GASVeM: A New Machine Learning Methodology for Multi-SNP Analysis of GWAS Data Based on Genetic Algorithms and Support Vector Machines

Genome-wide association studies (GWAS) are observational studies of a large set of genetic variants in an individual's sample in order to find if any of these variants are linked to a particular trait. In the last two decades, GWAS have contributed to several new discoveries in the field of genetics. This research presents a novel methodology to which GWAS can be applied to. It is mainly based on two machine learning methodologies, genetic algorithms and support vector machines. The database employed for the study consisted of information about 370,750 single-nucleotide polymorphisms belonging to 1076 cases of colorectal cancer and 973 controls. Ten pathways with different degrees of relationship with the trait under study were tested. The results obtained showed how the proposed methodology is able to detect relevant pathways for a certain trait: in this case, colorectal cancer

A New Algorithm for Multivariate Genome Wide Association Studies Based on Differential Evolution and Extreme Learning Machines

Genome-wide association studies (GWAS) are observational studies of a large set of genetic variants, whose aim is to find those that are linked to a certain trait or illness. Due to the multivariate nature of these kinds of studies, machine learning methodologies have been already applied in them, showing good performance. This work presents a new methodology for GWAS that makes use of extreme learning machines and differential evolution. The proposed methodology was tested with the help of the genetic information (370,750 single-nucleotide polymorphisms) of 2049 individuals, 1076 of whom suffer from colorectal cancer. The possible relationship of 10 different pathways with this illness was tested. The results achieved showed that the proposed methodology is suitable for detecting relevant pathways for the trait under analysis with a lower computational cost than other machine learning methodologies previously proposed

A Bi-Aspect Nonparametric Test for the Two-Sample Location Problem

Permutation methods are prized for their lack of assumptions concerning distributions of variables. A bi-aspect permutation test based on the Nonparametric Combination of Dependent Tests theory is developed for testing hypotheses of location shifts of two independent populations. The test is obtained by combining the traditional permutation test with a test that takes into account whethera sample observation is less than orequal to, orgr eaterthan the pooled sample median. The procedure to compute the proposed test is presented. The type-one error rate and power of the test are investigated for many distributions and sample-size settings via Monte Carlo simulations. These simulations show that the proposed test is remarkably more powerful than the traditional permutation test under heavy-tailed distributions like the Cauchy, the half-Cauchy, a 10% and a 30% outlier distribution. When sampling from the double exponential and the exponential distributions, the proposed test appears to be better on the whole than the traditional permutation test. Under normal, uniform, a chi-squared and a bimodal distribution, the bi-aspect test is practically as powerful as the traditional permutation test. Moreover, in these simulations the proposed test maintained its type-one error rate close to the nominal signi8cance level

A Bi-Aspect Nonparametric Test for the Two-Sample Location Problem

Permutation methods are prized for their lack of assumptions concerning distributions of variables. A bi-aspect permutation test based on the Nonparametric Combination of Dependent Tests theory is developed for testing hypotheses of location shifts of two independent populations. The test is obtained by combining the traditional permutation test with a test that takes into account whethera sample observation is less than orequal to, orgr eaterthan the pooled sample median. The procedure to compute the proposed test is presented. The type-one error rate and power of the test are investigated for many distributions and sample-size settings via Monte Carlo simulations. These simulations show that the proposed test is remarkably more powerful than the traditional permutation test under heavy-tailed distributions like the Cauchy, the half-Cauchy, a 10% and a 30% outlier distribution. When sampling from the double exponential and the exponential distributions, the proposed test appears to be better on the whole than the traditional permutation test. Under normal, uniform, a chi-squared and a bimodal distribution, the bi-aspect test is practically as powerful as the traditional permutation test. Moreover, in these simulations the proposed test maintained its type-one error rate close to the nominal signi8cance level

A Bi-Aspect Nonparametric Test for the Two-Sample Location Problem

Permutation methods are prized for their lack of assumptions concerning distributions of variables. A bi-aspect permutation test based on the Nonparametric Combination of Dependent Tests theory is developed for testing hypotheses of location shifts of two independent populations. The test is obtained by combining the traditional permutation test with a test that takes into account whethera sample observation is less than orequal to, orgr eaterthan the pooled sample median. The procedure to compute the proposed test is presented. The type-one error rate and power of the test are investigated for many distributions and sample-size settings via Monte Carlo simulations. These simulations show that the proposed test is remarkably more powerful than the traditional permutation test under heavy-tailed distributions like the Cauchy, the half-Cauchy, a 10% and a 30% outlier distribution. When sampling from the double exponential and the exponential distributions, the proposed test appears to be better on the whole than the traditional permutation test. Under normal, uniform, a chi-squared and a bimodal distribution, the bi-aspect test is practically as powerful as the traditional permutation test. Moreover, in these simulations the proposed test maintained its type-one error rate close to the nominal signi8cance level

A Bi-Aspect Nonparametric Test for the Two-Sample Location Problem

Permutation methods are prized for their lack of assumptions concerning distributions of variables. A bi-aspect permutation test based on the Nonparametric Combination of Dependent Tests theory is developed for testing hypotheses of location shifts of two independent populations. The test is obtained by combining the traditional permutation test with a test that takes into account whethera sample observation is less than orequal to, orgr eaterthan the pooled sample median. The procedure to compute the proposed test is presented. The type-one error rate and power of the test are investigated for many distributions and sample-size settings via Monte Carlo simulations. These simulations show that the proposed test is remarkably more powerful than the traditional permutation test under heavy-tailed distributions like the Cauchy, the half-Cauchy, a 10% and a 30% outlier distribution. When sampling from the double exponential and the exponential distributions, the proposed test appears to be better on the whole than the traditional permutation test. Under normal, uniform, a chi-squared and a bimodal distribution, the bi-aspect test is practically as powerful as the traditional permutation test. Moreover, in these simulations the proposed test maintained its type-one error rate close to the nominal signi8cance level

Multivariate Tri-Aspect Non-Parametric Testing

Permutation tests are prized for their lack of assumptions concerning distribution of underlying populations. The (usual) permutation test for the two-sample location problem based on comparison of sample means is generally effective with regular, roughly symmetric, unimodal, and light-tailed distributions, whereas it might not be so with highly asymmetric and/or heavy-tailed distributions. Another drawback is that it is not consistent for distributions for which first and second moments do not exist. Marozzi [Marozzi, M., 2004, A bi-aspect nonparametric test for the two-sample location problem. Computational Statistics and Data Analysis, 44, 639–648.] proposed a bi-aspect non-parametric test for comparing two populations obtained by non-parametric combining the usual permutation test (which addresses the numerical aspect Xi ) and a test based on comparison of frequencies over the pooled median (which addresses the categorical aspect related to the comparison of sample units with the pooled sample median). Unlike the usual permutation test, the bi-aspect test is consistent for every distribution and is very powerful with highly-skewed and/or heavy-tailed distributions. In the paper, the bi-aspect testing idea is extended by also considering the aspect based on ranks, with the role of third aspect. A simulation study with many sample size and distribution settings shows that the triaspect test is more powerful than the bi-aspect one. Moreover, the multivariate problem is addressed and formal proofs of exactness, unbiasedness, and consistency are given