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role that bacteria and viruses play unites the two types of illness and
enriches our understanding of both.
We often try to turn such pseudo-correlations to advantage in our
research, using readily measured proxy variables in place of their less easily
measured “causes.” Examples are our use of population change in place of
economic growth, M2 for the desire to invest, arm cuff blood pressure
measurement in place of the width of the arterial lumen, and tumor size
for mortality. At best, such surrogate responses are inadequate (as in
attempting to predict changes in stock prices); in other instances they may
actually point in the wrong direction.
At one time, the level of CD-4 lymphocytes in the blood appeared to
be associated with the severity of AIDs; the result was that a number of
clinical trials used changes in this level as an indicator of disease status.
Reviewing the results of 16 sets of such trials, Fleming [1995] found that
the concentration of CD-4 rose to favorable levels in 13 instances even
though clinical outcomes were only favorable in eight.
Stratification
Gender discrimination lawsuits based on the discrepancy in pay between
men and women could be defeated once it was realized that pay was
related to years in service and that women who had only recently arrived
on the job market in great numbers simply didn't have as many years on
the job as men.
These same discrimination lawsuits could be won once the gender com-
parison was made on a years-in-service basis—that is, when the salaries of
new female employees were compared with those of newly employed men,
when the salaries of women with three years of service were compared
with those of men with the same time in grade, and so forth. Within each
stratum, men always had the higher salaries.
If the effects of additional variables other than X on Y are suspected,
they should be accounted for either by stratifying or by performing a mul-
tivariate regression as described in the next chapter.
The two approaches are not equivalent unless all terms are included in
the multivariate model. Suppose we want to account for the possible
effects of gender. Let I [ ] be an indicator function that takes the value 1 if
its argument is true and 0 otherwise. Then to duplicate the effects of
stratification, we would have to write the multivariate model in the follow-
ing form:
[
] +- [
(
]
) +
[
] +- [
(
]
) +
Y =
aI
male
a
1
I
male
b I
male
X b
1
I
male
e
.
m
f
m
f
In a study by Kanarek et al. [1980], whose primary focus is the relation
between asbestos in drinking water and cancer, results are stratified by sex,
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