CHANCE News 3.03
        (13 February to 5 March 1994)


Prepared by J. Laurie Snell as part of the
CHANCE Course Project supported by the
National Science Foundation and the
New England Consortium for Undergraduate
Science Education.

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Public ignorance of the laws of evidence and of 
statistics can hardly be exaggerated.  



    >>>>>==========>> Stats you could die for. Discover, March 1994, p 30 John Allen Paulos

    Paulos turns his popular writing skills to the subject of the public's understanding of statistical issues in medicine. He begins by citing three general problems: (a) inability to confront numbers associated with health hazards objectively (b) ignorance about the oddities of statistical analysis (c) lack of factual knowledge of how the statistics were obtained. He then gives numerous examples to illustrate each of these problems. To illustrate the problem of being objective he describes the hysteria over the report on television of the man who claimed that there was a causal connection between his wife's frequent use of a cellular phone and her subsequent brain cancer. Misunderstanding of statistical ideas are illustrated in terms of examples such as Simpson's paradox. For instance, two studies, both found that a higher percent of minority group A were improved by a drug than was the case for minority B. But when the data for the two tests were combined, a higher percent of group B improved than group A. Lack of information is illustrated by the often quoted statistic that condoms fail 10 percent of the time, which apparently originated from asking couples whether condoms ever failed them in birth control. It was then applied to such things as protection against AIDS. Another example is the famous 10 percent homosexual estimate. Paulos remarks that we seem to be given numbers like 10 that we feel more comfortable with than numbers like 11 or 12. You'll find a wealth of examples here, some old favorites, some new favorites and some that you probably haven't heard of at all - but all written in the lively Paulos style. <<<========<<

    >>>>>==========>> The next item was provided by John Finn The False Promise of Gun Control. The Atlantic Monthly March 1994 by Daniel D. Polsby

    An argument *against* gun control in a liberal magazine! Polsby challenges a number of widely held beliefs, claiming that "guns don't increase national rates of crime and violence---but the continued proliferation of gun control laws almost certainly does." He says most major newspapers go along with the article by Arthur Kellerman and several associates in the 7 October 1993 New England Journal of Medicine, which intended to discredit the idea that having a gun is a useful means of self-protection.(See Chance news 2.17 and 3.02) Describing Kellerman's study, Polsby challenges Kellerman's conclusion that owning a handgun increases a person's risk of being murdered, claiming that the study may in fact indicate the opposite causal arrow; that the fear of being murdered makes people arm themselves. Polsby goes on to cite several examples which, he says. contradict notions commonly held by gun-control advocates: Switzerland, New Zealand and Israel have about the same guns-per-civilian-household rate as the US, yet lower rates of crime and violence; Mexico and South Africa have gun control, but murder rates twice as high as here. Besides citing statistics, Polsby also explains why he believes that gun control laws cannot bring about what they are intended to; those who really must have guns for their work, including some criminals, will continue to get them no matter what the costs. The climax of the article is his assertion that "the root cause of crime is that for certain people predation is a rational occupational choice", and he suggests progressive policies to remedy the social situations that make this true. This is an article that is really full of statistical assertions, but without any hard numbers. For instance "Mexico, which has tighter gun control laws than the US, has a much higher murder rate." DISCUSSION QUESTION: In reply to criticism of their article, Kellerman and his colleagues remark that their study is similar to the initial studies that led to the verification of a causal connection between smoking and lung cancer. Polsky, says that the difference here is that no-one thought that lung cancer could possibly cause smoking but with the gun issue both arrows are perfectly possible. What kind of further studies are necessary to clarify this point? <<<========<<

    >>>>>==========>> The cure that killed. Discover, March 1994, P 56 Larry Thompson

    An in-depth story of the study to test the drug fialuridine (FIAU) as a cure for hepatitis B that went wrong and was stopped after the death of several of the subjects. (See Chance News 2.15 for more details of this study) <<<========<<

    >>>>>==========>> Sex and the brain. Discover, March 1994, p 64 David Nimmons

    The story of the life and work of Simon LeVay since he discovered a minute but measurable difference in the size of a part of the brain of homosexual and heterosexual men. LeVay's instant fame and involvement with the gay community led him to give up his research career and help found an extension school for adults taught by lesbians and homosexuals, teaching a wide range of courses involving sexual orientation in law, science, literature, the arts etc. The article also reviews other studies that suggest that sex preference is a genetic trait. (See Chance News 2.13 and 2.14). <<<========<<

