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Bivariate microarray analysis: statistical interpretation of two-channel functional genomics data.

Hsiao A, Subramaniam S - Syst Synth Biol (2009)

Bottom Line: This method, bivariate microarray analysis (BMA), demonstrates dramatically improved sensitivity over existing approaches.We show that with only two array replicates, it is possible to detect gene expression changes that are at best detected with six array replicates by other methods.Further, we show that combining results from BMA with Gene Ontology annotation yields biologically significant results in a ligand-treated macrophage cell system.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of California, San Diego, La Jolla, CA, 92093, USA, alhsiao@ucsd.edu.

ABSTRACT
Conventional statistical methods for interpreting microarray data require large numbers of replicates in order to provide sufficient levels of sensitivity. We recently described a method for identifying differentially-expressed genes in one-channel microarray data 1. Based on the idea that the variance structure of microarray data can itself be a reliable measure of noise, this method allows statistically sound interpretation of as few as two replicates per treatment condition. Unlike the one-channel array, the two-channel platform simultaneously compares gene expression in two RNA samples. This leads to covariation of the measured signals. Hence, by accounting for covariation in the variance model, we can significantly increase the power of the statistical test. We believe that this approach has the potential to overcome limitations of existing methods. We present here a novel approach for the analysis of microarray data that involves modeling the variance structure of paired expression data in the context of a Bayesian framework. We also describe a novel statistical test that can be used to identify differentially-expressed genes. This method, bivariate microarray analysis (BMA), demonstrates dramatically improved sensitivity over existing approaches. We show that with only two array replicates, it is possible to detect gene expression changes that are at best detected with six array replicates by other methods. Further, we show that combining results from BMA with Gene Ontology annotation yields biologically significant results in a ligand-treated macrophage cell system.

No MeSH data available.


Depiction of the significance integral. The statistical test performed by BMA involves integration of a bivariate normal density. The peak of the density appears on one side of the diagonal line. The P-value is defined as the “tail volume” on the side opposite of the peak. Statistical significance is achieved when the P-value is smaller than a specified threshold. The bivariate normal density depicted in (a) was sufficiently distant from the diagonal, and was considered a “significant” change (αBonf = 0.05). The density depicted in (b) was too close to the diagonal, and therefore does not represent a significant difference in gene expression
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Fig2: Depiction of the significance integral. The statistical test performed by BMA involves integration of a bivariate normal density. The peak of the density appears on one side of the diagonal line. The P-value is defined as the “tail volume” on the side opposite of the peak. Statistical significance is achieved when the P-value is smaller than a specified threshold. The bivariate normal density depicted in (a) was sufficiently distant from the diagonal, and was considered a “significant” change (αBonf = 0.05). The density depicted in (b) was too close to the diagonal, and therefore does not represent a significant difference in gene expression

Mentions: The P-value of BMA is defined in a way similar to that of a t-test. In a t-test, the P-value is defined as an integral of a t-distribution. When the “tail area” of the t-distribution is sufficiently small, we consider experimental results to be statistically significant. In BMA, we define the P-value as a two-dimensional integral of a bivariate normal density. In other words, we determine whether the “tail volume” of this distribution is sufficiently small. If so, we consider the gene to be differentially-expressed. A depiction of the bivariate integral is shown in Fig. 2. Explicitly,5\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ p_{i} = \left\{ {\begin{array}{*{20}c} {\int_{ - \infty }^{\infty } {\int_{ - \infty }^{{\mu_{2} }} {\pi_{i} \left( {\mu_{1} ,\mu_{2} } \right)d\mu_{1} } \cdot d\mu_{2} ,} } & {E\left[ {\mu_{1} } \right] > E\left[ {\mu_{2} } \right]} \\ {\int_{ - \infty }^{\infty } {\int_{{\mu_{2} }}^{\infty } {\pi_{i} \left( {\mu_{1} ,\mu_{2} } \right)d\mu_{1} } \cdot d\mu_{2} } ,} & {E\left[ {\mu_{2} } \right] > E\left[ {\mu_{1} } \right]} \\ \end{array} } \right. $$\end{document}where πi is the joint posterior density for the “true” expression levels of the ith feature.Fig. 2


Bivariate microarray analysis: statistical interpretation of two-channel functional genomics data.

