Chance News 42

Quotation

No one can possibly win at roulette unless he steals money from the table while the croupier isn't looking. — Albert Einstein

Forsooth

"The potential public health benefits are huge" according to Dr. Paul M. Ridker lead author of The Jupiter Study referring to Crestor, a statin drug used to lower the risk of heart disease. "It's a breakthrough study. It's a blockbuster. It's absolutely paradigm-shifting" says Dr. Steven E. Nissen of the Cleveland Clinic who was not involved in the two-year study which consisted of about 18,000 people randomly assigned either to Crestor or to a placebo.

On the other hand, from Dr. Sidney M. Wolfe of Worst Pills, Best Pills, Crestor "can cause potentially serious kidney toxicity that is not seen with other cholesterol-lowering drugs, and it is the only drug of its type that caused rhabdomyolysis, a life-threatening adverse muscle reaction...there is no medical reason for you to be taking Crestor when there are three safer drugs on the market for reducing cardiovascular events."

Submitted by Paul Alper

How People Are Fooled by Ideomotor Action

Ray Hyman, as quoted here.

Some years ago I participated in a test of applied kinesiology at Dr. Wallace Sampson's medical office in Mountain View, California. A team of chiropractors came to demonstrate the procedure. Several physician observers and the chiropractors had agreed that chiropractors would first be free to illustrate applied kinesiology in whatever manner they chose. Afterward, we would try some double-blind tests of their claims.

The chiropractors presented as their major example a demonstration they believed showed that the human body could respond to the difference between glucose (a "bad" sugar) and fructose (a "good" sugar). The differential sensitivity was a truism among "alternative healers," though there was no scientific warrant for it. The chiropractors had volunteers lie on their backs and raise one arm vertically. They then would put a drop of glucose (in a solution of water) on the volunteer's tongue. The chiropractor then tried to push the volunteer's upraised arm down to a horizontal position while the volunteer tried to resist. In almost every case, the volunteer could not resist. The chiropractors stated the volunteer's body recognized glucose as a "bad" sugar. After the volunteer's mouth was rinsed out and a drop of fructose was placed on the tongue, the volunteer, in just about every test, resisted movement to the horizontal position. The body had recognized fructose as a "good" sugar.

After lunch a nurse brought us a large number of test tubes, each one coded with a secret number so that we could not tell from the tubes which contained fructose and which contained glucose. The nurse then left the room so that no one in the room during the subsequent testing would consciously know which tubes contained glucose and which fructose. The arm tests were repeated, but this time they were double-blind -- neither the volunteer, the chiropractors, nor the onlookers was aware of whether the solution being applied to the volunteer's tongue was glucose or fructose. As in the morning session, sometimes the volunteers were able to resist and other times they were not. We recorded the code number of the solution on each trial. Then the nurse returned with the key to the code. When we determined which trials involved glucose and which involved fructose, there was no connection between ability to resist and whether the volunteer was given the "good" or the "bad" sugar.

When these results were announced, the head chiropractor turned to me and said, "You see, that is why we never do double-blind testing anymore. It never works!" At first I thought he was joking. It turned it out he was quite serious. Since he "knew" that applied kinesiology works, and the best scientific method shows that it does not work, then -- in his mind -- there must be something wrong with the scientific method. This is both a form of loopholism as well as an illustration of what I call the plea for special dispensation. Many pseudo- and fringe-scientists often react to the failure of science to confirm their prized beliefs, not by gracefully accepting the possibility that they were wrong, but by arguing that science is defective.

Submitted by Steve Simon

Vitamin Supplements

Chances are that the person next to you is currently taking vitamin C and/or vitamin E supplements in the belief that the vitamins are efficacious, or at the very least, not harmful. Unfortunately, that belief is now strongly challenged as can be seen in the article by Susan Jeffrey in Medscape Medical News. (To see this article put "vitamin c vitamin e jeffrey" in Google). She refers to an article in the Journal of the American Medical Association, November 12, 2008 by Dr. J. Michael Gaziano and Dr. Howard D. Sesso, et al

The objective of the study was “To evaluate whether long-term vitamin E or vitamin C supplementation decreases the risk of major cardiovascular events among men.” This “Physicians' Health Study II was a randomized, double-blind, placebo-controlled factorial trial of vitamin E and vitamin C that began in 1997 and continued until its scheduled completion on August 31, 2007. There were 14 641 US male physicians enrolled, who were initially aged 50 years or older, including 754 men (5.1%) with prevalent cardiovascular disease at randomization.” This study was done entirely by mail; the cost was roughly $120 to $130 per person per year.

