a) Is it reasonable to compute the relative risk for endometrial cancer? Explain. b) Can we estimate relative risk for heart attacks? Explain.

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1 1. A 1980 study investigated the relationship between the use of oral contraceptives and the development of endometrial cancer. It was found that of 117 endometrial cancer patients, 6 had used oral contraceptives at some time in their lives while of the 395 controls, 8 had used oral contraceptives. a) Is it reasonable to compute the relative risk for endometrial cancer? Explain. b) Is it reasonable to compute the odds ratio for endometrial cancer? What is the estimated odds ratio? c) Compute a 95% confidence interval for the odds ratio. 2. A hypothesis has been suggested that the principal benefit of physical activity is to prevent sudden death from heart attack. The following study was designed to test this hypothesis. 100 men who died from a first heart attack and 100 men who survived a first heart attack in the age group were identified and their wives were each given a detailed questionnaire concerning their husband's physical activity in the year preceding their heart attacks. The men were then classified as active or inactive. Suppose 30 of the men who survived and 10 of the 100 who died were classified as physically active. a) What is the general design? b) Can we estimate relative risk for heart attacks? Explain. c) Can we estimate the odds ratio for heart attacks? d) When does the odds ratio approximate the relative risk? 3. Joseph Lister, a British physician of the late 19 th century, decided that something had to be done about the high death rate from post-operative complications, which were mostly due to infection. Based on work of Louis Pasteur, he thought that the infections had an organic cause, and decided to experiment with carbolic acid as a disinfectant for the operating room. Lister performed 75 amputations over a period of years. Forty of the amputations were done with carbolic acid and 35 were done without carbolic acid. For those done with carbolic acid, 34 of the patients lived; for those done without carbolic acid, 19 patients lived. Arrange these data in an appropriate table. a) What is the odds ratio of living if carbolic acid was used? b) Construct a 95% confidence interval for the odds ratio. c) Is it reasonable to compute the relative risk of living if carbolic acid was used? If so, what is the relative risk? d) Construct a 95% confidence interval for the relative risk.

2 4. A study was performed to test the effectiveness of aspirin in the treatment of cerebral ischemia (stroke). Patients were randomized to treatment or placebo. The study was double blinded (i.e., neither the patient nor the physicians who evaluated the patients knew whether the patient received aspirin or the placebo). After six months of treatment, patients were evaluated and their progress was recorded as either favorable or unfavorable. Of the 78 patients in the aspirin group, 63 had favorable outcomes; 43 of the 77 controls had favorable outcomes. a) State the null and alternative hypotheses. b) If it is reasonable, use the two-sample test of proportions to test the null hypothesis. c) What assumptions are made in using this method? d) Determine a 95% confidence interval for the difference between the two proportions. e) Can you construct a Pearson's chi-square test to test the null hypothesis? Compare your results for Pearson's chi-square test to that of the two-sample test of proportions. Comment on your findings. 5. Retinitis pigmentosa is a disease that manifests itself via different genetic modes of inheritance. Cases have been documented with a dominant, recessive, and sex-linked mode of inheritance. It has been conjectured that the mode of inheritance is related to ethnic origin of the individual. Cases of the disease have been surveyed in an English and a Swiss population with the following results: Out of 125 English cases, 46 had sex-linked disease, 25 had recessive disease, and 54 had dominant disease. Out of the 110 Swiss cases, 1 had sex-linked disease, 99 had recessive disease, and 10 had dominant disease. What statistical procedure would be appropriate to show if there is an association between ethnic origin and genetic type? 6. Improvement in control of blood glucose levels is an important motivation for the use of insulin pumps for diabetic patients. However, certain side effects have been reported with pump therapy. The table below provides data on the occurrence of diabetic ketoacidosis (DKA) in patients before and after the onset of pump therapy. Before Pump Therapy After Pump Therapy No DKA DKA No DKA DKA 19 7 What is the appropriate statistical procedure to test if the rate of DKA is different before and after the onset of pump therapy? 7. Two drugs (A and B) are compared for the medical treatment of duodenal ulcer. For this purpose patients are carefully matched on age, sex and clinical condition. The treatment results based on 200 matched pairs show that for 89 matched pairs both treatments are effective; for 90 matched pairs both treatments are ineffective; for 5 matched pairs drug A is effective, whereas drug B is ineffective; for 16 matched pairs drug B is effective, whereas drug A in ineffective. What is the appropriate statistical procedure to determine if there is any difference in effectiveness between the drugs?

