Joint effect of genes and environment distorted by selection biases: implications for hospital-based case-control...

The hospital-based case-control design enhances the response rates in studies that require the collection of biological samples from all of the participants. There are simple, established criteria for selecting controls so as to estimate the effect of a single factor without bias, but the analogous requirements for assessing an interaction are less clear. We derive these conditions by calculating the potential bias from selecting controls who were admitted for treatment of diseases related to either or both of the exposures of interest, designated as a gene variant (G) and an environmental agent (E). There is no bias in the estimate of the effect of E when G is associated with the control condition, whether causally or because of confounding. There is no bias in estimating multiplicative interaction between G and E for the disease of interest when there is no multiplicative G-E interaction for the control disease, even when the control condition is caused by G or E; if a mixture of several control diseases are used, however, the absence of G-E interaction in each individual disease does not ensure a lack of overall bias when controls are pooled. Hospital control designs are much less robust for assessing additive interaction. We conclude that the ideal control disease in a hospital-based study of gene-environment interaction is not caused by either G or E and that choosing controls from several conditions to act as a combined control group is a useful strategy. This formulation extends to the general problem of distortion of joint effects from selection biases or confounding.