notes for 2nd midterm

# notes for 2nd midterm - 8 Variables based on two rates (,...

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8 Variables based on two rates (Δ, RR, OR) NORMAL appx. of posterior distributions Starting with a uniform prior, we can approximate the posterior distributions of pop osed un in outcome adverse of odds pop osed in outcome adverse of odds OR p p RR p p n e c t exp exp = = - = , Reverse engineering of frequentist confidence intervals to obtain σ μ σ Δ ˆ = c t p p ˆ ˆ - c c c t t t n p p n p p ) ˆ 1 ( ˆ ) ˆ 1 ( ˆ - + - log RR RR log c c c t t t p n p p n p ˆ ) ˆ 1 ( ˆ ) ˆ 1 ( - + - log OR OR log ) , ( 1 ) , ( 1 ) , ( 1 ) , ( 1 NE NA NE A E NA E A + + + 8b. PROTOTYPE PROBLEMS for Δ, RR & OR (flat prior normal appx) Δ drug therapy: 144 of 200 patients succeed, control: 112 of 200 patients succeed. Find a 95% credible interval for Δ, and determine P(Δ > .10 | data). 90 . ) | 10 . ( 28 . 1 047 . 16 . 10 . ). 047 )(. 96 . 1 ( 16 . % 95 047 . 200 ) 44 )(. 56 (. 200 ) 28 )(. 72 (. , 16 . ˆ , 56 . 200 / 112 ˆ , 72 . 200 / 148 ˆ = - = - ± = = + = = = = = = = data P credible p p c t σ μ Suppose the frequentist confidence interval for Δ is (.08, .14) Determine P(Δ > .10 | data). .11 = midpoint 749 . ) | 10 . ( 67 .

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## This note was uploaded on 09/08/2008 for the course STAT 101 taught by Professor Russo during the Spring '08 term at University of Iowa.

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notes for 2nd midterm - 8 Variables based on two rates (,...

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