Limits...
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.

Show MeSH

Related in: MedlinePlus

Estimation results using unconstrained approaches. Estimates of mixture densities and their  components from the CME and MLE methods, and the local FDR. Upper panel: solid green curves are the spline-fitted mixture densities; the blue dashed and red dotted curves are the empirical  densities from the CME and MLE methods, respectively. Lower panel: the local FDR estimates from the CME (blue solid curve) and MLE (red dotted curve) methods.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3300069&req=5

Figure 2: Estimation results using unconstrained approaches. Estimates of mixture densities and their components from the CME and MLE methods, and the local FDR. Upper panel: solid green curves are the spline-fitted mixture densities; the blue dashed and red dotted curves are the empirical densities from the CME and MLE methods, respectively. Lower panel: the local FDR estimates from the CME (blue solid curve) and MLE (red dotted curve) methods.

Mentions: In the procedures described above, the mixture density and its component are estimated separately. The estimated component may be greater than the mixture density . Thus, there is no guarantee that we will have for all z. Indeed, we may end up awkwardly having that for some z1 <z2 < 0, as shown in Figure 2, where both approaches were implemented on the set of gels of interest.


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

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

Estimation results using unconstrained approaches. Estimates of mixture densities and their  components from the CME and MLE methods, and the local FDR. Upper panel: solid green curves are the spline-fitted mixture densities; the blue dashed and red dotted curves are the empirical  densities from the CME and MLE methods, respectively. Lower panel: the local FDR estimates from the CME (blue solid curve) and MLE (red dotted curve) methods.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Estimation results using unconstrained approaches. Estimates of mixture densities and their components from the CME and MLE methods, and the local FDR. Upper panel: solid green curves are the spline-fitted mixture densities; the blue dashed and red dotted curves are the empirical densities from the CME and MLE methods, respectively. Lower panel: the local FDR estimates from the CME (blue solid curve) and MLE (red dotted curve) methods.
Mentions: In the procedures described above, the mixture density and its component are estimated separately. The estimated component may be greater than the mixture density . Thus, there is no guarantee that we will have for all z. Indeed, we may end up awkwardly having that for some z1 <z2 < 0, as shown in Figure 2, where both approaches were implemented on the set of gels of interest.

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