Covariates as Random Effects (CaRE): An approach to modeling high-dimensional confounding and effect heterogeneity

Conventional single-level regression models estimate exposure-outcome associations by including covariates as main effects to account for potential confounding, 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 Covariates as Random Effects (CaRE) approach that treats combinations of covariates as strata, allowing for a parsimonious representation of both main effects and interactions. In this approach, stratum-level random intercepts provide a flexible alternative to strictly additive specifications by representing interactions between covariates through stratification and partial pooling, especially in settings with high-dimensional covariates. In addition, random slopes can be incorporated to explore how the exposure-outcome association varies across strata. To illustrate this approach, we use data from a sample of older adults in India, examining the association between years of education and cognitive function. 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 approach illustrates how multilevel regression can serve as an alternative for covariate adjustment and the assessment of effect heterogeneity in epidemiologic research.