Modern variable selection techniques in the generalised linear model with application in Biostatistics

Abstract

In a Biostatistics environment, the datasets to be analysed are frequently high-dimensional and multicollinearity is expected due to the nature of the features. However, many traditional approaches to statistical analysis and feature selection cease to be useful in the presence of high-dimensionality and multicollinearity. Penalised regression methods have proved to be practical and attractive for dealing with these problems. In this dissertation, we propose a new penalised approach, the modified elastic-net (MEnet), for statistical analysis and feature selection using a combination of the ridge and bridge penalties. This method is designed to deal with high-dimensional problems with highly correlated predictor variables. Furthermore, it has a closed-form solution, unlike the most frequently used penalised techniques, which makes it simple to implement on high-dimensional data. We show how this approach can be used to analyse high-dimensional data with binary responses, e.g., microarray data, and simultaneously select significant features. An extensive simulation study and analysis of a colon cancer dataset demonstrate the properties and practical aspects of the proposed method.