Overadjustment in case-control studies.

In analyzing data from case-control studies to identify association between an exposure variable and disease status, other variables may be considered as potential confounding variables. Even when a variable has no causal association with disease (we assume that in the underlying population it is not related to disease conditional on the exposure variable) and is not a source of selection bias, apparent confounding may occur by chance. Adjusting on such a variable increases variability in the estimate of relative risk. Furthermore, an approach that selects from such variables those which most decrease the relative risk leads to bias in the risk estimate. These two effects lead to reduced statistical significance of the relative risk estimate and can lead to declaring detectable associations as insignificant. Theoretical approximations for quantitating these effects are derived and the adequacy of these approximation is confirmed by simulation. These results demonstrate the danger of overadjustment.