Test for Additive Interaction in Proportional Hazards Models

Purpose We describe a method for testing and estimating a two-way additive interaction between two categorical variables, each of which has greater than or equal to two levels. Methods We test additive and multiplicative interactions in the same proportional hazards model and measure additivity by relative excess risk due to interaction (RERI), proportion of disease attributable to interaction (AP), and synergy index (S). A simulation study was used to compare the performance of these measures of additivity. Data from the Atherosclerosis Risk in Communities cohort study with a total of 15,792 subjects were used to exemplify the methods. Results The test and measures of departure from additivity depend neither on follow-up time nor on the covariates. The simulation study indicates that RERI is the best choice of measures of additivity using a proportional hazards model. The examples indicated that an interaction between two variables can be statistically significant on additive measure (RERI = 1.14, p = 0.04) but not on multiplicative measure (β3 = 0.59, p = 0.12) and that additive and multiplicative interactions can be in opposite directions (RERI = 0.08, β3 = –0.08). Conclusions The method has broader application for any regression models with a rate as the dependent variable. In the case that both additive and multiplicative interactions are statistically significant and in the opposite direction, the interpretation needs caution.