Data Analysis: Confounders, Mediators, and Moderators

A Evans
Data Analysis: Confounders, Mediators, and Moderators
Example 1:
Q: Is one type of procedure for treating kidney stones more effective than another?
Data: Procedure Success rate
Adjust for size of stone:
Conclusions
Open 78% (273/350)
Percutaneous 83% (289/350)
Small stones Open 93%
Percutaneous 83%
Large stones Open 73%
Percutaneous 69%
F
A ? B
Procedure
Stone size
?
Success
1. The association between procedure and success rate is confounded (mixed up
and confused) with stone size.
2. After adjusting for stone size, open procedure appears to be more effective.
A Evans, March 2006 Confounders, Mediators, Moderators 1

Example 2:
Q: Does smoking affect quality of life?
Data: Smoking mean QOL score
Adjust for lung disease:
Yes 75
No 85
No COPD Yes 90
No 90
COPD Yes 71
Confounder? Moderator? Mediator?
F
A ? B
No 71
?
Smoking
Lung
disease
?
QOL
A Evans, March 2006 Confounders, Mediators, Moderators 2

Example 3:
Q: Does hypertension cause strokes?
Data: Risk of stroke by hypertension and smoking:
Smoking No smoking
Hypertension 33 1.1
No hypertension 3 0.1
Questions:
1. Is smoking a potential confounder?
2. Does smoking modify the relationship between hypertension and disease?
3. In a logistic regression model, would the interaction term be significant?
Confounder? Moderator? Mediator?
A
F
?
smoking
Hypertension Stroke
B
hypertension*smoking
+ smoking
Hypertension
Stroke
– smoking
A Evans, March 2006 Confounders, Mediators, Moderators 3

Summary
Confounding is a bias you hope to prevent or control.
Effect modification (interaction) is a more detailed
description of the effect itself.
Confounding is something to avoid.
Effect modification is something to identify and report.
Mediators clarify the causal pathway.
Don’t control for a factor that is caused by the exposure
of interest.
Don’t control for a factor that is caused by the outcome
of interest.
Draw a conceptual model before analyzing data.
References
Weinberg. Toward a clearer definition of confounding. Am J Epidemiol 1993;137:1-8.
Greenland, Pearl, Robins. Causal diagrams for epidemiologic research. Epidemiology
1999;10:37-48.
Kaufman, Cooper. Commentary: Considerations for use of racial/ethnic classification in
etiologic research. Am J Epidemiol 201;154:291-8.
A Evans, March 2006 Confounders, Mediators, Moderators 4

Questions
1. Are there disparities across ethnic groups in the burden
of suffering from asthma?
Do you control for SES?
2. Is the disparity in asthma morbidity across ethnic groups
mediated by SES?
Do you control for depression score or local air pollution?
3. Is the effect of ethnicity on asthma morbidity modified
by socioeconomic factors?
Equivalent null hypotheses:
The difference in asthm morbidity between blacks and non-blacks is the
same for each level of each socioeconomic factor.
The interaction term between ethnic group and each socioeconomic
factor will have a coefficient of zero.
4. Which of the following are examples of confounding,
interaction, both, or neither?
Example Crude OR Stratum 1 Stratum 2 Adj OR
1 2.36 2.43 2.32 2.37
2 2.36 3.48 3.52 3.51
3 2.36 1.03 1.18 1.06
4 2.36 1.03 5.46 2.34
5 2.36 2.43 5.46 4.02
6 2.36 0.54 0.63 0.59
7 2.36 0.54 3.52 1.98
A Evans, March 2006 Confounders, Mediators, Moderators 5

5. Consider the two graphs below. Is there an interaction
between exposure and age? Incidence of disease is plotted
on the vertical axis and age (a potential confounder) is
plotted on the horizontal axis. Separate lines are drawn the
exposed (E+) and unexposed groups (E-).
AGE
E+
E–
AGE
A Evans, March 2006 Confounders, Mediators, Moderators 6
E+
E–

6. You perform a case control study to evaluate alcohol as
a cause of lung cancer. You (properly) select 150 cases and
150 controls. The results are below.
CA No CA
Alcohol 107 78
No 43 72
Total 150 150
OR = 2.3 (P