Control of Confounding in the Analysis - Stratified Analysis
One way of identifying confounding is to examine the primary association of interest at different levels of a potential confounding factor. The side by side tables below examine the relationship between obesity and incident CVD in persons less than 50 years of age and in persons 50 years of age and older, separately.
Table of Obesity and Incident Cardiovascular Disease by Age Group
|
|
Age ‹ 50 |
|
|
Age ≥ 50 |
||||
|---|---|---|---|---|---|---|---|---|
|
|
CVD |
No CVD |
Total |
CVD |
No CVD |
Total |
||
|
Obese |
10 |
90 |
100 |
Obese |
36 |
164 |
200 |
|
|
Not Obese |
35 |
465 |
500 |
Not Obese |
25 |
175 |
200 |
|
|
Total |
45 |
555 |
600 |
Total |
61 |
339 |
400 |
|
The stratum-specific risk ratios are as follows:
- Among those ‹50, the risk ratio is:
- Among those ≥ 50, the risk ratio is:
Recall that the risk ratio for the total, combined sample was RR = 1.79; this is sometimes referred to as the "crude" measure of association, because it is not adjusted for potential confounding factors. The risk ratios for the age-stratified analysis are similar (RR = 1.43 and 1.44, respectively), but less than the crude risk ratio. This indicates that there was confounding by age in the overall sample. We saw that obese subjects were more likely to be 50 and older, and we also saw that those over age 50 had a greater risk of CVD. As a result, the crude analysis overestimated the true association between obesity (per se) and CVD, because of the greater proportion of older subjects among the obese group.
Several things are noteworthy in this example. First, if you compare the cumulative incidence in young versus old active subjects, you can see that older subjects had a higher risk of CVD than younger subjects; this was true for both obese and non-obese subjects. Therefore, age and CVD (the outcome of interest) are associated. In addition, obesity was more common in older subjects, meaning that age and obesity were also associated. Finally, there is no reason to think that age is an intermediary variable in the causal chain between obesity and CVD. Therefore, these observations satisfy all three of the requirements for a confounder.
Comparing the crude and stratum-specific measures of association is a very practical way to determine whether confounding is present and how bad it is. You calculate an overall crude (unadjusted) relative risk (or odds ratio) and compare it to the stratum-specific relative risks (or odds ratios). If the stratum-specific measures of association are similar to the crude measure of association, then there is no confounding by that factor, and you can just use the crude measure of association. However, if the stratified estimates of association differ from the unadjusted estimate by 10% or more, then there is evidence of confounding.