Variable selection for censored data using Modified Correlation Adjusted coRrelation (MCAR) scores

Dealing with high-dimensional censored data is very challenging because of the complexities in data structure. This article focuses on developing a variable selection procedure for censored high-dimensional data with the AFT models using the Modified Correlation Adjusted coRrelation (MCAR) scores method. The latter is developed based on CAR scores method that provides a canonical ordering that encourages grouping of correlated predictors and down-weights antagonistic variables. The proposed MCAR scores method is developed as an extension of the CAR scores method using NOVEL integration of the sample and threshold estimator of the correlation matrix as suggested by Huang and Frylewicz. The proposed MCAR exhibits computationally more efficient estimates under model sparsity and can provide a canonical ordering among the predictors. The MCAR method is a greedy method that is also easy to understand and can perform estimation and variable selection simultaneously. Performances of variable selection by the MCAR method have been compared with other existing regularized techniques in literature-such as the lasso, elastic net and with a machine learning technique called boosting and with the censored CAR by a number of simulation studies and a real microarray data set called diffuse large-B-cell lymphoma. Results indicate that when correlation exists among the covariates, the MCAR method outperforms all five techniques while for uncorrelated data, the MCAR performs quite similar to the CAR method but clearly outperforms the other three methods. The empirical study further reveals that the MCAR method exhibits the best predictive performance among the methods.