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Abstract In a non-parametric regression setting, we introduce a novel concept of ‘individual variable importance’, which assesses the relevance of certain covariates to an outcome variable among individuals with specific characteristics. This concept holds practical importance for both risk assessment and association identification. For example, it can represent (i) the usefulness of expensive biomarkers in risk prediction for individuals at a specified baseline risk, or (ii) age-specific associations between physiological indicators. We quantify individual variable importance using a ratio parameter between two conditional mean squared errors. To estimate and infer this parameter, we develop fully non-parametric estimators and establish their asymptotic properties. Our method performs well in simulation studies. Applying our approach to analyse a real dataset reveals a scientifically interesting result: the association between body shape and systolic blood pressure diminishes with increasing age. Our finding aligns with the medical literature based on standard parametric regression techniques, but our approach is more reliable due to its robustness to model misspecification. More importantly, the fully non-parametric nature of our method allows it to be applied in settings with complex relationships between variables, which cannot be correctly characterized by traditional parametric interaction analyses.
Dai et al. (Mon,) studied this question.