Interaction Contrasts and Collider Bias Publisher Pubmed



Mansournia MA¹ ; Nazemipour M² ; Etminan M³
Source: American Journal of Epidemiology Published:2022

Abstract

Previous papers have mentioned that conditioning on a binary collider would introduce an association between its causes in at least 1 stratum. In this paper, we prove this statement and, along with intuitions, formally examine the direction and magnitude of the associations between 2 risk factors of a binary collider using interaction contrasts. Among level one of the collider, 2 variables are independent, positively associated, and negatively associated if multiplicative risk interaction contrast is equal to, more than, and less than 0, respectively; the same results hold for the other level of the collider if the multiplicative survival interaction contrast, equal to multiplicative risk interaction contrast minus the additive risk interaction contrast, is compared with 0. The strength of the association depends on the magnitude of the interaction contrast: The stronger the interaction is, the larger the magnitude of the association will be. However, the common conditional odds ratio under the homogeneity assumption will be bounded. A figure is presented that succinctly illustrates our results and helps researchers to better visualize the associations introduced upon conditioning on a collider. © 2022 The Author(s). Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved.