# Chance News 35

## Quotation

USA Today has come out with a new survey: Apparently three out of four people make up 75 percent of the population.

David Letterman,

04/12/1947 -

We (Laurie Snell) were not able to find any evidence that this really appeared in USA Today.

## Forsooth

Our first item was suggested by Fred Hoppe at MacMaster University who's research is in probability and statistics with a hobby of lottery problems.

## In this lottery it was better to win third than second place

The Lotto 6/49 in Ontario Canada asks you to choose six numbers from 1 to 49 on up to 10 boards (each board costs \$2) or ask for a Quick Pick and the lottery terminal will randomly select your numbers. The Lotto officials randomly draw 6 numbers from 1 to 49 and a bonus number from 1 to 49. The payoffs are

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

47% of LOTTO 6/49 draw sales is dedicated to the Prize Fund. The total amount of \$5 and \$10 prizes are paid from the Prize Fund and the balance of the fund (the Pools Fund) is then allocated between the 4/6, 5/6, 5/6 + Bonus and 6/6 prize categories as indicated in the table above. Any amount not won in the 6/6 or 5/6 + Bonus prize categories is added to the 6/6 Jackpot prize for the next draw. Here is how this came out for the March 19 Lotto 6/49

http://www.dartmouth.edu/~chance/forwiki/lotto2.jpg

Fred writes:

In the March 19, 2008 Lotto 6/49 numbers drawn were 23 - 40 - 41 - 42 - 44 - 45 and the bonus was 43.

Can you imagine the consternation of the poor folks who, against the odds, matched 5/6 numbers and the bonus number, then found their excitement turned to dismay upon learning their share was only \$1,193.70 because of the 239 who matched likewise. The third place winners (match 5/6 only) each took home \$2,223.40.

### Discussion

It would be interesting to estimate the probability that there will be more third place winners than second place winners assuming quickpicks. Can you see how this might be done?

## Intuitive and non-intuitive medical news

"The study of more than 6,000 people found the more fat they had in their guts in their early to mid-40s the greater their chances of becoming forgetful or confused or showing other signs of senility as they aged. Those who had the most impressive midsections faced more than twice the risk of the leanest." So says Rob Stein of The Washington Post on March 26, 2008. He is referring to the publication "Central obesity and increased risk of dementia more than three decades later" published on March 26, 2008 in Neurology. Even if an individual is not obese or even overweight, "A large belly independent of total weight is a potent predictor of dementia," comments the lead author of the study. According to Stein, "The researchers used a complicated method for measuring fat known as sagittal abdominal diameter (SAD). Those with a SAD score above 25 had the biggest bellies and the greatest risk. That is roughly equivalent to a waist of at least 39 inches. Of the 6583 participants who had their SAD measured between 1964 and 1973, 1059 (15.9%) were eventually diagnosed with dementia.

Nevertheless, claims a Dutch study ("Lifetime Medical Costs of Obesity: Prevention No Cure for Increasing Health Expenditure," Public Library of Science, ) preventing obesity in general and presumably SAD as well, turns out to be expensive because it costs more to care for healthy people who live years longer, long enough to contract diseases which are truly high-priced. The lead researcher says "Lung cancer is a cheap disease to treat because people don't survive very long. But if they are old enough to get Alzheimer's one day, they may survive longer and cost more." In February, 2008, the AP review of the article claims looking at a lifetime, "the thin and healthy group cost the most, about \$417,000" and the "cost of care for obese people was \$371,000, and for smokers, about \$326,000."

Turning now to a much smaller study and much smaller time period for measurements, Josephine Marcotty in the Minneapolis Start Tribune of March 27, 2008, writes about a before and after investigation pertaining to the recent Minnesota statewide smoking ban. "Dr. Dorothy Hatsukami, who heads the university's tobacco research center, recruited 24 nonsmokers from around the state who worked at bars, restaurants and bowling alleys that permitted smoking. Before the ban went into effect, she tested their urine for nicotine and a carcinogen. Then she tested them again after the ban. The study will be submitted for publication in the journal Cancer Epidemiology, Biomarkers & Prevention." Marcotty writes, "On average, the levels of nicotine and the carcinogen dropped by more than 80 percent."

Speaking of lung cancer, Gardiner Harris in the New York Times of March 26, 2008 wrote, "In October 2006, Dr. Claudia Henschke of Weill Cornell Medical College jolted the cancer world with a study saying that 80 percent of lung cancer deaths could be prevented through widespread use of CT scans." She stated that "after screening 31,567 people from seven countries, CT scans uncovered 484 lung cancers, 412 of them at a very early stage. Three years later, most of those patients were still alive, and she projected that 80 percent would be alive after 10 years and assumed that they would have died without the screens." The publication was in the prestigious New England Journal of Medicine which failed to note Henschke's research "was underwritten almost entirely by \$3.6 million in grants from the parent company of the Liggett Group, maker of Liggett Select, Eve, Grand Prix, Quest and Pyramid cigarette brands." As the chief medical officer of the American Cancer Society put it, "If you're using blood money, you need to tell people you're using blood money." A former editor of the New England Journal of Medicine reasoned that the tobacco companies "want to show that lung cancer is not so bad as everybody thinks because screening can save people; and that's outrageous." Furthermore, it was "recently reported that" Dr. Henschke, the biggest advocate of screening for lung cancer, "had failed to disclose in articles and educational lectures a patent and 10 pending patents related to CT screening and follow-up."

## Discussion

1. The SAD measurement was one of a number of measurements made on each participant. What statistical problem does this introduce?

2. The SAD study started with 8664 participants but the final sample size was only 6583. Why might that be an issue?

3. Presumably the Dutch study of obesity dealt with Dutch data concerning costs. Why might things be different when dealing with the United States?

4. The Minnesota study dealt with the effect of passive smoking and was funded by ClearWay, an advocacy group for banning smoking. How is ClearWay providing funds different from/similar to the Liggett group providing funds?

5. CT scans of the lung, just like mammograms which are commonly used to detect breast cancer, may have false positives. To distinguish a true positive from a false positive, biopsies and/or surgery are often done afterward. What makes the follow-up procedure in the former riskier than in the latter?

Submitted by Paul Alper