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_Homework_exam1solutions

_Homework_exam1solutions - BST STA 225 Exam 1 Spring 2006...

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BST/ STA 225, Exam 1: Spring, 2006. Brief solutions 1. A Phase II clinical trial in refractory acute leukemia will treat 20 patients with a new chemotherapy drug. Bone marrow will be sampled at baseline and at 4 weeks after treatment. The primary outcome measure Y i for patient i will be the change in blast level (on the log scale). Previous studies suggest the change is normally distributed with a standard deviation of about 0.3 on the log scale. If the true mean change is a decrease of 0.3 or more, the treatment will be worth pursuing, but if the change is 0.1 or less, the new treatment is not worth further study. The investigator wants to have at most a 5% chance of proposing further studies if the true mean change is 0.1 or less. No interim analysis is planned, though a DSMC will monitor the study for safety. a. Find an appropriate critical value C such that if the mean change observed is greater than C , you should conclude the new treatment is worth studying. Answer : One-sided hypothesis test with H 0 : μ 0 . 1 and H 1 : μ > 0 . 1. We assume normal distribution. Technically with small n we should use t test (one tailed, 19 df). We reject if T = ¯ X - 0 . 1 S/ n > 1 . 729 . Alternatively, ¯ X > 0 . 1 + 1 . 729 S/ n. Note that you shouldn’t use the SD from previous studies as the variability in your study might differ. Most people proposed a Z test here. b. Using your critical value, what is the power of this study? Answer : The power for the change of clinical interest would be the probability that you exceed 0 . 1 + 1 . 729 S/ n if the true mean is 0.3. I found this using swogstat to be 0.91, assuming the true SD is around 0.3. Note that this is based on normal approximation and used critical value of 1.645. The true power might be somewhat less, because we had to estimate the SD and used a greater critical value. One should be mindful in small samples that this is a potential problem with assuming known SD and actually computing test statistic using (as you should!) the observed SD. c. Since this is a common pediatric condition with a poor prognosis even under the best available treatment, accrual to the study is rapid. The DSMC looks at the results from the first 9 patients and sees a mean change in blast level of 0.4. Should they consider stopping the trial early? Why or why not? Give your reasons, briefly.

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