The cross-validated AUC for MCP-logistic regression with high-dimensional data.

We propose a cross-validated area under the receiving operator characteristic (ROC) curve (CV-AUC) criterion for tuning parameter selection for penalized methods in sparse, high-dimensional logistic regression models. We use this criterion in combination with the minimax concave penalty (MCP) method for variable selection. The CV-AUC criterion is specifically designed for optimizing the classification performance for binary outcome data. To implement the proposed approach, we derive an efficient coordinate descent algorithm to compute the MCP-logistic regression solution surface. Simulation studies are conducted to evaluate the finite sample performance of the proposed method and its comparison with the existing methods including the Akaike information criterion (AIC), Bayesian information criterion (BIC) or Extended BIC (EBIC). The model selected based on the CV-AUC criterion tends to have a larger predictive AUC and smaller classification error than those with tuning parameters selected using the AIC, BIC or EBIC. We illustrate the application of the MCP-logistic regression with the CV-AUC criterion on three microarray datasets from the studies that attempt to identify genes related to cancers. Our simulation studies and data examples demonstrate that the CV-AUC is an attractive method for tuning parameter selection for penalized methods in high-dimensional logistic regression models.