    >>>>>==========>> Quest for AIDS vaccine raises ethical questions on tests. The Boston Globe, 21 February 1994, p3 Richard Saltus

    Discusses ethical questions related to conducting trials of experimental AIDS vaccines in a way that respects the rights of research subjects. One concern is that the urgency surrounding the epidemic may lead to premature human testing of new treatments. There have also been reports that treatments which show promise in the lab can be less effective in the real world, apparently because of differences among strains of the virus. Vaccines currently under development to reduce vulnerability to HIV infection are not expected to be more than 50-60% effective, making it all the more important that people understand and weigh the risks and benefits of vaccination. Finally, it is noted that some high risk groups such as IV drug users, young gay males, and persons of color tend to have less access to medical care, and may be difficult to recruit for testing. <<<========<<

    >>>>>==========>> Jury fails to convict hair dye as a cancer risk. The New York Times, 2 March 1994, C14 Jane E. Brodey

    This review was motivated by a recent study reported in the Journal of the National Cancer Institute and characterized in an accompanying editorial as showing "conclusively that use of permanent hair dyes does not increase risk of cancer mortality." In 1982 about 500,000 women age 30 and over, enrolled in a cancer prevention study conducted by the American Cancer Society. Among the information obtained was their use of hair dyes, including the color, type and length of use. Researchers then measured death rates from cancer among these women through 1989. After controlling for smoking and other risk factors for cancer, they found that hair dye showed no relation to cancer deaths. As in previous studies, there was a suggestion that long use of dark dyes, especially black dye, could increase the risk of non-Hodgkin's lymphoma and multiple myeloma, two potentially fatal cancers. A similar study, the Harvard nurses study, has also not found an overall increase in cancer risk among users of hair dyes, though this study is still in progress. Concern has been expressed about the use of hair dye based on the work of Bruce Ames at Berkeley who pointed out that the colorants are derived from coal tars, known to be carcinogenic. In addition, animal tests using very high doses of dyes did indicate that permanent hair dyes might be carcinogenic. I think coal tars are no longer used. Previous studies had indicated some risk, but it is claimed that this was not a consistent finding and the authors did not control for smoking and other known risk factors. <<<========<<

    >>>>>==========>> So you consider hair dye safe? The New York Times, 16 Feb 1994, A20 Letter to the editor from Samuel S. Epstein

    Epstein is chairman of the Cancer Prevention Coalition and writes that the recent study of the American Cancer Society showing little danger in using hair dyes is "seriously flawed in design and interpretation." One concern is that the study was based on women whose average age was only 56 when they were first enrolled in the study, and only 63 when they were no longer being followed. Epstein observes that the really high rates for the cancers of concern occur after age 63 and that most of these would be missed by the study. He also feels that the study did not control for some important risk factors such as duration of oral contraceptive use and a history of mammogram tests. In addition, those who started using hair dye after the beginning of the study were counted as non-users. He claims that "a well designed study in Nebraska found that hair dye use would account for about 20 percent of all non-Hodgkin's lymphoma deaths in women". He considers the accompanying editorial even more recklessly misleading than the study and recommends that women switch to non carcinogenic organic hair dyes. <<<========<<

    >>>>>==========>> Hair dye isn't linked to cancer death risk. The New York Times, 1 March 1994, A22 Letter to the Editor from Michael J. Thun and Clark W. Heath Jr.

