A - Confounding Lesson

Confounding

A confounder is a third variable that can make it appear that an observed exposure is associated with an outcome. In other words, a confounder is an 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

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)
  • 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 One

You think that the risk of heart attack 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. Coffee appears to be associated with heart attacks. 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 heart attacks, 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 heart attacks. 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
Heart Attack
Yes		 Heart Attack
No
Coffee Drinker
Yes		 45
(A)		 30
(B)
Coffee Drinker
No		 30
(C)		 45
(D)

Crude Odds Ratio: Calculation

The crude odds ratio can be calculated by the following formula:

           Crude Odds Ratio = LaTeX: \frac{AD}{BC}=\frac{45\ast45}{30\ast30}=\frac{2025}{900}=2.25ADBC=45∗4530∗30=2025900=2.25

 

Without considering the effect of smoking status, the odds of having a heart attack are 2.25 higher in those that drink coffee than those that do not drink coffee.

Stratified Odds Ratio: 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.

Stratified Odds Ratio: Data
Smokers Heart Attack Non-Smokers Heart Attack
Yes No Yes No
Coffee Drinker 40 20 5 10
Non-Coffee Drinker 10 5 20 40

Stratified Odds Ratio: Calculations

                               Odds Ratio for Smokers = LaTeX: \frac{AD}{BC}=\frac{40\ast5}{20\ast10}=\frac{200}{200}=1ADBC=40∗520∗10=200200=1

                              Odds Ratio for Nonsmokers = LaTeX: \frac{AD}{BC}=\frac{5\ast40}{10\ast20}=\frac{200}{200}=1ADBC=5∗4010∗20=200200=1

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 heart attacks seen in the crude odds ratio is actually caused by the confounder, smoking status.

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