It is tempting to begin by testing for G-E association in controls and then decide whether to use the case-only test (for greater power if there is no G-E association) or the case-control test (for greater validity if there is). However, this naïve procedure leads to biased tests and estimates because it fails to take proper account of this two-step inference procedure33. More appropriate empirical Bayes34 or Bayes model averaging35 approaches have been developed that essentially provide weighted averages of the case-only and case-control estimators, yielding an acceptable trade-off between bias and efficiency. For example, Mukherjee et al.34 reanalyzed data on glutathione-S-transferase (GSTM1) and N-acetyl-transferase (NAT2) genotypes in relation to smoking and dietary factors. They found a strong association between NAT2 and smoking, so that their empirical Bayes estimate of the interaction between the two was closer to the case-control estimate than to the case-only one, which was in the opposite direction. However, there was no association between GSTM1 and fruit consumption, so the empirical Bayes estimate of that interaction was similar to both the case-control and case-only estimates, but took advantage of the smaller standard error of the latter.
