Epi 201 Lab 5.docx - Epi 201 Lab 5 1 The table below shows the data collected in a study of 12 individuals The goal was to estimate the effect of daily

Epi 201 Lab 5.docx - Epi 201 Lab 5 1 The table below shows...

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Epi 201 Lab 5 1. The table below shows the data collected in a study of 12 individuals. The goal was to estimate the effect of daily low-dose aspirin (81 mg/day) (A=1) versus no aspirin (A=0) on the cumulative incidence of stroke (Y=1) over a 5-year period. The table also shows the values of the counterfactual outcomes that would have been observed under treatment (Y a=1 ) and under no treatment (Y a=0 ) with aspirin. For the purposes of this question, disregard random variability. a. Compute the following and provide a brief interpretation of these quantities. For this and all the questions below, use the notation discussed in class to identify each quantity, e.g., Pr{Y=1} is the observed cumulative incidence. Observed cumulative incidence of stroke ObservedCI of stroke = Pr [ Y = 1 ] = 6 12 = 0.5 a 5 year period. The cumulative incidence if everybody had been treated CI had everybodytreated = Pr [ Y a = 1 = 1 ] = 4 12 = 0.67 a 5 year pediod . The cumulative incidence if everybody had remained untreated CI had everybody remained untreated = Pr [ Y a = 1 = 1 ] = 8 12 = 0.33 5 y b. Compute the causal cumulative incidence difference CausalCID = Pr [ Y a = 1 = 1 ] Pr [ Y a = 0 = 1 ] = 4 12 8 12 =− 0.33 CI of stroke had the population been treated with low-dose aspirin is 0.33 fewer than CI of stroke had the population been untreated. ID A Y Y a=1 Y a=0 1 0 1 0 1 2 0 1 0 1 3 0 0 0 0 4 0 0 0 0 5 0 1 1 1 6 0 1 1 1 7 1 0 0 1 8 1 0 0 1 9 1 0 0 0 10 1 0 0 0 11 1 1 1 1 12 1 1 1 1
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Causal cumulative incidence ratio CaudalCIR = Pr [ Y a = 1 = 1 ] Pr [ Y a = 0 = 1 ] = 4 / 12 8 / 12 = 2 3 = 0.667 CI of stroke had the population been treated with low-dose aspirin is 0.667 times higher than CI of stroke had the population been untreated. Causal odds ratio Causal ¿ Pr [ Y a = 1 = 1 ]/ Pr [ Y a = 1 = 0 ] Pr [ Y a = 0 = 1 ]/ Pr [ Y a = 0 = 0 ] = 0.25 Odds of stroke had the population been treated with low-dose aspirin is 0.25 times higher than odds of stroke had the population
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