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

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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