Residual confounding

Ideally, in order to account for confounding between exposure and disease, we stratify according to the confounding variable. When the confounding variable lends itself to few strata (i.e. gender, which has two strata: male or female), there tends to be sufficient data for results of the stratification to have sufficient power: lending to an overall strength of inference.

Strata can have a biological meaning or a quantitative rationale. Whatever the choice, the variable of interest is no longer a confounder within the stratum. If the dataset is stratified according to 10 year age groups, then it must be verified that age is no longer a confounder within those 10 year age group strata. If we stratified further to examine for confounding, there would be cells containing little or no data: which would need to be compensated for using modeling assumptions.

Typically these assumptions form a regression model - which will never be entirely correct. The bias remaining is 'residual confounding' - that which remains after confounding has been adjusted for as much as possible [1].

Cancelling out 

Factors may not appear to be confounders if they cancel each other out.

In a (hypothetical) study examining the risk of lung cancer amongst those exposed to silica dust; exposure is found to be a risk factor for disease. However, if 50% of those exposed to silica dust were also tobacco smokers, while only 30% of the unexposed were tobacco smokers, then smoking appears to be confounding the relationship between exposure to silica dust and development of lung cancer.

If the exposed are also younger than the unexposed, but the young are less likely to develop lung cancer (regardless of smoking); then the two confounders (age and smoking) are affecting the original association (between exposure to silica dust and lung cancer) in opposite directions. Neither may appear to be a confounding variable; they have cancelled each other out.

It is hoped that situations such as these are rare, but while an exact cancellation of two confounding factors may be rare, they will both have an effect on the total confounding within the model [2].   

References

1. K.J.Rothman, S.Greenland, T.L.Lash. Modern Epidemiology. Third ed. Philadelphia, USA: Lipincott Williams and Wilkins; 2008.

2. McNamee R. Confounding and confounders. Occupational and Environmental Medicine 2003 Mar 1;60(3):227-34.