Modeling Confounding and Heterogeneity in Regression Models: A Multilevel Approach

Conventional single-level regression models estimate exposure–outcome associations by including covariates as main effects, but they rest on the additivity assumption—that each covariate contributes independently, without interactions. This assumption may yield misspecified models and misleading estimates of conditional associations and obscure variation across subgroups, particularly in high-dimensional settings with complex confounding structures. To address these challenges, we present a tutorial framework based on multilevel modeling that treats combinations of covariates as strata, allowing the model to accommodate both main effects and interactions in a parsimonious way. In this framework, stratum-level random intercepts provide a flexible alternative to strictly additive specifications by representing interactions among covariates through stratification and partial pooling. In addition, random slopes can be incorporated to explore departures from homogeneity and to summarize variability around the average association. Using real-world data, we compare conventional single-level models with multilevel specifications and show that the multilevel approach yields similar average associations while offering a more compact representation of complex covariate structures and highlighting variability across strata. This tutorial approach illustrates how multilevel regression can serve as a scalable alternative for covariate adjustment and assessment of heterogeneity in epidemiologic research.