Valid and efficient inference for nonparametric variable importance in two-phase studies.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Nonparametric regression often involves easily obtainable covariates (X) and costly covariates (Z).
• Deciding whether to include expensive covariates (Z) in predictive models requires assessing their importance against data collection costs.

Purpose of the Study:

• To develop a nonparametric variable importance measure for costly covariates (Z).
• To infer the importance of Z in predicting Y, considering the presence of easily obtainable covariates (X).
• To address the challenge of missing Z data in two-phase studies.

Main Methods:

• Proposed a nonparametric variable importance measure for Z, aggregating maximum potential contributions.
• Developed a novel inference approach for two-phase data with missing Z values.
• Utilized functions of (Y, X) to impute contributions to predictive loss for individuals with missing Z.

Main Results:

• The proposed approach provides unified and efficient inference for Z's importance, regardless of its actual contribution.
• Demonstrated superior performance through simulations and real-world data analysis.
• Established novel theoretical results in semi-supervised inference and two-phase nonparametric estimation.

Conclusions:

• The developed variable importance measure effectively assesses the utility of costly covariates in prediction.
• The novel inference method is robust to missing data, offering practical advantages in two-phase studies.
• This research contributes to efficient model building when dealing with variable data collection costs.