    The authors of the hair dye study reply to the above letter from Epstein. They disagree with Epstein's concern about their not controlling for mammography use, saying that there is no evidence that women who use hair dye have mammography more or less than women who use no dye. They remark that they did recommend that carcinogens be removed from hair dye and that women avoid long-term use of black dye. <<<========<<

    >>>>>==========>> Executive Health's Good Health Report. Vol 29; No. 6 March, 1993

    This is an account of the Nebraska study mentioned by Epstein in his letter. It was also carried out by scientists at the National Cancer Institute. Researchers conducted a phone survey of 583 blood-related cancer cases and 1,432 controls, all white men and women living in 66 eastern Nebraska counties. The study was published in the American Journal of Public Health. Among women, use of all hair coloring products was associated with non-Hodgkin's lymphoma, Hodgkin's disease, and multiple myeloma. Permanent hair coloring methods caused more risk then non-permanent coloring. The risk to men who used hair coloring was higher but not significantly so. <<<========<<

    >>>>>==========>> Leading scientists say hair dye study wrong, needlessly alarmist. PR Newswire, 1 July 1992

    This is a report issued by the Cosmetic, Toiletry, and Fragrance Association which quotes a number of leading epidemiologists saying that the Nebraska study made claims that were not at all supported by the data. References are given to other studies that support the fact that hair dyes do not cause cancer. PROJECT SUGGESTION: Look up the original articles on cancer and hair dye and determine your own opinion about the present state of this argument. <<<========<<

    >>>>>==========>> How to use an article about a diagnostic test. Part A. Are the results of the study valid? Journal of American Medical Association, 2 Feb 1994, Pg. 389

    Part B. What are the results and will they help me in caring for my patients? Journal of American Medical Association, 2 Mar 1994, Pg. 703 Roman Jaeschke and others

    The authors start with a clinical scenario that leads you (the doctor) to suspect that your patient has a pulmonary embolus (PE) (an obstruction in the lungs). You request a ventilation-perfusion scan (V/Q scan)(seems to measure rate of flow through the lungs), and the result, reported to the nurse over the telephone, is "intermediate probability for PE". Should you proceed to treat the patient as if she has PE? In part A the authors show how you can find in the literature studies that tell you the meaning and the basis for the "intermediate probability". In particular, you find a study in which 731 patients suspected of having PE were given V/Q tests with the results reported as high probability, intermediate probability, low probability, or normal for having PE. Then by an independent, essentially foolproof, test determined if the patient did have PE. The results of this experiment were: For those reported as high probability, 102 had PE and 14 did not, for intermediate probability 105 had PE and 217 did not, for low probability 39 had PE and 273 did not and for near normal 5 had PE and 126 did not. Part B shows you how to combine results from this study with your prior probability for the patient having PE to obtain a posterior probability. To emphasize the role of the prior probability two patients are considered, one young and one old, with comparable symptoms. The authors also discuss the method of sensitivity and specificity but suggest that this older method is a less useful approach and they mention it only because it is still used in the literature. DISCUSSION QUESTION: Before getting the results of the V/Q scan, on the basis of the patients other symptoms, the doctor assigned a 40 percent chance that the patient had PE. What probability should the doctor assign after the test and the result "intermediate probability for PE"? <<<========<<

    >>>>>==========>> In major finding, drug limits H.I.V. infection in newborns. The New York Times, 21 Feb 1994, A1 Lawrence K. Altman

    A study designed to see if the drug AZT would help prevent the HIV virus from being passed on to the child of an HIV positive pregnant women, has been stopped early because of its unexpected success. The study involved 477 women in 50 medical centers in the United States and 9 in France who had tested positive for the HIV virus but still have more than a 200 CD-4 count. The women were enrolled between the 14th and 34rd week of their pregnancy and agreed to receive either AZT or placebo pills during pregnancy and labor. The 477 women gave birth to 421 babies. Of the 364 babies for whom at least one culture test was available, 53 were HIV positive. 40 of these were from mothers who had placebo while 13 were from mothers who had taken AZT pills. It has been estimated that about 25% of the time a child of a mother infected with HIV will be infected, so that the 26% in the placebo group reassured the investigators. So far, no added birth defects have been attributed to the AZT. The results of this study provide a host of problems ethical and otherwise. The transmission of AIDS through childbirth is a major problem in the developing countries and those involved will not be able to afford the AZT. The results argue for more aggressive testing of pregnant women which conflicts with privacy rights etc. Needless to say, panels have been established to study these problems. DISCUSSION QUESTION: Given the mixed results on AZT in previous studies, do you think the researchers were justified in stopping the study before they had time to look for side effects? Do you think that there should be mandatory testing for the HIV virus of pregnant women. <<<========<<

    >>>>>==========>> AIDS in San Francisco Hit Peak in '92, Officials Say. The New York Times, 16 Feb 1994, A10 Gina Kolata

