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Chapter 12 Homework
Multi-sample Inference
1. Some common strategies for treating hypertensive patients by nonpharmacologic methods include (1) weight reduction and (2) trying to get the patient to relax more by mediational or other techniques. Suppose these strategies are evaluated by randomizing hypertensive patients to four group who receive the following types of nonpharmacologic therapy: Group 1 : Patients receive counseling for both weight reduction and meditation. Group 2 : Patients receive counseling for weight reduction but not for meditation. Group 3 : Patients receive counseling for meditation but not for weight reduction. Group 4 : Patients receive no counseling at all. Suppose 20 hypertensive patients are assigned at random to each of the four groups, and the change in diastolic blood pressure (DBP) is noted in these patients after 1-month period. The results are given in the table below.
Change in DBP among hypertensive patients who receive different kinds of nonpharmacologic therapy Group Mean change in DBP (baseline-follow up) (mm-Hg) sd change n
1 8.6 6.2 20 2 5.3 5.4 20 3 4.9 7.0 20 4 1.1 6.5 20
(a) Test the hypothesis that mean change in DBP is the same among the four groups.
(b) Analyze whether counseling for weight reduction has a significant effect on reducing blood pres- sure.
(c) Analyze whether meditation instruction has a significant effect on reducing blood pressure.
(d) Is there any relationship between the effects of weight-reduction counseling and meditation coun- seling on blood-pressure reduction? That is, does weight-reduction counseling work better for people who receive meditational counseling or for people who do not receive meditation counsel- ing, or is there no difference in effect between these two subgroups?
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2. A randomized trial examined the effects of lipid-modifying therapy (simvastatin plus niacin) and an- tioxidants (vitamins E and C, beta-carotene, and selenium) on cardiovascular protection in patients with clinical coronary disease, low HDL cholesterol, and normal LDL cholesterol. A total of 160 patients were randomized into four groups: placebo lipid-lowering and placebo antioxidants, active lipid-lowering and placebo antioxidants, placebo lipid-lowering and active antioxidants, or active lipid- lowering and active antioxidants. All participants had substantial stenoses (blockages) of the coronary arteries quantified by catheteriza- tion at baseline, and the primary endpoint was the percent change in a person’s stenoses after 3 years of treatment, with a positive change indicating an increased amount of stenosis, as shown in the table below. Because some patients did not complete the study, the primary endpoint was assessed in 146 participants.
Mean changes (±sd), per patient, in the percentage of stenosis by treatment group Placebo Simvastain-niacin Antioxidants Simvastatin-niacin (n = 34) (n = 33) (n = 39) plus antioxidants (n = 40)
Mean change in stenosis 3.9(±5.2) −0.4(±2.8) 1.8(±4.2) 0.7(±3.2) (% of diameter)
Source: Based on The New England Journal of Medicine, 312(6), 329-334, 1985
(a) Perform a one-way ANOVA to assess whether there are significant differences in mean change in percent stenosis among the four groups.
(b) Using the LSD method, identify which pairs of groups are significantly different.
(c) Are there significant interaction effects between simvastatin-niacin and antioxidants? What does an interaction effect mean in the context of this trial? (Hint: Use the linear contrast y, y4 − y2 − y3 + y1, where the group numbers are in the same order as in the table above.
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3. Suppose we have separately analyzed the effects of 10 SNPs comparing people with type I diabetes vs. controls. The p-values from these separate analyses are given in the table below.
Effects of 10 SNPs on type I diabetes SNP p-value SNP p-value
1 .04 6 .62 2 .10 7 .001 3 .40 8 .01 4 .55 9 .80 5 .34 10 .005
(a) Use the Bonferroni method to correct for multiple comparisons. Which SNPs show statistically significant effects?
(b) Use the FDR method to correct for multiple comparisons using an FDR=.05. Which SNPs show statistically significant effects? How do the results compare with those in part (a)?
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