higher rates of any randomly-occurring disease than other counties. The Central Limit Theorem proves it. Which counties is anyone’s guess, but because of the Law of Large Numbers (not subject to repeal), small counties are more likely than large ones to end up with unusually high (or low) rates. Sanity check: When was the last time you read about a disease cluster the size of a large city, as opposed to a census tract, county, or neighborhood?

Science.

Do some diseases have non-random environmental causes? Sure. Cholera, to give a famous example. That’s why local and national governmental agencies like the CDC and the National Cancer Institute take reports of disease clusters seriously. But the good scientists there also understand the math, and I trust their advice about public health policy more than what I hear on the local newscast, on Oprah, or from yet another celebrity non-scientist.

Reminder: John Snow was a scientist. (He also drew a map to make his point, which was a darn good idea.)

By the way, you don’t even have to be in a red county to jump on the bandwagon of fear and woo. You can still decide your neighborhood is a disease cluster (when it’s not), get everyone riled up, and make a scary video. Or you can write for a shameful woo-purveying media giant. For free. Specifically, the one behind the recent stench of pseudoscience in the air about disease clusters, and who’s getting no link from here. If the miasma theory of disease were true, scientists would be dropping like flies from what they read.

Pseudoscience and pandering to unjustified fear waste society’s resources and sidetrack scientists from research that might make the world a better and less scary place.

Via Alan Boyle of Cosmic Log: this has to be embarrassing.

You create the first synthetic life form. You thoughtfully encode in its DNA wise words from three giants of literature and science: Joyce, Oppenheimer (quoting Felix Adler), and Feynman.

And you get one of the quotes wrong.

At least you can fix it. Imagine if there had been a typo on the Golden Record. Or if you’d flubbed the first words ever spoken from someone standing on the surface of the moon.

(I remember very well being befuddled when I heard Neil’s flub live – well, give or take a second or so, though this calculation is wrong – and I remained befuddled when I read it the next day, and I was unconvinced by the initial explanation a couple of weeks later.)

[To decode this post’s title, use the DNA decoding table here.]