    San Francisco is one of the very few success stories in attempts to stop the spread of AIDS. The San Francisco Department of Public Health reported that 3,326 people developed AIDS in the peak year of 1992. The number dropped to 1,507 in 1993. It is expected that the number in the coming years will continue to decline, but slowly. This dramatic decrease is attributed to the extensive education campaigning carried out among the groups at highest risk for AIDS: gay and bisexual men and intravenous drug users. Experts say that for the immediate future, educational programs hold out more hope than vaccines in stopping the spread of AIDS. <<<========<<

    >>>>>==========>> Obstacle-Strewn Road to Rethinking the Numbers on AIDS. The New York Times, 1 March 1994, C3 Lawrence K. Altman The usual estimate for the number of people with the HIV virus in the United States is one million, which is based upon the 1989 estimate of the Centers for Disease Control that the number is between 800,000 and 1,200,000. The CDC plans to make a new estimate in July, and, in preparation, the agency invited independent experts to meet last week to report and review relevant data. Although some of the estimates went as high as a million, most ranged from 600,000 to 800,000. The article discusses the many difficulties in making reliable estimates for the number of people with AIDS: the social stigma makes people afraid to report the disease. In addition, where it occurs is constantly shifting. For example, the biggest group has been white gay men, but the number in the group is thought to be declining while the number of black women in the South is increasing. Figures are not kept on a yearly basis and so it is hard to estimate trends. Plans are being made to remedy this by making spot surveys on an annual basis. Government officials point out that an estimate that the number of HIV people is decreasing could have serious consequences in government policy for providing money for the fight against AIDS. This will leave the CDC with the problem that "letting the data speak for itself" may not be the best way to fight the disease. DISCUSSION QUESTION: Should the CDC let the data speak for itself? <<<========<<

    >>>>>==========>> Inner-City Alcoholics Have High HIV Rate. UCSF researchers say risky sex a big factor. San Francisco Chronicle, 16 Feb 1994, A12 Charles Petit

    A study reported in the current Journal of the American Statistical Association shows that inner-city alcoholics have a surprisingly high rate of HIV infection. Researchers reviewed the records of 639 men and 221 women who underwent treatment for alcoholism at five city-operated neighborhood health centers in San Francisco and who identified themselves as heterosexual. Previous studies would have suggested that about 1/2 a percent of heterosexuals with a similar background should be HIV infected. In this group they found about 5 percent. Among the group studied, about 1/4 were homeless and 3/4 were unemployed. Still, of the 139 who said they worked full time and have a place to live, about 4 percent were HIV positive. Of course, the obvious explanation would be that the use of alcohol leads to unprotected sex. DISCUSSION QUESTION: What are other explanations for the difference in incidence of HIV infection in the group studied? <<<========<<

    >>>>>==========>> Breast cancer drug raises new fears; Benefit of treatment tried on thousands of women under question. The Independent, 18 Feb 1994, News page 7 Celia Hall

    The current issue of Lancet has an article reporting on a Dutch study that showed that women who had been taking tamoxifen for more than two years were more than twice as likely to develop endometrial cancer than those not taking the drug. The risk increased with time and the amount taken. Women taking the drug for more than five years were three times more likely to have endometrial cancer. The risk for cancer has been known for some time but the benefits of tamoxifen for women already diagnosed as having breast cancer is felt to outweigh the increased risk for endometrial cancer. Studies to test the use of tamoxifen to prevent breast cancer for those at high risk are just starting in England and have been going on for some time in the United States and in other countries as part of a large international study. A member of the research team for this study is quoted as saying: "It is debatable whether the use of a medical intervention can be justified when it prevents breast cancer in some women at the cost of inducing endometrial cancer in others." The chairman of the international study stated that they were aware of the Dutch study and, in fact, the risks they found were lower than those that they had assumed in planning the study. He commented: We have been working on the possibility of a threefold risk. This level means that over the five years the women in the trial are taking tamoxifen, their risk of developing endometrial cancer rises from 2 per 1,000 women to 5 per 1,000. But we do not see it as a reason for denying the option of taking part in the trial to the women at increased risk of breast cancer. They are being informed of the potential risks as well as the potential benefits." An article on this topic in 18 February issue of Science comments that some changes have been made in the US study in the informed consent form on the basis of these news studies. DISCUSSION QUESTION: Is it fair to say that the tamoxifen study "prevents breast cancer in some women at the cost of inducing endometrial cancer in others"? <<<========<<

