Expanding the Scope: In-depth Review of Interaction in Regression Models

Abstract

KEY WORDS Interaction, Effect modification, Regression 1. SCE NA RI O In the research lab, Dr. X and his team were investigating the interaction between gene Z and smoking in relation to the onset of diabetes. They used a logistic regression model, incorporating an interaction term, and performed the Wald test for evaluating the statistical significance of the interaction term. However, their lab boss suddenly urged them to consider marginal effects instead. He said it was introduced in JAMA and told Dr. X to read the paper [1]. Dr. X read it but could not understand why his original analysis was inappropriate. For him, we will review regression analysis and interaction term, and explain what the marginal effect is. The article is structured as follows. Section 2 briefly explains linear regression, generalized linear regression, and nonlinear regression, encompassing a review of the interpretation of coefficients in regression analysis. Section 3 reviewed the interpretation of an interaction term in multiple linear regression and logistic regression. It highlights a notable misapprehension and offers a rationale for an alternative approach. In Section 4, we introduce the concept of marginal effects. Lastly, in Section 5, we present our systematic review concerning gene-environment interactions (GEI) to evaluate the appropri-ateness of interpretation of an interaction term.