4. You are asked to design a clinical trial where the primary elupomy a i.e., response or non-response. A two-arm randomized double-blind placebo-controlled trial is proposed to assess whether a new treatment is effective. Based on historical data, the best estimate for the response is 0.20. A treatment that can increase the response rate by 0.15 (i.e., from 0.20 to 0.35) is considered an important advance and we would want to declare such a treatment as significantly better with at least 90% power using a test at the 0.05 one-sided level of significance. Note: Here are some values that you may want to use for answering the question: . 20.99 = 2.33, 20.975 = 1.96, 20.95 = 1.64, 20.90 = 1.28, zo.80 = 0.84, zo.5 = 0.5 . sin '(v0.20) = 0.464, sin '(V0.35) = 0.633 3 P = 0.9 -0 B = 0.1 D= 0.15 171 = 0.2 12=0.35 71= 0.275 x=0.05 one-side (b) (3 pts) After discussion with the investigators it was decided that we would ran- domize using a 3:1 ratio; that is, with probability 0.75 (3/4) to the new treatment and 0.25 (1/4) to the placebo in order to get some additional experience on possible side effects for the new treatment. How large a sample size would you recommend for this clinical trial? Note: Be clear what test you would use to answer the question above and keep in mind that we are not using equal allocation to the two treatments. (c) (2 pts) Regardless of the results you obtained in (b), a randomized study was con- ducted and as a result of this trial 110 patients were randomized to the new treatment of which 30 responded, and 120 patients were randomized to placebo of which 40 re- sponded. Using the same test statistic that you used to answer part (b) what is the value of the test statistic with these data? Note: If needed you can use the following: . sin '(30/110) = 0.549, sin 1(\\40/120) = 0.615 ssp. S 5 ( 85.1. + 12. 1 ). 2 8PS (d) (2 pts) As best you can, give a range for the p-value based on the data in (c). What are your conclusions? 1 ( s. OV )'mic - ( 2 2.07 ) ' med