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Assignment 2

# Assignment 2 - PHC 6020 Homework Assignment 2 Due...

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PHC 6020 – Homework Assignment 2 Due Tuesday October 11, 2011 (Please show all your work, i.e. the steps that are necessary to reach your results.) 1. (12 pts) In a small clinical trial, permuted block randomization was used to assign one of two treatments (A or B) to six patients. Two blocks are chosen; the first block size was four (two A's and two B's chosen at random) and the second block size was two (one A and one B chosen at random). The end point of interest was change from baseline in log HIV viral RNA counts after eight weeks on treatment. The results of this trial are summarized as follows: Block 1 Treatment A B B A Response 0.6 0.8 1.5 0.7 Block 2 Treatment B A Response 1.0 0.2 The test statistic used to evaluate whether treatment B has better response than treatment A is based on ܻ െ ܻ , where ܻ is the average response among patients assigned to treatment B and ܻ is the average response for treatment A. We assume the sharp null hypothesis and reject in favor of treatment B if the test statistic is sufficiently large. a. Find the distribution of the test statistic that is induced by the permuted block randomization under the sharp null hypothesis. b. What is the p-value for the clinical trial described above? 2. (12 pts) Let the random variable ܺ~ܾሺ݊, ߨሻ . The sample proportion is denoted by ݌ ൌ ܺ/݊ . a. Prove that ௡ିଵ ቁ ݌ሺ1 െ ݌ሻ is an unbiased estimator for ߨሺ1 െ ߨሻ , ݊ ൒ 2 . Consider data from N studies using the same treatment regimen. We observe ሺܺ , ݊ , ݅ ൌ 1, ڮ , ܰ , where ݊ denotes the number of patients in the i -th study and ܺ denotes the number of these patients that respond to treatment. It will be assumed that these

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