Table 6

Hypothetical example in which the control condition is caused independently by G and E in an additive model, yet neither additive nor multiplicative interaction is estimated without bias

In this hypothetical example, both E and G increase the odds of the disease used for improper controls by a factor of 3 according to an additive model. Nonetheless, the additive interaction using proper controls is estimated as −0.27 = (1.40 − 1.33) − (1.33 − 1). Not surprisingly, the multiplicative interaction is also estimated with bias either.

Proper controls100100100100
Improper (CVD) controls100300300500
Cases (lung cancer)100400400700
Odds ratio: cases vs. proper controlsReference447
Odds ratio: cases vs. improper controlsReference1.31.31.4
Odds ratio: improper vs. proper controlsReference335