Moving beyond Population Variable Importance: Concept and Theory of Individual Variable Importance

Oregon Convention Center 

In nonparametric regression settings we propose a novel concept of "individual variable importance'', referring to the relevance of some covariates with respect to an outcome variable among individuals with certain features. This concept holds practical importance for risk assessment and association identification. It can represent usefulness of expensive biomarkers in disease prediction for individuals at certain baseline risk, or age-specific associations between physiological indicators. We quantify the individual variable importance by a ratio parameter between two conditional mean squared errors, for which we develop nonparametric estimators. We demonstrate our approaches through a real data application, showing a scientifically interesting result: the association between body shape and systolic blood pressure decays with increasing age. While aligning with the existing medical literature based on parametric regression, our finding is more reliable since its validity is not affected by model misspecification. The fully nonparametric nature equips the individual variable importance framework with broader applicability in contexts that go beyond traditional parametric modeling.

Confidence interval

Convergence rate

Individual variable importance

Kernel smoothing

Nonparametric regression 

IMS