    >>>>>==========>> The Aged Reject CPR Use. The New York Times, 1 March, 1994, C6

    The current issue of the New England Journal of Medicine gives the results of a study that surveyed 371 patients over one year at a geriatrics clinic at the medical center. Initially 41 percent said they would like to have CPR if their hearts stopped while they were being treated for an acute illness. (CPR is used to shock the heart back to life after cardiac arrest.) But when they were told that their chances of surviving were only 10 to 17 percent, the percentage who would like to have it dropped to 22%. The article suggests that making sure patients understand the chances for success might cut down health costs, but another article in the same issue points out that this is not so obvious. <<<========<<

    >>>>>==========>> Insurers are called illogical; some patients get treatments, others are refused, study says. Boston Globe, 17 Feb 1994, National/Foreign Pg. 3 Richard A. Knox

    A study reported in the current New England Journal of Medicine indicates the decision of Insurance companies to pay for the care of patients seems "capricious and arbitrary". The authors, Dr. William P. Peters and Dr. Mark C. Rogers of Duke University, stated that about a 1/4 of insurance companies refused to pay for women to have bone marrow transplants and high-dose chemotherapy as part of a federally sponsored clinical trial. For two very similar patients, one may be supported and the other not. Of the 533 women who wanted to enter the study of bone marrow transplants and high-dose chemotherapy for advanced breast cancer, 411 got assurances that their health insurance companies would pay. Of the 121 who were told they would be denied payment, 62 had the transplant anyway. 39 later managed to persuade their insurance companies to reverse the decision not to pay, and about half of them did this after getting a lawyer and threatening to sue. Insurance companies point out since the subjects are participating in a trial the treatment is clearly experimental and therefore they really don't have to pay for the treatment. A researcher countered by saying that if a subject received placebo they would receive payment for the treatment. DISCUSSION QUESTION: Do you think that it is reasonable that drug companies not pay for treatments that are considered experimental? If so, how do you think the insurance companies should decide if a treatment is experimental? <<<========<<

    >>>>>==========>> New S.A.T sets students cramming. The New York Times, 28 Feb 1994, A12 Richard L. Berke

    The College Board is making the first major revision in its S.A.T. exams in 20 years. The revised verbal section puts more emphasis on ability to analyze passages of text, and the math section has students solve problems rather than pick multiple-choice answers. And students may use calculators. All this has been a boon to the coaching companies who report that business is booming. To avoid making coaching available only to the rich, schools are offering free coaching. There is, of course, the usual argument about how much coaching can help. The ETS people say only about 30 to 50 points beyond the normal 25 point gain between the preliminary and actual tests. It is claimed that recent audits by two independent accounting firms concluded that students who took a preparation course typically increased their scores by up to 125 points. It would be interesting to see how these audits were carried out. The executive director of the National Center for Fair and Open Testing comments that the changes are only cosmetic and feels that, despite the efforts of the ETS to avoid bias, the test is still unfair to minorities who cannot afford to learn the tricks from the coaching services. DISCUSSION QUESTION. Why is it so difficult to determine how much coaching improves students with SAT scores? What kind of test would you design to settle this matter once and for all? <<<========<<

    >>>>>==========>> Teaching by Design. Teaching Statistics, Spring 1994 Adrian Bowman

    The author tells of his experience with the following activity. Students were told that was their job to design and carry out an experiment which would investigate the operation of short term (working) memory. The students decided to work in pairs, one person constructing a list of 12 words which were read to the partner and the partner then asked to recall as many as possible. A discussion moderated by the instructor led to a number of conditions to be met on the choice of words, how they should be read, time between answering, etc. In the first experiment the words were unrelated, in the second they were related, and in the third they were unrelated and, between reading and recalling, the student who is trying to recall the words was given the exercise of counting backwards in 7's from 256. The students plotted the outcomes in terms of the proportion who remembered questions in the various positions in the list. It was observed that the beginning and the end of the list are remembered best, that the counting exercise makes it harder, etc. The aim is to show that interesting things can be learned by very simple statistical experiments. <<<========<<

