Databases Reference
In-Depth Information
Here we have 100 people in both the treatment and control groups,
and in both the actual and counterfactual cases, we have a causal effect
of 0.3 - 0.2 = 0.1, or 10%.
But when we split this up by gender, we might introduce a problem,
especially as the numbers get smaller, as seen in Tables
12-2
and
12-3
.
Table 12-2. Stratified: Men
Treatment:
Drugged
Treatment:
Counterfactual
Control: Counterfactual
Control: No Drug
Y=1
15
2
5
5
Y=0
35
8
65
15
P(Y=1)
0.3
0.2
0.07
0.25
Table 12-3. Stratified: Women
Treatment:
Drugged
Treatment:
Counterfactual
Control: Counterfactual
Control: No Drug
Y=1
15
18
25
15
Y=0
35
72
5
65
P(Y=1)
0.3
0.2
0.83
0.1875
Our causal estimate for men is 0.3 - 0.25 = 0.05, and for women is 0.3
- 0.1875 = 0.1125. A headline might proclaim that the drug has side
effects twice as strong for women as for men.
In other words, stratification doesn't just solve problems. There are no
guarantees your estimates will be better if you stratify. In fact, you
should have very good evidence that stratification helps before you
decide to do it.
What Do People Do About Confounding Things in
Practice?
In spite of the raised objections, experts in this field essentially use
stratification as a major method to working through studies. They deal
with confounding variables, or rather variables they deem potentially
confounding, by stratifying with respect to them or make other sorts
of model-based adjustments, such as propensity score matching, for
example. So if taking aspirin is believed to be a potentially confounding
factor, they adjust or stratify with respect to it.