This 2x2x2x2 factorial trial compared vitamin E with a placebo, vitamin C with a placebo or a multivitamin with a placebo. “The primary end point was a composite of major cardiovascular events, including nonfatal MI, nonfatal stroke, and cardiovascular disease death.” According to Gaziano, vitamin E –vs-placebo comparison had “virtually superimposable” curves. Likewise, almost identical outcomes for vitamin C-vs. placebo. Moreover, while “Neither vitamin E nor vitamin C had any effect on total mortality,” the “treatment with vitamin E was associated with an increased risk for hemorrhagic stroke, although the association was only marginally significant.”

Discussion

1. Dr. Barbara V. Howard, the current chair of the American Heart Association Council on Nutrition, commented that “people don’t eat a nutrient, they eat food.” She also said, “in these hard economic times, maybe we can save some money and not buy these supplements.” Annette Dickinson, a former president of a supplement industry group, says that more research is needed to determine whether a higher dose or different form of vitamin E would be more effective. Compare and contrast those two views.

2. There were roughly 120,000 person years of study. Calculate the approximate cost.

3. The sample consisted entirely of male physicians as did a previous study decades ago regarding aspirin as a means of preventing heart attacks. Why were physicians chosen for the trials? Women objected to the conclusions of that aspirin study. Why? Should they object to the vitamin C/vitamin E conclusions?

4. Most physicians are (still) white. Should the conclusions apply to non-white ethnic groups?

5. Study after study fails to show benefits from supplements, yet the supplement industry is booming. For example, there is a fourth cohort to this study, beta carotene vs placebo, which was reported in 2003 and showed no benefit from beta-carotene supplements. In addition, using the same patients, Gaziano and Sesso looked at whether vitamin C and/or vitamin E affects cancer here. "The researchers said the results showed that vitamin E did not have a significant effect on prostate cancer, and both vitamin E and vitamin C showed a similar lack of effect on cancer overall." Further, Gaziano said that this long term study showed that: "Individual vitamin supplements such as vitamin E and C do not appear to provide the same potential advantages as vitamins included as part of a healthy, balanced diet." Explain this phenomenon whereby scientific studies indicate no benefit but the public keeps on purchasing supplements.

6. The tables below are taken from Jeffrey's summary of JAMA article.

Physicians' Health Study II: Outcomes With Vitamin E vs Placebo

End Point	Hazard Ratio (95% CI)	P
Composite primary end point	1.01 (0.90 – 1.13)	.86
Total MI	0.90 (0.75 – 1.07)	.22
Total stroke	1.07 (0.89 – 1.29)	.45
Cardiovascular mortality	1.07 (0.90 – 1.28)	.43

Physicians' Health Study II: Outcomes With Vitamin C vs Placebo

End point	Hazard Ratio (95% CI)	P
Composite primary end point	0.99 (0.89 – 1.11)	.91
Total MI	1.04 (0.87 – 1.24)	.65
Total stroke	0.89 (0.74 – 1.07)	.21
Cardiovascular mortality	1.02 (0.85 – 1.21)	.86

Physicians' Health Study II: Total Mortality With Vitamin E and Vitamin C vs Placebo and Hemorrhagic Stroke With Vitamin E vs Placebo

End Point	Hazard Ratio (95% CI)	P
Total mortality with vitamin E vs placebo	1.07 (0.97 – 1.18)	.15
Total mortality with vitamin C vs placebo	1.07 (0.97 – 1.18)	.16
Hemorrhagic stroke with vitamin E vs placebo	1.74 (1.04 – 2.91)	.04

Why do these tables of odds-ratios support Gaziano's comments pertaining to vitamin C and vitamin E regarding cardiovascular mortality, total mortality and hemorrhagic stroke?

Submitted by Paul Alper

Googling an epidemic

Google Uses Searches to Track Flu’s Spread. Miguel Helft, The New York Times, November 11, 2008.

When people start to get sick, many of them go to the Internet for help. Some of them will do a web search on a phrase lie "flu symptoms" on Google. If there is a sudden surge in these searches, you might be able to notice a flu outbreak faster than standard epidemiologic methods for tracking epidemics. Google has packaged such a system on their website and calls it "Flu Trends."

