Variable selection in high-dimensional logistic regression models using a whitening approach

Abstract: In bioinformatics, the rapid development of sequencing technology has enabled us to collect an increasing amount of omics data. Classification based on omics data is one of the central problems in biomedical research. However, omics data usually has a limited sample size but high feature dimensions, and it is assumed that only a few features (biomarkers) are active, i.e. informative to discriminate between different categories (cancer subtypes, responder/non-responder to treatment, for example). Identifying active biomarkers for classification has therefore become fundamental for omics data analysis. Focusing on binary classification, we propose an innovative feature selection method aiming at dealing with the high correlations between the biomarkers. Various research has shown the notorious influence of correlated biomarkers and the difficulty of accurately identifying active ones. Our method, WLogit, consists in whitening the design matrix to remove the correlations between biomarkers, then using a penalized criterion adapted to the logistic regression model to select features. The performance of WLogit is assessed using synthetic data in several scenarios and compared with other approaches. The results suggest that WLogit can identify almost all active biomarkers even in the cases where the biomarkers are highly correlated, while the other methods fail, which consequently leads to higher classification accuracy. The performance is also evaluated on the classification of two Lymphoma subtypes, and the obtained classifier also outperformed other methods. Our method is implemented in the \texttt{WLogit} R package available from the Comprehensive R Archive Network (CRAN).