Conditions for confounding of interactions1. Issue 3 (16th December 2015) - Liu, Aihua; Abrahamowicz, Michal; Siemiatycki, Jack
Abstract: Purpose: Pharmaco‐epidemiology increasingly investigates drug–drug or drug–covariate interactions. Yet, conditions for confounding of interactions have not been elucidated. We explored the conditions under which the estimates of interactions in logistic regression are affected by confounding bias. Methods: We rely on analytical derivations to investigate the conditions and then use simulations to confirm our analytical results and to quantify the impact of selected parameters on the bias of the interaction estimates. Results: Failure to adjust for a risk factor U results in a biased estimate of the interaction between exposures E 1 and E 2 on a binary outcome Y if the association between U and E 1 varies depending on the value of E 2. The resulting confounding bias increases with increase in the following: (i) prevalence of confounder U ; (ii) strength of U–Y association; and (iii) heterogeneity in the association of E 1 with U across the strata of E 2. A variable that is not a confounder for the main effects of E 1 and E 2 may still act as an important confounder for their interaction. Conclusions: Studies of interactions should attempt to identify—as potential confounders—those risk factors whose associations with one of the exposures in the interaction term may be modified by the other exposure. Copyright © 2015 John Wiley & Sons, Ltd.