    >>>>>==========>> A Tale of Six Cities. Teaching Statistics, Spring 1994, 5-8 Neville Hunt

    The author shows the students a number of quotations from the newspapers that describe a "rule of thumb". For example, from the Guardian: "As a rough rule of thumb, withdrawal symptoms are thought to last a month for every year on tranquilizers." The author describes an activity designed to have the students develop their own "rule of thumb". To do this, students are asked to pick 6 cities at random from a list of the 42 cities in England. For each of the 15 possible pairs of cities in their group the students are asked to find two measurements: (a) how far apart they are "as the crow flies" and (b) how far apart by driving on reasonable roads. They then are asked to make a scatter plot, fit a line by eye, and determine the "rule of thumb" from the equation of this line. Students can check the rule and determine confidence intervals etc. <<<========<<

    >>>>>==========>> More Computer Generated Thinking. Teaching Statistics, Spring 1994, 9-11 Gerd Riehl

    If you are trying to determine basketball shots or the up and down of a stock that exhibits streaky behavior, you are apt to want to find the distribution for the number of runs. If you condition on the number of successes, there are simple combinatorial expressions for the probabilities for r runs. If you do not want to condition this way, there do not seem to be reasonable expressions for the probability of r runs. The author observes that these probabilities can be computed recursively very simply. This is described in terms of Markov Chains, but no knowledge of Markov Chains is necessary to understand the calculation. Some interesting properties of these probabilities are discussed and proven. For example, the probability that the number of runs is odd is independent of the number of trials, provided there are 2 or more trials. <<<========<<

    >>>>>==========>> Patients, Medicines, Policies and Statistics. Teaching Statistics, Spring 1994 Simon Day

    This is a brief discussion from a statistician working at Lilly on how trials are carried out. The author illustrates the procedure in terms of a trial comparing four groups of patients being treated for stomach ulcers: group 1 receiving placebo, group 2, active drug at dose d twice a day, group 3, active drug at dose 2d once per day, and group 4, active drug at dose 2d twice per day. The use of logistic regression illustrates both the effectiveness of the four different treatment procedures and risk factors such as drinking, age etc. DISCUSSION QUESTION. In the log regression analysis, the parameter for the drinking variable (yes or no) translates to an odds ratio of about 2 to 1. The authors concludes from this that "the odds of being cured if you are a drinker vs. not being a drinker) are about 1:2. Why can they say this? Karl Pearson and R.A. Fisher on statistical tests: A 1935 Exchange from Nature American Statistician, Feb 1994, Page 2 Henry F. Inman The meaning of statistical tests is still a hot issue on statistical discussion groups and it is interesting to see what the masters argued about. This exchange of letters was prompted by a letter from a practicing statistician Buchanan-Wollaston criticizing the work of the British school. He wrote "The fact that British methods 'work' is due to the prevalence in Nature of distributions similar to the Gaussian rather than to any peculiar virtue of the methods themselves. Pearson replies that his chi-squared test has nothing to do with any normal assumption and is just a way to measure the goodness of fit of the data by a particular distribution. "If Continental statisticians in the bulk do indeed hold the views of Mr. Buchanan-Wollaston, it can only be that they have not really studied and grasped the fundamental literature of the subject." Fisher writes that Pearson's own writings show that he certainly does use the chi-squared to test hypotheses. He agrees with Buchanan-Wollaston that the chi-squared test is relevant for rejecting a hypothesis but not for acceptance. Fisher writes: "'errors of the second kind' are committed only by those who misunderstand the nature and application of tests of significance." Pearson replies ridiculing the idea that you can test whether a hypothesis is true but not if a hypothesis is false. He concludes his second letter with "The 'laws of Nature' are only constructs of our minds, none of them can be asserted to be true or to be false, they are good in so far as they give good fits to our observations of Nature." I have given quotes out of context just to whet your appetites to real the letters. <<<========<<

    >>>>>==========>> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 3.03 (13 February to 5 March 1994) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: jlsnell@dartmouth.edu >>>==========>>|<<==========<<< >>>==========>>|<<==========<<<