Sometimes a simple question arises: how does the distance between two samples in multivariate space compare to another scalar value associated with each sample. Here, inspired by the Kendall rank correlation coefficient, we propose theory for a non-parametric test to statistically test this association based on the neighbors principle implicit in any machine learning algorithm which says that samples with similar labels should be close to one another in feature space as well. Our test, REVA, is independent of the scale of the scalar data, and thus generalizable to any comparison of samples with both high-dimensional data and a scalar. We use U-statistic theory to derive the asymptotic distribution of the new correlation coefficient, developing additional large and finite sample properties along the way. To establish the admissibility of the REVA statistic, and explore the utility and limitations of our model, we compared it to the most widely used distance based correlation coefficient in a range of simulated conditions, demonstrating that REVA does not depend on an assumption of linearity, and is robust to high levels of noise, high dimensions, and the presence of outliers. We apply the resulting statistic to problems in cancer biology motivated by the model that cancer cells with more similar gene expression profiles to one another can be expected to have a more similar response to therapy.

Motivation: Current bioinformatics methods to detect changes in gene isoform usage in distinct phenotypes compare the relative expected isoform usage in phenotypes. These statistics model differences in isoform usage in normal tissues, which have stable regulation of gene splicing. Pathological conditions, such as cancer, can have broken regulation of splicing that increases the heterogeneity of the expression of splice variants. Inferring events with such differential heterogeneity in gene isoform usage requires new statistical approaches. Results: We introduce Splice Expression Variability Analysis (SEVA) to model increased heterogeneity of splice variant usage between conditions (e.g. tumor and normal samples). SEVA uses a rank-based multivariate statistic that compares the variability of junction expression profiles within one condition to the variability within another. Simulated data show that SEVA is unique in modeling heterogeneity of gene isoform usage, and benchmark SEVA's performance against EBSeq, DiffSplice and rMATS that model differential isoform usage instead of heterogeneity. We confirm the accuracy of SEVA in identifying known splice variants in head and neck cancer and perform cross-study validation of novel splice variants. A novel comparison of splice variant heterogeneity between subtypes of head and neck cancer demonstrated unanticipated similarity between the heterogeneity of gene isoform usage in HPV-positive and HPV-negative subtypes and anticipated increased heterogeneity among HPV-negative samples with mutations in genes that regulate the splice variant machinery. These results show that SEVA accurately models differential heterogeneity of gene isoform usage from RNA-seq data. Availability and implementation: SEVA is implemented in the R/Bioconductor package GSReg. Contact: [email protected] or [email protected] or [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

UNLABELLED: k-Top Scoring Pairs (kTSP) is a classification method for prediction from high-throughput data based on a set of the paired measurements. Each of the two possible orderings of a pair of measurements (e.g. a reversal in the expression of two genes) is associated with one of two classes. The kTSP prediction rule is the aggregation of voting among such individual two-feature decision rules based on order switching. kTSP, like its predecessor, Top Scoring Pair (TSP), is a parameter-free classifier relying only on ranking of a small subset of features, rendering it robust to noise and potentially easy to interpret in biological terms. In contrast to TSP, kTSP has comparable accuracy to standard genomics classification techniques, including Support Vector Machines and Prediction Analysis for Microarrays. Here, we describe 'switchBox', an R package for kTSP-based prediction. AVAILABILITY: The 'switchBox' package is freely available from Bioconductor: http://www.bioconductor.org. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: A major challenge in computational biology is to extract knowledge about the genetic nature of disease from high-throughput data. However, an important obstacle to both biological understanding and clinical applications is the "black box" nature of the decision rules provided by most machine learning approaches, which usually involve many genes combined in a highly complex fashion. Achieving biologically relevant results argues for a different strategy. A promising alternative is to base prediction entirely upon the relative expression ordering of a small number of genes. RESULTS: We present a three-gene version of "relative expression analysis" (RXA), a rigorous and systematic comparison with earlier approaches in a variety of cancer studies, a clinically relevant application to predicting germline BRCA1 mutations in breast cancer and a cross-study validation for predicting ER status. In the BRCA1 study, RXA yields high accuracy with a simple decision rule: in tumors carrying mutations, the expression of a "reference gene" falls between the expression of two differentially expressed genes, PPP1CB and RNF14. An analysis of the protein-protein interactions among the triplet of genes and BRCA1 suggests that the classifier has a biological foundation. CONCLUSION: RXA has the potential to identify genomic "marker interactions" with plausible biological interpretation and direct clinical applicability. It provides a general framework for understanding the roles of the genes involved in decision rules, as illustrated for the difficult and clinically relevant problem of identifying BRCA1 mutation carriers.

We describe our contribution to the ICMLA2008 “Automated Micro-Array Classification Challenge”. The design of our classifier is motivated by the special scenario encountered in molecular cancer classification based on the mRNA concentrations provided by gene microarray data. Our classifier is rank-based; it only depends on expression comparisons among selected pairs of genes. Such comparisons are invariant to most of the transformations involved in preprocessing and normalization. Every pair of genes determines a binary classifier - choose the class for which the observed ordering is most likely. Pairs are scored by maximizing accuracy. In our k-TSP (k-disjoint Top Scoring Pairs) classifier, k disjoint pairs of genes are learned from training data; the discriminant function is simply the difference in the number of votes for the two classes. This rule involves exactly 2k genes, is readily interpretable, and provides some state-of-the-art results in cancer diagnosis and prognosis for small values of k, even k=1.