solution

The paper “The Effect of an Endothelin-Receptor Antagonist, Bosentan, on Blood Pressure in Patients with Essential Hypertension’’ [The New England Journal of Medicine (1998)] discussed the contribution of bosentan to blood pressure regulation in patients with essential hypertension. The study involved 243 patients with mild-to-moderate essential hypertension. After a placebo run-in period, patients were randomly assigned to receive one of four oral doses of bosentan (100, 500, or 1,000 mg once daily or 1,000 mg twice daily) or a placebo. The blood pressure was measured before treatment began and after a 4-week treatment period. The primary end point of the study was the change in blood pressure from the baseline obtained prior to treatment to the blood pressure at the conclusion of the 4-week treatment period. A summary of the data is given in the following table.

a. Which of the dose levels were associated with a significantly greater reduction in the diastolic pressure in comparison to the placebo? Use a 5 .05.

b. Why was it important to include a placebo treatment in the study?

c. Using just the four treatments (ignore the placebo), construct a contrast to test for an increasing linear trend in the size of the systolic pressure reductions as the dose levels are increased. See Exercise 9.25 for the method for creating such a contrast.

d. Use Tukey’s W procedure to test for pairwise differences in the mean systolic blood pressure reductions for the four treatment doses. Use a  .05.

e. The researchers referred to their study as a double-blind study. Explain the meaning of this terminology.

Exercise 9.25

The article “The Ames Salmonell/Microsome Mutagenicity Assay: Issues of Inference and Validation” [Journal of American Statistical Association (1989) 84:651–661] discusses the importance of chemically induced mutation for human health and the biological basis for the primary in vitro assay for mutagenicity, the Ames Salmonell/microsome assay. In an Ames test, the response obtained from a single sample is the number of visible colonies that result from plating approximately 108 microbes. A common protocol for an Ames test includes multiple samples at a control dose and four or five logarithmically spaced doses of a test compound. The following data are from one such experiment with 20 samples per dose level. The dose levels were mg/sample.

We want to determine whether there is an increasing trend in the mean number of colonies as the dose level increases. One method of making such a determination is to use a contrast with constants ai determined in the following fashion. Suppose the treatment levels are t values of a continuous variable  is significantly different from zero and positive, then we state there is a positive trend in the mi s. If l ^ is significantly different from zero and negative, then we state there is a negative trend in the mi s. In this experiment, the dose levels are the treatments  Thus, the coefficients for the contrasts are   need to evaluate the significance of the following contrast in the treatment means given by  If the contrast is significantly different from zero and is positive, we conclude that there is an increasing trend in the dose means.

a. Test whether there is an increasing trend in the dose mean. Use a  .05.

b. Do there appear to be any violations in the conditions necessary to conduct the test in part (a)? If there are violations, suggest a method that would enable us to validly test whether the positive trend exists.