Conditions for confounding of interactions

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 E1 and E2 on a binary outcome Y if the association between U and E1 varies depending on the value of E2. 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 E1 with U across the strata of E2. A variable that is not a confounder for the main effects of E1 and E2 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.

Keywords: confounding bias; effect modification; interaction; logistic regression; pharmacoepidemiology; simulations.