3 8. Much controversy has arisen recently on the possible association of myocardial infarction (MI) and coffee drinking. Suppose we obtain information on coffee drinking (cups per day) and prior MI status from year-old adults in the general population. What statistical procedure would be appropriate to determine if there is an association between history of MI and coffee drinking status, which is categorized as 0, 1, 2, 3 or more cups/day? 9. One important aspect of medical diagnosis is its reproducibility. Suppose that two different doctors examine 100 patients for dyspnea in a respiratory disease clinic and that 15 patients are diagnosed as having dyspnea by doctor A, 10 patients diagnosed as having dyspnea by doctor B, and 7 patients are diagnosed as having dyspnea by both doctor A and B. What statistical procedure would be appropriate to determine whether or not the diagnoses of the two doctors are similar? 10. McNemar s chi-square test is appropriate for comparing (two/more than two) factors, where the samples are (independent/correlated), and where the variable of interest contains (two/more than two) categories. 11. Each of 500 women who had defective babies during a given period was matched with a control that had a normal baby during the same period. Each pair was matched in terms of age, parity, and other potentially contributing factors. It was then determined which of the subjects had participated in "hot tub" baths during pregnancy. The results are given below. With defective baby With normal baby Frequency Hot tub + Hot tub Hot tub + Hot tub - 75 Hot tub - Hot tub + 20 Hot tub - Hot tub a) Set up the appropriate two-way table. b) State the appropriate null hypothesis. c) State the appropriate alternative hypothesis. d) Using the above values, set up the calculations for the appropriate test statistic. e) What are the degrees of freedom associated with the appropriate test statistic? f) Compute the odds ratio. 12. A study of methods for detecting cytomegalovirus (CMV) reported the results of different assays on 195 broncho-alveolar lavage (BAL) specimens from bone-marrow-transplant recipients with pneumonia. The table below shows the distribution of the BAL specimens according to cytological examination result and immunofluorescence (IF) assay results. Do the data provide evidence that the population proportion of BAL specimens with positive cytological examination results differs from the population proportion of BAL specimens with positive IF assay results? IF Assay Result Cytological Exam Results Positive Negative Positive Negative In a double-blind study of aspartame and headaches, 40 subjects were given aspartame and placebo at different times. All of these subjects had reported that headaches occurred after consuming products

4 containing aspartame. The table below shows the number of subjects who reported headaches after consuming aspartame during the study and the number of subjects who reported headaches after consuming the placebo. Aspartame Placebo Headache No Headache Headache 6 12 No Headache Use the appropriate test statistic to determine if the data provide evidence that the occurrence of headaches is different in the aspartame and placebo groups. 15. A study was carried out to see if patients whose skin did not respond to dinitrochlorobenzene (DNCB), a contact allergen, would show an equally negative response to croton oil, a skin irritant. The following table shows the results of simultaneous skin reaction tests to DHCB and croton oil in 173 patients with skin cancer. DNCB Positive Negative Total Croton Oil Positive Negative Total a) State the null and alternative hypotheses. b) Using information in the table, set up the calculations for the appropriate test. 16. Suppose we are interested in comparing the effectiveness of two different antibiotics, A and B, in treating gonorrhea. Each person receiving antibiotic A is matched with an equivalent person (age within 5 years, same sex), to whom antibiotic B is given. These patients are asked to return to the clinic within 1 week to see if the gonorrhea has been eliminated. The results are as follows: For 40 pairs of patients, both antibiotics are successful. For 20 pairs, antibiotic A is effective whereas antibiotic B is not. For 16 pairs, antibiotic B is effective, whereas Antibiotic A is not. For 3 pairs, neither antibiotic is effective. a) Set up the appropriate table. b) State the null and alternative hypotheses. c) Using numbers from the table, set up the calculations for the appropriate test statistic. 17. Suppose we have 500 pairs of pregnant women who participate in a study of premature births and are paired in such a way that the body weight of the women in a pair are within 5 lbs. of each other (i.e., matching on body weight). We then give one of the two women a placebo and the other drug A. Wish to test whether drug A has an effect in preventing premature births. Suppose that in 30 pairs of women, both women in a pair have a premature child; in 420 pairs of women, both women have a normal child; in 35 pairs of women, the woman taking drug A has a normal child and the woman taking the placebo has a premature child; in 15 pairs of women, the woman taking drug A has a premature child and the woman taking the placebo has a normal child. Display the numbers in a table and indicate what statistical procedure would be appropriate. 18. A study is designed to compare the effectiveness of a commonly used drug therapy to an experimental treatment involving mental imaging and diet therapy. For this purpose patients were carefully matched on age, sex and clinical condition. One patient in each pair was given the drug therapy while the other

5 received the competing regimen. The treatment results based on 120 matched pairs show that for 89 matched pairs both therapies are ineffective; for 14 pairs both therapies are effective; for 5 matched pairs the drug therapy is effective, whereas the imaging and diet therapy was ineffective; for 12 matched pairs the imaging and diet were effective, whereas the drug therapy was ineffective. a) How many pairs in this study would be considered concordant? b) How many pairs would be considered discordant? c) Perform a significance test to assess any differences in effectiveness between the two therapies. d) Compute the odds ratio.