STAT 641 Lecture Notes - Lecture 2: Restricted Maximum Likelihood, Mixed Model, Point Estimation
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Solutions: suppose that we have a phase ii, single arm trial using a two stage design. The hypotheses of interest are h0 : 0. 15 versus h1 : 0. 4 where is the true success rate. Let yk be the total number of successes through stage k, k = 1, 2. Find the stopping probabilities under both h0 and h1. Under h0, the stopping probability is pr{y1 3} = . 7899, and under h1 it is . 0651. [1] 0. 06514674 (b) at stage 2 we enroll an additional 16 subjects and reject h0 if y2 > 8. Compute the overall probabilities of rejection under both h0 and h1 for the two-stage trial. We accept h0 if y1 3 and y2 8. Pr{y1 = i} pr{x2 8 i} = . 9659. > pbinom(3, 16, . 15) + sum(dbinom(4:8,16,. 15)*pbinom(4:0, 16, . 15)) > pbinom(3, 16, . 40) + sum(dbinom(4:8,16,. 40)*pbinom(4:0, 16, . 40)) Therefore, the rejection probabilities are 1-0. 9659=0. 0341 and 1-0. 0969=0. 9031 under.
