Table 1.

Additive and multiplicative interactions in a hypothetical case of smoking, age, and mortality.

(a) Additive Interaction
	Old Age	Young Age
Smoker	${\mu }_{11}^A=\left({\mu }_{10}-{\mu }_{00}\right)+\left({\mu }_{01}-{\mu }_{00}\right)+{\mu }_{00}$	${\mu }_{01}$
Non-Smoker	${\mu }_{10}$	${\mu }_{00}$
(b) Multiplicative Interaction
	Old Age	Young Age
Smoker	${\mu }_{11}^M=H{R}_{01}\ast H{R}_{10}\ast {\mu }_{00}$	${\mu }_{01}$
Non-Smoker	${\mu }_{10}$	${\mu }_{00}$

Note: $\mu$ is the rate of death and HR is the hazard ratio. The superscripts A and M denote the additive and multiplicative predictions, respectively.