The Centers for Disease Control and Prevention use a more traditional method for tracking epidemics, which is slower because

they rely on data collected and compiled from thousands of health care providers, labs and other sources.

The concept has been validated using data from a rival search engine, Yahoo. Google hopes to extend this from the United States to a worldwide system and track other diseases as well.

There is potential even beyond disease tracking.

Researchers have long said that the material published on the Web amounts to a form of “collective intelligence” that can be used to spot trends and make predictions.

But the data collected by search engines is particularly powerful, because the keywords and phrases that people type into them represent their most immediate intentions. People may search for “Kauai hotel” when they are planning a vacation and for “foreclosure” when they have trouble with their mortgage. Those queries express the world’s collective desires and needs, its wants and likes.

Internal research at Yahoo suggests that increases in searches for certain terms can help forecast what technology products will be hits, for instance. Yahoo has begun using search traffic to help it decide what material to feature on its site.

Some privacy advocates have raised concerns about this system, but it reports a single aggregate number for each state.

Submitted by Steve Simon

Questions

1. The data from Google searches is not in any sense a random sample. What potential biases can be caused by this non-random sample? Are there any ways to adjust or control for these biases?

2. What other trends might be easily tracked using search data from Google or Yahoo?

We're Down $700 Billion. Let's Go Double or Nothing!

How the financial markets fell for a 400-year-old sucker bet.
Slate Magazine,Oct. 2, 2008
Jordan Ellenberg

Jordan begins with:

Here's how to make money flipping a coin. Bet 100 bucks on heads. If you win, you walk away $100 richer. If you lose, no problem; on the next flip, bet $200 on heads, and if you win this time, take your $100 profit and quit. If you lose, you're down $300 on the day; so you double down again and bet $400. The coin can't come up tails forever! Eventually, you've got to win your $100 back.

This doubling game, sometimes called "the martingale," offers something for nothing—certain profits, with no risk. You can see why it's so appealing to gamblers. But five more minutes of thought reveals that the martingale can lead to disaster. The coin will come up heads eventually—but "eventually" might be too late. Most of the time, one of the first few flips will land heads and you'll come out on top. But suppose you get 11 tails in a row. Just like that, you're out $204,700.* The next step is to bet $204,800—if you've got it. If you're out of cash, the game is over, and you're going home 200 grand lighter.

But wait a minute, maybe somebody will loan you the $200,000 you need to stay in the game. After all, you've got a great track record; up until this moment, you've always ended up ahead! If people keep staking you money, you can just keep betting until, eventually, you win big time.

Of course Jordan does not claim that the current stock financial problems are due to "the martingale" but rather writes:

The carefully synthesized financial instruments now seeping toxically [sic] from the hulls of Lehman Bros. and Washington Mutual are vastly more complicated than the martingale. But they suffer the same fundamental flaw: They claim to create returns out of nothing, with no attendant risk. That's not just suspicious. In many cases, it's mathematically impossible.

Jordan has much more to say and we recommend your reading the whole article.

We shall add some of our own comments.

A stochastic process is a sequence of random variables x(0), x(1), x(2), .... A martingale is stochastic process for which the expected value of x(n+1), given all the previous outcomes, is equal to the x(n). As such it can be thought of as representing a fair game. The coin toss martingale described above is a martingale in this sense.

For a stochastic process representing a game, it is natural to ask if there is an optimal stopping rule. For such a stopping rule the decision to stop at time n must depend only on the outcomes of the previous plays--no clairvoyance. Doob proved that, if a stochastic process x(0), x(1),x(2) ... is a martingale with values bounded by a number B, then there is no stopping rule with expected winning greater than the expected value of x(0). For the coin tossing martingale this would not be true if we could continue to play forever but then Doob's bounded condition is not satisfied.

Additional Reading

The Wizard of Oz

Ian Sharpe

Submitted by Laurie Snell

Failure of Statistical Literacy

The following is an illustration of the failure of statistical literacy. Two items appeared in the Minneapolis Star Tribune on November 25, 2008. The first was a reprint of a NYT article of Gina Kolata. She was reporting on an important study which purported to show that some invasive cancers can go away on their own. The Star Tribune, probably because of space limitations, duly copied the first half of her article; it ended with how many woman were in each arm of the study but cut out the second half of the article which dealt with the results pertaining to the number of cancers thus, leaving the reader completely in the dark.