Hsiao A, Subramaniam S - Syst Synth Biol (2009)

Depiction of the significance integral. The statistical test performed by BMA involves integration of a bivariate normal density. The peak of the density appears on one side of the diagonal line. The P-value is defined as the “tail volume” on the side opposite of the peak. Statistical significance is achieved when the P-value is smaller than a specified threshold. The bivariate normal density depicted in (a) was sufficiently distant from the diagonal, and was considered a “significant” change (αBonf = 0.05). The density depicted in (b) was too close to the diagonal, and therefore does not represent a significant difference in gene expression
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2735646&req=5

Fig2: Depiction of the significance integral. The statistical test performed by BMA involves integration of a bivariate normal density. The peak of the density appears on one side of the diagonal line. The P-value is defined as the “tail volume” on the side opposite of the peak. Statistical significance is achieved when the P-value is smaller than a specified threshold. The bivariate normal density depicted in (a) was sufficiently distant from the diagonal, and was considered a “significant” change (αBonf = 0.05). The density depicted in (b) was too close to the diagonal, and therefore does not represent a significant difference in gene expression
Mentions: The P-value of BMA is defined in a way similar to that of a t-test. In a t-test, the P-value is defined as an integral of a t-distribution. When the “tail area” of the t-distribution is sufficiently small, we consider experimental results to be statistically significant. In BMA, we define the P-value as a two-dimensional integral of a bivariate normal density. In other words, we determine whether the “tail volume” of this distribution is sufficiently small. If so, we consider the gene to be differentially-expressed. A depiction of the bivariate integral is shown in Fig. 2. Explicitly,5\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ p_{i} = \left\{ {\begin{array}{*{20}c} {\int_{ - \infty }^{\infty } {\int_{ - \infty }^{{\mu_{2} }} {\pi_{i} \left( {\mu_{1} ,\mu_{2} } \right)d\mu_{1} } \cdot d\mu_{2} ,} } & {E\left[ {\mu_{1} } \right] > E\left[ {\mu_{2} } \right]} \\ {\int_{ - \infty }^{\infty } {\int_{{\mu_{2} }}^{\infty } {\pi_{i} \left( {\mu_{1} ,\mu_{2} } \right)d\mu_{1} } \cdot d\mu_{2} } ,} & {E\left[ {\mu_{2} } \right] > E\left[ {\mu_{1} } \right]} \\ \end{array} } \right. $$\end{document}where πi is the joint posterior density for the “true” expression levels of the ith feature.Fig. 2

Bottom Line: This method, bivariate microarray analysis (BMA), demonstrates dramatically improved sensitivity over existing approaches.We show that with only two array replicates, it is possible to detect gene expression changes that are at best detected with six array replicates by other methods.Further, we show that combining results from BMA with Gene Ontology annotation yields biologically significant results in a ligand-treated macrophage cell system.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of California, San Diego, La Jolla, CA, 92093, USA, alhsiao@ucsd.edu.

ABSTRACT
Conventional statistical methods for interpreting microarray data require large numbers of replicates in order to provide sufficient levels of sensitivity. We recently described a method for identifying differentially-expressed genes in one-channel microarray data 1. Based on the idea that the variance structure of microarray data can itself be a reliable measure of noise, this method allows statistically sound interpretation of as few as two replicates per treatment condition. Unlike the one-channel array, the two-channel platform simultaneously compares gene expression in two RNA samples. This leads to covariation of the measured signals. Hence, by accounting for covariation in the variance model, we can significantly increase the power of the statistical test. We believe that this approach has the potential to overcome limitations of existing methods. We present here a novel approach for the analysis of microarray data that involves modeling the variance structure of paired expression data in the context of a Bayesian framework. We also describe a novel statistical test that can be used to identify differentially-expressed genes. This method, bivariate microarray analysis (BMA), demonstrates dramatically improved sensitivity over existing approaches. We show that with only two array replicates, it is possible to detect gene expression changes that are at best detected with six array replicates by other methods. Further, we show that combining results from BMA with Gene Ontology annotation yields biologically significant results in a ligand-treated macrophage cell system.

No MeSH data available.