title: Variable selection for classification in complex ophthalmic data: a multivariate statistical framework
Creators: name: Walsh, PE
Publisher: name: University of Liverpool Repository
Year: 2018

description: Variable selection is an essential part of the process of model-building for classification or prediction. Some of the challenges of variable selection are heterogeneous variance-covariance matrices, differing scales of variables, non-normally distributed data and missing data. Statistical methods exist for variable selection however these are often univariate, make restrictive assumptions about the distribution of data or are expensive in terms of the computational power required. In this thesis I focus on filter methods of variable selection that are computationally fast and propose a metric of discrimination. The main objectives of this thesis are (1) to propose a novel Signal-to-Noise Ratio (SNR) discrimination metric accommodating heterogeneous variance-covariance matrices, (2) to develop a multiple forward selection (MFS) algorithm employing the novel SNR metric, (3) to assess the performance of the MFS-SNR algorithm compared to alternative methods of variable selection, (4) to investigate the ability of the MFS-SNR algorithm to carry out variable selection when data are not normally distributed and (5) to apply the MFS-SNR algorithm to the task of variable selection from real datasets. The MFS-SNR algorithm was implemented in the R programming environment. It calculates the SNR for subsets of variables, identifying the optimal variable during each round of selection as whichever causes the largest increase in SNR. A dataset was simulated comprising 10 variables: 2 discriminating variables, 7 non-discriminating variables and one non-discriminating variable which enhanced the discriminatory performance of other variables. In simulations the frequency of each variable’s selection was recorded. The probability of correct classification (PCC) and area under the curve (AUC) were calculated for sets of selected variables. I assessed the ability of the MFS-SNR algorithm to select variables when data are not normally distributed using simulated data. I compared the MFS-SNR algorithm to filter methods utilising information gain, chi-square statistics and the Relief-F algorithm as well as a support vector machines and an embedded method using random forests. A version of the MFS algorithm utilising Hotelling’s T2 statistic (MFS-T2) was included in this comparison. The MFS-SNR algorithm selected all 3 variables relevant to discrimination with higher or equivalent frequencies to competing methods in all scenarios. Following non-normal variable transformation the MFS-SNR algorithm still selected the variables known to be relevant to discrimination in the simulated scenarios. Finally, I studied both the MFS-SNR and MFS-T2 algorithm’s ability to carry out variable selection for disease classification using several clinical datasets from ophthalmology. These datasets represented a spectrum of quality issues such as missingness, imbalanced group sizes, heterogeneous variance-covariance matrices and differing variable scales. In 3 out of 4 datasets the MFS-SNR algorithm out-performed the MFS-T2 algorithm. In the fourth study both MFS-T2 and MFS-SNR produced the same variable selection results. In conclusion I have demonstrated that the novel SNR is an extension of Hotelling’s T2 statistic accommodating heterogeneity of variance-covariance matrices. The MFS-SNR algorithm is capable of selecting the relevant variables whether data are normally distributed or not. In the simulated scenarios the MFS-SNR algorithm performs at least as well as competing methods and outperforms the MFS-T2 algorithm when selecting variables from real clinical datasets.