5. (22pts) Table 1 shows the data collected in a study of 12 individuals. The goal was to estimate the effect of daily l

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5 22pts Table 1 Shows The Data Collected In A Study Of 12 Individuals The Goal Was To Estimate The Effect Of Daily L 1 (158.17 KiB) Viewed 107 times

5. (22pts) Table 1 shows the data collected in a study of 12 individuals. The goal was to estimate the effect of daily low-dose aspirin (A = 1) versus no aspirin (A = 0) on the risk of heart disease (Y = 1). The table also shows the values of the potential outcomes that would have been observed under treatment and under no treatment with aspirin. ID AYY(1) Y(0) 1 0 0 0 0 2 0 0 0 0 3 0 1 0 1 4 0 1 0 5 0 1 0 1 6 0 1 1 1 7 1 0 0 1 8 1 0 0 1 9 1 0 0 0 10 1 1 1 0 11 1 1 1 1 12 1 1 1 1 Table 1: Potential outcome data (a) (4pts) Can the data come from a randomized experiment? Ignore uncertainty here. (b) (4pts) Can you find an L so that the data come from a conditional randomized experiment? Ignore uncertainty here. (c) (4pts) Given the first three columns, can you rule out the null hypothesis that the causal risk difference is equal to 0? If not, fill in example values of Y(0) and Y(1) for each subject so that the causal risk difference is equal to 0. (d) (4pts) Given the first three columns, can you rule out that the causal risk difference is equal to 1? If not, fill in example values of Y(0) and Y(1) for each subject so that the causal risk difference is equal to 1. (e) (6pts) Given the first three columns, which are the possible values for the causal risk difference? Fill in example values of Y(0) and Y(1) for each subject so that the causal risk difference is equal to the minimal and maximal values you give. Given no data at all, which are the possible values for the causal risk difference?