Confounding
Definition: A confounder is a third variable that can make it appear (sometimes incorrectly) that an observed exposure is associated with an outcome. In other words, a confounder is an unobserved exposure associated with the exposure of interest and is a potential cause of the outcome of interest. Confounders lead to bias that distorts the magnitude of the relationship between two factors of interest.
Conditions for a Factor to be a Potential Confounder:
- Must be a risk factor for the outcome (disease)
- Must be associated with the exposure.
- Must not be an intermediate step in the causal path
- Should not be a surrogate for exposure
From this diagram one can see the observed exposure appears to be associated with the disease along with the third confounding variable. In addition, the confounding variable (unobserved) is associated with the disease. Therefore, the confounding variable may be distorting the true relationship between the observed exposure and the disease.
Criteria for Determining Confounders are:
- There should be an association of the confounder and the disease among the unexposed.
- To determine this calculation among the exposed, calculate:
(Odds those cases have the confounder) / (Odds those controls have the confounder)
- To determine this calculation among the exposed, calculate:
- The distribution of the confounding variable should differ between exposed and unexposed groups.
- To determine if this is the case, calculate among the controls:
(Odds of having the confounder in the exposed) / (Odds of having the confounder in the unexposed)
Example: You think that the risk of myocardial infarction may be increased among coffee drinkers compared to non-coffee drinkers. You also think smoking may be a confounder in this association because people who drink coffee also tend to smoke.
From this diagram, coffee appears to be associated with myocardial infarction. However, it is believed that smoking is a confounder because it is associated with both coffee drinking and with myocardial infarction. Smoking status is most likely confounding the relationship between coffee drinking and myocardial infarction, making it appear there is a relationship when in fact there is none.
To determine if smoking is a confounder:
- Calculate the crude odds ratio (the odds ratio of the entire group)
- Calculate the stratified odds ratios (the odds ratios for smokers and non-smokers).
A crude odds ratio greater than 1.0 indicates an association between coffee drinking and myocardial infarction. However, if the stratum-specific odds ratios are different from the crude and equal to each other then this will indicate smoking is a confounder.
Crude Odds Ratio: Data
| Myocardial Infarction Yes |
Myocardial Infarction No |
|
| Coffee Drinker Yes |
90 (A) |
60 (B) |
| Non-Coffee Drinker No |
60 (C) |
90 (D) |
Crude Odds Ratio: Calculation
The crude odds ratio can be calculated by the following formula:
Crude odds ratio =
( A · D ) / ( B · C ) = ( 90 · 90 ) / ( 60 · 60 )
=
8100 / 3600 =
2.25
Without considering the effect of smoking status, the odds of having a myocardial infarction are 2.25 higher in those that drink coffee than those that do not drink coffee.
Stratified Odds Ratios: Data
Next, the stratum-specific odds ratios would be calculated for those that smoke and do not smoke. The same formula as above can be used.
| Smokers Myocardial Infarction |
Non-Smokers Myocardial Infarction |
|||
| Yes | No | Yes | No | |
| Coffee Drinker | 80 | 40 | 10 | 20 |
| Non-Coffee Drinker | 20 | 10 | 40 | 80 |
Stratified Odds Ratios: Calculations
- Odds ratio for those that smoke =
( A · D ) / ( B · C ) =
( 80 · 10 ) / ( 40 · 20 )
= 800 / 800 = 1.0 - Odds ratio for those that do not smoke =
( A · D ) / ( B · C ) =
( 10 · 80 ) / (20 · 40 )
= 800 / 800 = 1.0
Although the crude odds ratio is 2.25, the stratified odds ratios are 1.0 when smoking status is stratified, indicating no association. The apparent association between coffee drinking and myocardial infarction seen in the crude odds ratio is actually caused by the confounder, smoking status.
