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solutions7

solutions7 - Stat 665(Spring 2011 Kaizar Solutions 7...

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Stat 665 (Spring 2011) Kaizar Solutions 7 Exercises 40 points total 1. Nominal Regression (a) The prediction equations: log( ˆ μ 1 / ˆ μ 4 ) = 0 . 13 + 0 . 79 * A log( ˆ μ 2 / ˆ μ 4 ) = 0 . 71 + 0 . 18 * A log( ˆ μ 3 / ˆ μ 4 ) = 0 . 19 - 0 . 10 * A Where A = braceleftBigg 1 if alternating treatment 0 sequential treatment and μ 1 = probability of progressive disease μ 2 = probability of no change μ 3 = probability of partial remission μ 4 = probability of complete remission (b) Looking at the reported coefficients, I estimate that the odds of progressive disease (logit = 0.79) or no change (logit = 0.18) vs. complete remission is larger for those who recieved alternating treatment. However, the odds of partial remission vs. complete remission (logit = -0.10) is smaller for those recieving alternating treatment. Although not always necessary, it is generally a good idea to examine the other relation- ships as well: log( ˆ μ 1 / ˆ μ 3 ) = 0 . 792 + 0 . 103 = 0 . 90 log( ˆ μ 2 / ˆ μ 3 ) = 0 . 176 + 0 . 103 = 0 . 28 log( ˆ μ 1 / ˆ μ 2 ) = 0 . 792 - 0 . 176 = 0 . 61 Looking at these comparisons, I estimate that the odds of progressive disease (logit = 0.90) or no change (logit = 0.28) vs. partial remission is greater for those receiving alternating treatment. Finally, the odds of progressive disease vs. no change is also greater for those receiving alternating treatment (logit = 0.61). Thus, no matter how you look at it, alternating treatment seems to decrease the odds of a successful outcome. (c) probability of complete remission = e 1 e 0 . 792 + e 0 . 176 + e - 0 . 103 + e 1 = 0 . 387 1

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(d) LRT = 16 . 47901 - 7 . 79364 = 8 . 685 χ 2 3 (8 . 685) = 0 . 0337 Since the p-value is so small, I conclude that the type of treatment does have a significant association with the response. 2. (a) logit π 1 ) = - 1 . 22 + 0 . 57 A logit π 2 ) = 0 . 34 + 0 . 57 A logit π 3 ) = 1 . 38 + 0 . 57 A Where A = braceleftBigg 1 if alternating treatment 0 sequential treatment and π 1 = probability of progressive disease π 2 = probability of progressive disease or no change π 3 =
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