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      A novel approach for biomarker selection and the integration of repeated measures experiments from two assays

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          Abstract

          Background

          High throughput ’omics’ experiments are usually designed to compare changes observed between different conditions (or interventions) and to identify biomarkers capable of characterizing each condition. We consider the complex structure of repeated measurements from different assays where different conditions are applied on the same subjects.

          Results

          We propose a two-step analysis combining a multilevel approach and a multivariate approach to reveal separately the effects of conditions within subjects from the biological variation between subjects. The approach is extended to two-factor designs and to the integration of two matched data sets. It allows internal variable selection to highlight genes able to discriminate the net condition effect within subjects. A simulation study was performed to demonstrate the good performance of the multilevel multivariate approach compared to a classical multivariate method. The multilevel multivariate approach outperformed the classical multivariate approach with respect to the classification error rate and the selection of relevant genes. The approach was applied to an HIV-vaccine trial evaluating the response with gene expression and cytokine secretion. The discriminant multilevel analysis selected a relevant subset of genes while the integrative multilevel analysis highlighted clusters of genes and cytokines that were highly correlated across the samples.

          Conclusions

          Our combined multilevel multivariate approach may help in finding signatures of vaccine effect and allows for a better understanding of immunological mechanisms activated by the intervention. The integrative analysis revealed clusters of genes, that were associated with cytokine secretion. These clusters can be seen as gene signatures to predict future cytokine response. The approach is implemented in the R package mixOmics ( http://cran.r-project.org/) with associated tutorials to perform the analysis a.

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          Most cited references11

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          A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis.

          We present a penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix. We approximate the matrix X as circumflexX = sigma(k=1)(K) d(k)u(k)v(k)(T), where d(k), u(k), and v(k) minimize the squared Frobenius norm of X - circumflexX, subject to penalties on u(k) and v(k). This results in a regularized version of the singular value decomposition. Of particular interest is the use of L(1)-penalties on u(k) and v(k), which yields a decomposition of X using sparse vectors. We show that when the PMD is applied using an L(1)-penalty on v(k) but not on u(k), a method for sparse principal components results. In fact, this yields an efficient algorithm for the "SCoTLASS" proposal (Jolliffe and others 2003) for obtaining sparse principal components. This method is demonstrated on a publicly available gene expression data set. We also establish connections between the SCoTLASS method for sparse principal component analysis and the method of Zou and others (2006). In addition, we show that when the PMD is applied to a cross-products matrix, it results in a method for penalized canonical correlation analysis (CCA). We apply this penalized CCA method to simulated data and to a genomic data set consisting of gene expression and DNA copy number measurements on the same set of samples.
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            Small sample inference for fixed effects from restricted maximum likelihood.

            Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T2 type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different REML analyses and the methods are illustrated using three examples.
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              Multivariate paired data analysis: multilevel PLSDA versus OPLSDA

              Metabolomics data obtained from (human) nutritional intervention studies can have a rather complex structure that depends on the underlying experimental design. In this paper we discuss the complex structure in data caused by a cross-over designed experiment. In such a design, each subject in the study population acts as his or her own control and makes the data paired. For a single univariate response a paired t-test or repeated measures ANOVA can be used to test the differences between the paired observations. The same principle holds for multivariate data. In the current paper we compare a method that exploits the paired data structure in cross-over multivariate data (multilevel PLSDA) with a method that is often used by default but that ignores the paired structure (OPLSDA). The results from both methods have been evaluated in a small simulated example as well as in a genuine data set from a cross-over designed nutritional metabolomics study. It is shown that exploiting the paired data structure underlying the cross-over design considerably improves the power and the interpretability of the multivariate solution. Furthermore, the multilevel approach provides complementary information about (I) the diversity and abundance of the treatment effects within the different (subsets of) subjects across the study population, and (II) the intrinsic differences between these study subjects.
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                Author and article information

                Journal
                BMC Bioinformatics
                BMC Bioinformatics
                BMC Bioinformatics
                BioMed Central
                1471-2105
                2012
                6 December 2012
                : 13
                : 325
                Affiliations
                [1 ]Univ. Bordeaux, ISPED, centre INSERM U-897-Epidémiologie-Biostatistique, Bordeaux, F-33000, FRANCE
                [2 ]INSERM, ISPED, centre INSERM U-897-Epidémiologie-Biostatistique, Bordeaux, F-33000, FRANCE
                [3 ]Queensland Facility for Advanced Bioinformatics and the institute for Molecular Bioscience, The University of Queensland, Brisbane, QLD 4072, Australia
                [4 ]INSERM U955 Eq 16, UPEC Université, Créteil, FRANCE
                [5 ]Vaccine Research Institute ANRS, Paris, France
                Article
                1471-2105-13-325
                10.1186/1471-2105-13-325
                3627901
                23216942
                b4d5f47e-3050-4553-8f42-2efc4d246228
                Copyright ©2012 Liquet et al.; licensee BioMed Central Ltd.

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 21 May 2012
                : 26 November 2012
                Categories
                Methodology Article

                Bioinformatics & Computational biology
                Bioinformatics & Computational biology

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