4.2.3 Evaluation of Interventions
In e¤orts to determine the e¤ect of a risk factor or an intervention, we may
want to estimate the di¤erence of means: say, between the population of
cases and the population of controls. However, we choose not to present the
methodology with much detail at this level—with one exception, the case of
matched design or before-and-after intervention, where each experimental unit
serves as its own control. This design makes it possible to control for con-
founding variables that are di‰cult to measure (e.g. environmental exposure)
and therefore di‰cult to adjust at the analysis stage. The main reason to
include this method here, however, is because we treat the data as one sample
and the aim is still estimating the (population) mean. That is, data from
matched or before-and-after experiments should not be considered as coming
from two independent samples. The procedure is to reduce the data to a one-
sample problem by computing before-and-after (or control-and-case) di¤er-
ences for each subject (or pairs of matched subjects). By doing this with paired
observations, we get a set of di¤erences that can be handled as a single sample
problem. The mean to be estimated, using the sample of di¤erences, represents
the e¤ects of the intervention (or the e¤ects of of the disease) under investigation.
Example 4.6 The systolic blood pressures of 12 women between the ages of 20
and 35 were measured before and after administration of a newly developed
oral contraceptive. Given the data in Table 4.6, we have from the column of
di¤erences, thedi’s,
n¼ 12
X
di¼ 31
X
di^2 ¼ 185TABLE 4.6
Systolic Blood
Pressure (mmHg)Subject Before After
After–Before
Di¤erence,di di^2
1 122 127 5 25
2 126 128 2 4
3 132 140 8 64
4 120 119 11
5 142 145 3 9
6 130 130 0 0
7 142 148 6 36
8 137 135 24
9 128 129 1 1
10 132 137 5 25
11 128 128 0 0
12 129 133 4 16
158 ESTIMATION OF PARAMETERS