Homework 5: Statistical Analysis for Clinical Trials - Prof. Daowen Zhang, Assignments of Statistics

Download Homework 5: Statistical Analysis for Clinical Trials - Prof. Daowen Zhang and more Assignments Statistics in PDF only on Docsity! ST520, Fall 2008 Homework 5, due: Thursday, 10/23/2008 1. (10 pts) Suppose we would like to compare a new treatment (treatment 1) to the standard treat- ment (treatment 2) in reducing weight where treatment assignment will be done by permuted block randomization so that the two-sample t-test will be appropriate to compare these two treat- ments. Assume the population variance of the weight distribution is 64. We wish to detect a 5 unit weight difference between the new treatment and the standard treatment with 90% power at the significance level α = 0.05 using a two-sided t-test. (a) Find the necessary sample size for the study for the given design characteristics assuming equal allocation. (b) If the size of the treatment effect turned out to be what you expected, what is the p-value? (c) How large should the estimated treatment effect be to make the p-value significant (≤ 0.05)? 2. (10 pts) Suppose in the following table are blood pressures from 20 patients receiving treatment 1 (new treatment) and treatment 0 (standard treatment) in a clinical trial. The treatment assign- ment was permuted block randomization stratified on gender where female is coded as gender=0 and male is coded as gender=1: 1 trt gender y=blood pressure 0 0 132 0 0 140 0 0 119 0 0 132 0 0 133 0 1 117 0 1 118 0 1 115 0 1 123 0 1 118 1 0 131 1 0 120 1 0 123 1 0 120 1 0 122 1 1 115 1 1 120 1 1 113 1 1 119 1 1 108 (a) Conduct a two-sided two-sample t-test to compare treatment 1 to treatment 0. (b) Conduct the following regression analysis to compare treatment 1 to treatment 0: yi = β0 + β1trti + β2genderi + ei. (c) Comment the similarity and difference between the above two methods. Which method do you think is right? 3. (10 pts) Suppose we want to compare the response rates between two treatments (1 & 2) in a clinical trial. The best guess of the response rate for treatment 2 is 0.3 and we would like to detect a 10% increase in the response rate for treatment 1 using two-sided testing procedures at significance level 0.05 with power 90%. Assume equal allocation. How large should the sample size be for the study using the two testing procedures discussed in class? 4. (10 pts) In class we derived the sample size formula for comparing two treatments which produce binary responses using variance stabilizing arcsin transformation. It turns out that the following transformation for sample proportion gives us what is called a symmetry transformation: g(p) = ∫ p 0 1 [x(1− x)]1/3 dx, 2