BIOST 511 Activity 16 – Non-parametric Tests and Categorical Data I

1. Much attention has been given in recent years to the role of transcendental meditation in improving health, particularly in lowering blood pressure. One hypothesis that emerges from this work is that transcendental meditation might also be useful in treating psychiatric patients with symptoms of anxiety. Suppose that a protocol of meditational therapy is administered once per day to 20 patients with anxiety. The patients are given a psychiatric exam at baseline and at a follow-up exam two months later. The degree of improvement is rated on a 10-point scale, with 1 indicating the most improvement and 10 the least improvement. Similarly, 26 comparable affected patients with anxiety are given standard psychotherapy and are asked to come back two months later for a follow-up exam. What statistical procedure would be appropriate to determine the effectiveness of transcendental meditation?

2. Suppose we wish to compare the length of stay in the hospital for patients with the same diagnosis at two different hospitals. What statistical procedure is appropriate?

3. Suppose we are conducting a study of the effectiveness of lithium therapy for manic-depressive patients. The study is carried out at two different centers, and we wish to determine if the patient populations are comparable at baseline. We administer a self-rating questionnaire to the prospective patients at the two different centers about their general psychological well-being, in which the outcome measure is a four-category scale as follows: 1=feel okay; 2=usually feel okay; 3=feel nervous some of the time; 4=feel nervous most of the time. What statistical procedure would be appropriate if there is any significant difference in the response of the two patient populations?

4. Researchers asked several smokers how many cigarettes they had smoked the previous day. There were four women and six men in the sample. Here are the data:

Women Men 4 2 7 3 19 5 20 6 8 16

Conduct a test of the hypothesis that there is no difference between men and women. Could we conduct a sign test here?

5. A recent study investigated the relationship between cigarette smoking and subsequent mortality in men with prior history of coronary disease. It was found that 264 out of 1731 non-smokers and 208 out of 1058 smokers had died in the 5-year period after the study began. Assume that the age distributions of the two groups are comparable, what is an appropriate statistical procedure to compare the mortality rates in the two groups?

6. 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 50-59 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. What is the general design? What is the appropriate statistical procedure for assessing the relationship between physical activity and sudden death from a heart attack? 7. Joseph Lister, a British physician of the late 19th 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

Medical Biometry I Autumn 2012 BIOST 511 Activity 16 – Non-parametric Tests and Categorical Data I

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 study design?

b) Determine if there is a significant association between mortality rate and the use of carbolic acid.

c) What is the odds ratio of living if carbolic acid was used? (Lecture 18)

d) Is it reasonable to compute the relative risk of living if carbolic acid was used? If so, what is the relative risk? (Lecture 18)

8. [Ref: The final report on the aspirin component of the ongoing Physician’s Health Study. NEJM (1989) 231(3): 129-135.] Does aspirin really help prevent heart attacks? During the 1980’s, approximately 22,000 physicians over the age of 40 agreed to participate in a long-term health study for which one important question was to determine whether aspirin helps to lower the rate of heart attacks (myocardial infarctions). The treatments of this part of the study were aspirin or placebo, and the physicians were randomly assigned to one treatment or the other as they entered the study. After the assignment, neither the participating physicians nor the medical personnel who treated them knew who was taking aspirin and who was taking placebo (double-blinded study). The physicians were observed carefully for an extended period of time and all heart attacks as well as other problems that occurred were recorded.

Other than aspirin, there are many variables that could affect the rate of heart attacks for the two groups of physicians. For example, the amount of exercise they get and whether they smoke are two prime examples of factors that could be controlled in the study so that the true effect of aspirin can be measured.

Heart Attack Treatment Yes No Total Assignment Aspirin 139 10782 10921 Placebo 239 10668 10907 Total 378 21450 21828

a) What is the study design?

The results of this study reported that 139 heart attacks were reported among the aspirin users and 239 were reported for the placebo group. What are the appropriate conditional proportions to study if we want to compare the rates of heart attacks for the two treatment groups? Is it reasonable to compute the relative risk for heart attacks for aspirin users to non-aspirin users? How about the odds ratio? The difference in the two rates of heart attacks? Explain.

b) Is there a significant association between heart attacks and aspirin use?

c) Heart attacks are not the only cause for concern in the Physician’s Health Study. Another is that too much aspirin can cause an increased risk of stroke. Among the aspirin users in the study, 119 had strokes during the observation period. Within the placebo group, only 98 participants had strokes. Place these data in appropriate two-way table and comment upon the association between aspirin use and strokes.

d) Is there a significant association between strokes and aspirin use?

Medical Biometry I Autumn 2012