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Analyzing 2D gel images using a two-component empirical Bayes model.

Li F, Seillier-Moiseiwitsch F - BMC Bioinformatics (2011)

Bottom Line: The estimation of the mixture density does not take into account assumptions about the density.The proposed constrained estimation method always yields valid estimates and more stable results.The proposed estimation approach proposed can be applied to other contexts where large-scale hypothesis testing occurs.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD, USA. feng.li@fda.hhs.gov

ABSTRACT

Background: Two-dimensional polyacrylomide gel electrophoresis (2D gel, 2D PAGE, 2-DE) is a powerful tool for analyzing the proteome of a organism. Differential analysis of 2D gel images aims at finding proteins that change under different conditions, which leads to large-scale hypothesis testing as in microarray data analysis. Two-component empirical Bayes (EB) models have been widely discussed for large-scale hypothesis testing and applied in the context of genomic data. They have not been implemented for the differential analysis of 2D gel data. In the literature, the mixture and densities of the test statistics are estimated separately. The estimation of the mixture density does not take into account assumptions about the density. Thus, there is no guarantee that the estimated component will be no greater than the mixture density as it should be.

Results: We present an implementation of a two-component EB model for the analysis of 2D gel images. In contrast to the published estimation method, we propose to estimate the mixture and densities simultaneously using a constrained estimation approach, which relies on an iteratively re-weighted least-squares algorithm. The assumption about the density is naturally taken into account in the estimation of the mixture density. This strategy is illustrated using a set of 2D gel images from a factorial experiment. The proposed approach is validated using a set of simulated gels.

Conclusions: The two-component EB model is a very useful for large-scale hypothesis testing. In proteomic analysis, the theoretical density is often not appropriate. We demonstrate how to implement a two-component EB model for analyzing a set of 2D gel images. We show that it is necessary to estimate the mixture density and empirical component simultaneously. The proposed constrained estimation method always yields valid estimates and more stable results. The proposed estimation approach proposed can be applied to other contexts where large-scale hypothesis testing occurs.

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Estimation results for simulated z-values. Histogram of simulated z-values, estimated mixture densities (green solid curves) and  components (blue dashed curves) using the CME approach (left column) and the constrained estimation approach (right column). The lower panel displays the estimated local FDR for each approach.
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Figure 4: Estimation results for simulated z-values. Histogram of simulated z-values, estimated mixture densities (green solid curves) and components (blue dashed curves) using the CME approach (left column) and the constrained estimation approach (right column). The lower panel displays the estimated local FDR for each approach.

Mentions: In this section, we compare the proposed constrained estimation procedure with the CME approach without constraint using numerical simulations. The simulation model consists of zi ~ N(-1, 1), i = 1, ..., 5000, and zi ~ N(3, 1), i = 5001, ..., 5500. Thus, the first 5000 belong to the distribution and the last 500 to the non- distribution, and the proportion p0 = 0.909. The interval [-2, 0] was used for estimating the component. The estimated mixture density and its component are displayed in Figure 4, with the left column showing the results from the CME approach without constraint and the right column showing the results from the proposed constrained estimation approach. The upper panel shows the histogram of the simulated z-values from one run, the estimated mixture density (solid green curve) and the empirical component (blue dashed curve). The lower panel shows the estimated local FDR from each approach.


Analyzing 2D gel images using a two-component empirical Bayes model.

Li F, Seillier-Moiseiwitsch F - BMC Bioinformatics (2011)

Estimation results for simulated z-values. Histogram of simulated z-values, estimated mixture densities (green solid curves) and  components (blue dashed curves) using the CME approach (left column) and the constrained estimation approach (right column). The lower panel displays the estimated local FDR for each approach.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3300069&req=5

Figure 4: Estimation results for simulated z-values. Histogram of simulated z-values, estimated mixture densities (green solid curves) and components (blue dashed curves) using the CME approach (left column) and the constrained estimation approach (right column). The lower panel displays the estimated local FDR for each approach.
Mentions: In this section, we compare the proposed constrained estimation procedure with the CME approach without constraint using numerical simulations. The simulation model consists of zi ~ N(-1, 1), i = 1, ..., 5000, and zi ~ N(3, 1), i = 5001, ..., 5500. Thus, the first 5000 belong to the distribution and the last 500 to the non- distribution, and the proportion p0 = 0.909. The interval [-2, 0] was used for estimating the component. The estimated mixture density and its component are displayed in Figure 4, with the left column showing the results from the CME approach without constraint and the right column showing the results from the proposed constrained estimation approach. The upper panel shows the histogram of the simulated z-values from one run, the estimated mixture density (solid green curve) and the empirical component (blue dashed curve). The lower panel shows the estimated local FDR from each approach.

Bottom Line: The estimation of the mixture density does not take into account assumptions about the density.The proposed constrained estimation method always yields valid estimates and more stable results.The proposed estimation approach proposed can be applied to other contexts where large-scale hypothesis testing occurs.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD, USA. feng.li@fda.hhs.gov

ABSTRACT

Background: Two-dimensional polyacrylomide gel electrophoresis (2D gel, 2D PAGE, 2-DE) is a powerful tool for analyzing the proteome of a organism. Differential analysis of 2D gel images aims at finding proteins that change under different conditions, which leads to large-scale hypothesis testing as in microarray data analysis. Two-component empirical Bayes (EB) models have been widely discussed for large-scale hypothesis testing and applied in the context of genomic data. They have not been implemented for the differential analysis of 2D gel data. In the literature, the mixture and densities of the test statistics are estimated separately. The estimation of the mixture density does not take into account assumptions about the density. Thus, there is no guarantee that the estimated component will be no greater than the mixture density as it should be.

Results: We present an implementation of a two-component EB model for the analysis of 2D gel images. In contrast to the published estimation method, we propose to estimate the mixture and densities simultaneously using a constrained estimation approach, which relies on an iteratively re-weighted least-squares algorithm. The assumption about the density is naturally taken into account in the estimation of the mixture density. This strategy is illustrated using a set of 2D gel images from a factorial experiment. The proposed approach is validated using a set of simulated gels.

Conclusions: The two-component EB model is a very useful for large-scale hypothesis testing. In proteomic analysis, the theoretical density is often not appropriate. We demonstrate how to implement a two-component EB model for analyzing a set of 2D gel images. We show that it is necessary to estimate the mixture density and empirical component simultaneously. The proposed constrained estimation method always yields valid estimates and more stable results. The proposed estimation approach proposed can be applied to other contexts where large-scale hypothesis testing occurs.

Show MeSH
Related in: MedlinePlus