Table 4

Hypothetical example in which the effect of G is estimated without bias even though the control disease is caused by E and there is confounding of the effect of G by E

In this example, G and E are associated, E increases the risk by a factor of 2 in both G− and G+, and the effect of G is confounded by E. The odds ratio for G when E is ignored is 3 with proper controls and 3.2 with improper controls, instead of the true 2. Nevertheless, the effect of G is estimated correctly in subgroups defined by E+ and E− and, therefore, in adjusted analyses.

Proper controls100200200100
Improper (CVD) controls100200400200
Cases (lung cancer)100400800800
Odds ratio: cases vs. proper controlsReference248
Odds ratio: cases vs. improper controlsReference224
Odds ratio: improper vs. proper controlsReference122