Concordance Measure-based Feature Screening and Variable Selection

The C-statistic, measuring the rank concordance between predictors and outcomes, has become a standard metric of predictive accuracy and is therefore a natural criterion for variable screening and selection. However, as the C-statistic is a step function, its optimization requires brute-force search, prohibiting its direct usage in the presence of high-dimensional predictors. We develop a smoothed version of the C-statistic to facilitate variable screening and selection. Specifically, we propose a smoothed C-statistic sure screening (C-SS) method for screening ultrahighdimensional data, and a penalized C-statistic (PSC) variable selection method for regularized modeling based on the screening results. We have shown that these two coherent procedures form an integrated framework for screening and variable selection: the C-SS possesses the sure screening property, and the PSC possesses the oracle property. Specifically, the PSC achieves the oracle property if mn = o(n ), where mn is the cardinality of the set of predictors captured by the CSS. Our extensive simulations reveal that, compared to existing procedures, our proposal is more robust and efficient. Our procedure has been applied to analyze a multiple myeloma study, and has identified several novel genes that can predict patients response to treatment. 2 YUNBEI MA, YI LI, HUAZHEN LIN AND YI LI