C Inverse probability weighting L A Y obs fAL 1fAL Pseudo 1 1 1 60 34 43 80 1 1

# C inverse probability weighting l a y obs fal 1fal

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C: Inverse probability weighting L A Y # obs f[A|L] 1/f[A|L] Pseudo 1 1 1 60 3/4 4/3 80 1 1 0 90 3/4 4/3 120 1 0 1 40 1/4 4 160 1 0 0 10 1/4 4 40
0 1 1 75 3/5 5/3 125 0 1 0 75 3/5 5/3 125 0 0 1 60 2/5 5/2 150 0 0 0 40 2/5 5/2 100 Pseudo A=1 A=0 Total Y=1 205 310 515 Y=0 245 140 385 Total 450 450 900 Causalrisk ratio = Pr [ Y a = 1 = 1 ] Pr [ Y a = 0 = 1 ] = 205 / 450 310 / 450 = 0.6613 5 years If everyone in the study had taken aspirin, we would have observed 0.66 times the 5-year cumulative incidence of stroke compared to if no one in the study had taken aspirin, assuming no residual confounding by sex, no confounding by other variables, no selection bias and no information bias.
2. Using standardization, compute the cumulative incidence ratio for the exposed. Male ASA No ASA Total Female ASA No ASA Total Stroke 60 40 100 Smoke 75 60 135 No stroke 90 10 100 No Smoke 75 40 115 Total 150 50 200 Total 150 100 250 Pr [ Y a = 1 = 1 | A = 1 ] Pr [ Y a = 0 = 1 | A = 1 ] = Pr [ Y = 1 | A = 1, L = 0 ] Pr [ L = 0 A = 1 ] + Pr [ Y = 1 | A = 1, L = 1 ] Pr [ L = 1 | A = 1 ] Pr [ Y = 1 | A = 0, L = 0 ] Pr [ L = 0 A = 1 ] + Pr [ Y = 1 | A = 0, L = 1 ] Pr [ L = 1 | A = 1 ] ¿ 75 150 × 150 300 + 60 150 × 150 300 60 100 × 150 300 + 40 50 × 150 300 = 135 / 150 140 / 100 = 0.643 5 year If all the exposed had taken aspirin, we would have observed 0.64 times the 5-year cumulative incidence of stroke compared to if none of the exposed had taken aspirin, assuming no residual confounding by sex, no confounding by other variables, no selection bias, and no information bias. Traditional approach ^ SMR = a i b i N 1 i N 0 i = 60 + 75 40 × 150 50 + 60 × 150 100 = 135 120 + 90 = 0.643 5 years If all the exposed had taken aspirin, we would have observed 0.64

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• Summer '14
• FrancisCook

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