The other item--which appeared in many other newspapers--was an AP dispatch which indicated that “taking a nap may boost a sophisticated kind of memory that helps us see the big picture and get creative.” According to the dispatch, “First, they taught 20 English-speaking college students lists of Chinese words spelled with two characters — such as sister, mother, maid. Then half the students took a [90 minute nap] nap.” Next, “Upon awakening, they took a multiple-choice test of Chinese words they'd never seen before. The nappers did much better at automatically learning that the first of the two-pair characters in the words they'd memorized earlier always meant the same thing — female, for example. So they also were more likely than non-nappers to choose that a new word containing that character meant ‘princess’ and not ‘ape’ than those who did not nap.”

Nowhere do we find any numbers (even average is missing, let alone any hint of variation) to justify “The nappers did much better.” Nor do we know if the subjects were randomized. About all we know for sure is that they are college students and there were 10 (!) in each group.

Discussion

1. The full Kolata article refers to an investigation by Dr. H. Gilbert Welch, Dr. Per-Henrik Zahl and Dr Jan Maehlen which will be published in the Archives of Internal Medicine. They studied 109,784 Norwegian women from 1992 to 1997 who did not use mammography screening because Norway did not initiate it until 1996. The other group of 119,472 Norwegian women were followed from 1996 to 2001 who did have mammography screening.

http://www.dartmouth.edu/~chance/forwiki/42.jpg

The major assertion is

“It might be expected that the two groups would have roughly the same number of breast cancers, either detected at the end or found along the way. Instead, the researchers report, the women who had regular routine screenings had 22 percent more cancers. For every 100,000 women who were screened regularly, 1,909 were diagnosed with invasive breast cancer over six years, compared with 1,564 women who did not have regular screening. There are other explanations, but researchers say that they are less likely than the conclusion that the tumors disappeared. The most likely explanation, Dr. Welch said, is that ‘there are some women who had cancer at one point and who later don’t have that cancer.’” Kolata quotes other experts who vehemently disagree and defend routine mammography. Read Kolata’s article and compare the reasoning used by either side. In particular, check on what axes the individuals have to grind. For example, look up Welch’s previous writings regarding screening.

2. Why is this napping study trivial in comparison to the cancer study? Why did the napping study receive so much ink? What statistical modifications could be made to the napping study which would improve it?

Submitted by Paul Alper

Two great lossses to probability and statistics

Kioshi Ito died November 10. He was one of the great probabilists of our time. You can read about his work here including this wonderfull commentary he wrote on the beauty of mathematics:

In precisely built mathematical structures, mathematicians find the same sort of beauty others find in enchanting pieces of music, or in magnificent architecture. There is, however, one great difference between the beauty of mathematical structures and that of great art. Music by Mozart, for instance, impresses greatly even those who do not know musical theory; the cathedral in Cologne overwhelms spectators even if they know nothing about Christianity. The beauty in mathematical structures, however, cannot be appreciated without understanding of a group of numerical formulae that express laws of logic. Only mathematicians can read "musical scores" containing many numerical formulae, and play that "music" in their hearts. Accordingly, I once believed that without numerical formulae, I could never communicate the sweet melody played in my heart. Stochastic differential equations, called "Ito Formula," are currently in wide use for describing phenomena of random fluctuations over time. When I first set forth stochastic differential equations, however, my paper did not attract attention. It was over ten years after my paper that other mathematicians began reading my "musical scores" and playing my "music" with their "instruments." By developing my "original musical scores" into more elaborate "music," these researchers have contributed greatly to developing "Ito Formula."

My advisor Joe Doob received the stochastic differnetial equation for publication while at Cornell and remarked, "It will be at least ten years before the importance of this paper will be recognized". My first mathematical job was to help the Cornell secretary prepare the paper for publication. I was paid $35 for this.

Famous Statistician David Freedman has died at 70

It is not often that you find a truly great textbook. One example is William Feller's "An Introduction to Probability Theory and Its Applications" and another is David Freedman's "Statistics," with co-authors Robert Pisani and Roger Purves. Starks writes about this book:

The book is "a widely used undergraduate textbook, crystal clear, a delight to read and to teach from, broad, deep and meticulously accurate in every detail, It transformed the way many people taught statistics from a formula-driven, plug-in-the-numbers approach to a focus on critical thinking.

Freedman is equally well known for his statistical research which is described here.