Additive interaction between continuous risk factors using logistic regression.

To the Editor: Interaction of two risk factors with respect to a health outcome may be better evaluated through deviations from additivity rather than multiplicativity of their effects.1,2 Certain publications, focusing on dichotomous risk factors, have explored additive interaction through rothman’s indexes.2–7 Continuous risk factors have been investigated for specific cases only8 (eAppendix 1; http://links.lww.com/eDe/ A771). We consider here the setting of continuous risk factors X, Y for disease D (0 = absence, 1 = presence), such as the probability that D = 1 increases with higher values of X, Y.7 Let x0→x1 and y0→y1 denote the arbitrary increments dx = x1 − x0, dy = y1 − y0 of X, Y, whereas x0→x0 and y0→y0, denote that X, Y are fixed at a background level of exposure. Now, consider the following logistic regression, including X, Y, their product term XY, and covariates Zi, i = 1, 2, ..., n: