Using a supervised principal components analysis for variable selection in high-dimensional datasets reduces false discovery rates

Abstract

High-dimensional datasets, where the number of variables p is much larger compared to the number of samples n, are ubiquitous and often render standard classification and regression techniques unreliable due to overfitting. An important research problem is feature selection -- ranking of candidate variables based on their relevance to the outcome variable and retaining those that satisfy a chosen criterion. In this article, we propose a computationally efficient variable selection method based on principal component analysis. The method is very simple, accessible, and suitable for the analysis of high-dimensional datasets. It allows to correct for population structure in genome-wide association studies (GWAS) which otherwise would induce spurious associations and is less likely to overfit. We expect our method to accurately identify important features but at the same time reduce the False Discovery Rate (FDR) (the expected proportion of erroneously rejected null hypotheses) through accounting for the correlation between variables and through de-noising data in the training phase, which also make it robust to outliers in the training data. Being almost as fast as univariate filters, our method allows for valid statistical inference. The ability to make such inferences sets this method apart from most of the current multivariate statistical tools designed for todays high-dimensional data. We demonstrate the superior performance of our method through extensive simulations. A semi-real gene-expression dataset, a challenging childhood acute lymphoblastic leukemia (CALL) gene expression study, and a GWAS that attempts to identify single-nucleotide polymorphisms (SNPs) associated with the rice grain length further demonstrate the usefulness of our method in genomic applications. Author summaryAn integral part of modern statistical research is feature selection, which has claimed various scientific discoveries, especially in the emerging genomics applications such as gene expression and proteomics studies, where data has thousands or tens of thousands of features but a limited number of samples. However, in practice, due to unavailability of suitable multivariate methods, researchers often resort to univariate filters when it comes to deal with a large number of variables. These univariate filters do not take into account the dependencies between variables because they independently assess variables one-by-one. This leads to loss of information, loss of statistical power (the probability of correctly rejecting the null hypothesis) and potentially biased estimates. In our paper, we propose a new variable selection method. Being computationally efficient, our method allows for valid inference. The ability to make such inferences sets this method apart from most of the current multivariate statistical tools designed for todays high-dimensional data.