Consider a Phase III clinical trial to test the effectiveness of an antihypertensive drug. The trial will compare the drug to a placebo, and study participants will be randomly assigned into two equal-sized homogeneous groups. The patients in the treatment group will be given the drug, and those in the control group will be given the placebo. The primary endpoint will be taken as the mean reduction in blood pressure after six weeks. It is known from published studies that the reduction in the blood pressure of hypertensive patients can be regarded as being normally distributed during treatment with either the placebo or the drug. It is also known that the placebo has no mean effectiveness in reducing the blood pressure of hypertensive patients, while a Phase II study indicated that the drug reduces 65 the blood pressure of hypertensive patients by a mean hypertensive patients by a mean value of about 5 mm Hg. This is regarded as a clinically relevant improvement. Moreover, clinical knowledge suggests that the standard deviation of the reduction in blood pressure of hypertensive patients with either the placebo or the drug can be taken as 25 mm Hg. To clarify whether the drug causes a statistically significantly reduction in blood pressure, a one-tailed Z-test will be performed. To ensure that neither too few nor too many patients are included in the study, the sample size will be planned in advance. This will require the pre- specification of statistical power and the level of significance of the statistical test. The level of significance is the probability of obtaining a statistically significant test result given there is no real obtaining a statistically significant test result given there is no real difference in the reduction in blood pressure between the placebo and the drug. The standard convention of 2.5% for one-tailed tests will be used. The statistical power is the probability of obtaining a statistically significant test result given that the drug reduces blood pressure by a mean value of 5 mm Hg more than the placebo, and will be taken as 90%. Problem 3 1 point possible (graded) What is the power of the test if the drug reduces the blood pressure of hypertensive patients by a mean value of 5 mm Hg, but we use the sample size calculated in Problem 2? (Note: Your answer should be a number in percentage form. Do not enter '%'.) Power = % Hint. This problem can be solved using the equations covered in lecture or the interactive calculator. Note that if you have a weak treatment effect and choose a small sample size, either to mitigate your costs or because you are overconfident about the effectiveness of your drug, then you are taking an enormous risk, because your study will be underpowered. Consider a Phase III clinical trial to test the effectiveness of an antihypertensive drug. The trial will compare the drug to a placebo, and study participants will be randomly assigned into two equal-sized homogeneous groups. The patients in the treatment group will be given the drug, and those in the control group will be given the placebo. The primary endpoint will be taken as the mean reduction in blood pressure after six weeks. It is known from published studies that the reduction in the blood pressure of hypertensive patients can be regarded as being normally distributed during treatment with either the placebo or the drug. It is also known that the placebo has no mean effectiveness in reducing the blood pressure of hypertensive patients, while a Phase II study indicated that the drug reduces 65 the blood pressure of hypertensive patients by a mean hypertensive patients by a mean value of about 5 mm Hg. This is regarded as a clinically relevant improvement. Moreover, clinical knowledge suggests that the standard deviation of the reduction in blood pressure of hypertensive patients with either the placebo or the drug can be taken as 25 mm Hg. To clarify whether the drug causes a statistically significantly reduction in blood pressure, a one-tailed Z-test will be performed. To ensure that neither too few nor too many patients are included in the study, the sample size will be planned in advance. This will require the pre- specification of statistical power and the level of significance of the statistical test. The level of significance is the probability of obtaining a statistically significant test result given there is no real obtaining a statistically significant test result given there is no real difference in the reduction in blood pressure between the placebo and the drug. The standard convention of 2.5% for one-tailed tests will be used. The statistical power is the probability of obtaining a statistically significant test result given that the drug reduces blood pressure by a mean value of 5 mm Hg more than the placebo, and will be taken as 90%. Problem 3 1 point possible (graded) What is the power of the test if the drug reduces the blood pressure of hypertensive patients by a mean value of 5 mm Hg, but we use the sample size calculated in Problem 2? (Note: Your answer should be a number in percentage form. Do not enter '%'.) Power = % Hint. This problem can be solved using the equations covered in lecture or the interactive calculator. Note that if you have a weak treatment effect and choose a small sample size, either to mitigate your costs or because you are overconfident about the effectiveness of your drug, then you are taking an enormous risk, because your study will be underpowered