Chance News 35
to be continued
This Forsooth is from the April 2008 issue of the RSS News.
Probability - the chance, or likelihood, of a certain/particular event occurring which can be expressed as a quantitative description, often ranging from 0 (rare event) to 1 (common event.Learning lessons from the 2007 floods:
an independent review by Sir Michael Pitt
Cabinet Office, UKDecember 2007
USA Today has come out with a new survey: Apparently three out of four people make up 75 percent of the population.David Letterman,
Paul Alper suggested this as a bad English forsooth:
VYTORIN is a medicine used to lower levels of LDL (bad) cholesterol in addition to a healthy diet.Vytorin ad
Star Tribune sports pages
April 4, 2008
Paul also suggested this Forsooth:
Having a husband creates an extra seven hours a week of housework for women, according to a University of Michigan study of a nationally representative sample of U.S. families. For men, the picture is very different: A wife saves men from about an hour of housework a week.ScienceDaily
April 3, 2008
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
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
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.
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."
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
Vytorin is in the news again
History plays out in strange ways. In mid January, 2008, Vytorin's failure in the ENHANCE study to reduce plaque and heart attacks (over Zocor by itself) hit the news to the point that a commentary appeared even in Chance News 33 "Cholesterol Significance". Then suddenly, because of a medical conference in Chicago at the end of March, the media found Vytorin again even though there was nothing new to report during the two-month interval.
An AP dispatch by Marilynn Marchionne on March 30, 2008 reported that "The results show the drug had "no result - zilch. In no subgroup, in no segment, was there any added benefit" for reducing plaque, said Dr. John Kastelein, the Dutch scientist who led the study. Kastelein said the data were far more consistent than anticipated and ample to show that the drug simply did not work." An interesting observation from another leading cardiologist lends credence to the discipline of statistics: "but the reason we do research is so we don't have to rely on our 'beliefs' - we can rely on data." In this instance, the belief is that combining two drugs which have different mechanisms ought intuitively to be synergistic. The clinical trial proved otherwise.
1. An editorial in the Minneapolis Star Tribune, criticizes the "$200 million ad campaign" of the manufacturers of Vytorin. The Minneapolis Star Tribune ran a full two-page ad for four days in January and a similar full two-page ad at the end of March for two days. Determine how much the newspaper received for those ads.
2. Vytorin did reduce LDL in a statistically significant manner but the criticism has to do with practical significance because LDL is an inexact marker or indicator of future heart problems. Name some other inexact markers in medicine. Name some other inexact markers for education, piety, and basketball success.
3. From here we read "The "American College of Cardiology recommends that major clinical decisions not be made on the basis of the ENHANCE study alone." From here we read "since 2003 the ACC has received nearly $5 million from Merck, $1 million from Schering-Plough and more than $5 million from the companies' joint venture that sells cholesterol drugs Vytorin and Zetia." Defend and criticize a financial relationship between the pharmaceutical industry and the medical profession.
Submitted by Paul Alper
Not everyone has high blood pressure but from scanning the news it would seem that way. From the AP. we find that in a clinical, randomized trial of "11,462 people in the United States and Nordic countries" a combination of an ACE-calcium blocker plus benazepril ( an ACE inhibitor) did better than a diuretic plus benazepril. The study was "stopped early so the surprising benefits could be made known."
1. There were 531 "heart-related problems or strokes" in the 5,721 people who had the combination of an ACE-calcium blocker plus benazepril whereas there were "653 events among the 5,741 others. Perform a two-sample test for difference in proportions to demonstrate that the results are "statistically significant."
2. "The study was paid for by Novartis, which sells Lotrel, the combo that proved better and [Kenneth] Jamerson consults for the company." In addition, the study does not as yet appear in a peer-reviewed journal but only at a conference of cardiologists in March, 2008. How does this information affect your attitude towards the conclusion?
3. Determine the monthly cost for Lotrel under various health plans and how it compares with a diuretic plus benazepril.
Blood Pressure Again
High blood pressure in those over 80 years of age is of especial concern. From the NHS referring to an article in the NEJM of March 31, 2008, we find that "3,845 people who were eligible were randomly assigned to receive either the diuretic indapamide (1.5mg sustained release pills) or an inactive placebo." There were 1933 patients in the active or treatment arm and 1912 in the placebo arm. The study was stopped in July, 2007 when it was seen the active group had 39% fewer strokes and 21% fewer deaths from any cause.
A quick summary of some of the results is as follows:
Active Group Placebo Group P Value Fatal or nonfatal stroke 51 69 .06 Death from stroke 27 42 .046 Adverse events 358 448 .001 Death, any cause 196 235 .02
1. "The study was funded by the British Heart Foundation and the Institut de Recherches Internationales Servier." Why is this better than being funded by the makers of indapamide?
2. The study appears in the NEJM. Why is this better than being presented only at a conference?
3. The study took place at "195 centres in Europe, China, Australasia and Tunisia" over a four-year period. Thus, it is important to take into account that events do not take place uniformly because of deaths, dropouts, refusals, closing of centers by the data monitoring committee, etc. Ignoring any lack of uniformity and considering what might be called "a final snapshot," then a simple two-sample t-test for "Death, any cause" would yield
Test and CI for Two Proportions
Sample X N Sample p 1 236 1912 0.123431 2 196 1933 0.101397
Difference = p (1) - p (2)
Estimate for difference: 0.0220342
95% CI for difference: (0.00207287, 0.0419955)
Test for difference = 0 (vs not = 0): Z = 2.16 P-Value = 0.031
Fisher's exact test: P-Value = 0.032
which is fairly close to the P Value of .02 reported in the study. Carry out the same calculation for the other three rows in the table and compare results of the table with this snapshot approach.
4. Notice that "Fatal or nonfatal stroke" "did not quite reach statistical significance" but was still deemed important. Translate that sentence into English.
5. One caveat of this study is that the patients in this sample were healthier than normal for their age. Why is this a caveat?
The Deathless Monty Hall Problem!
And behind door No. 1, a fatal flaw.
New York Times, 8 April 2008
This article describes an application of the infamous Monty Hall Problem to an experiment in cognitive psychology. More on this to follow.
As a supplement, the The New York Times web site has posted an interactive simulation of the game show . Certainly not the first of its kind, but it has nice graphics, along with an intelligible, nontechnical discussion of why it makes sense to trade doors.
Submitted by Bill Peterson, based on a suggestion from Priscilla Bremser.