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. 2005 Jan 21:6:14.
doi: 10.1186/1471-2105-6-14.

A robust two-way semi-linear model for normalization of cDNA microarray data

Deli Wang  1 , Jian Huang, Hehuang Xie, Liliana Manzella, Marcelo Bento Soares
Affiliations

A robust two-way semi-linear model for normalization of cDNA microarray data

Deli Wang et al. BMC Bioinformatics. .

Abstract

Background: Normalization is a basic step in microarray data analysis. A proper normalization procedure ensures that the intensity ratios provide meaningful measures of relative expression values.

Methods: We propose a robust semiparametric method in a two-way semi-linear model (TW-SLM) for normalization of cDNA microarray data. This method does not make the usual assumptions underlying some of the existing methods. For example, it does not assume that: (i) the percentage of differentially expressed genes is small; or (ii) the numbers of up- and down-regulated genes are about the same, as required in the LOWESS normalization method. We conduct simulation studies to evaluate the proposed method and use a real data set from a specially designed microarray experiment to compare the performance of the proposed method with that of the LOWESS normalization approach.

Results: The simulation results show that the proposed method performs better than the LOWESS normalization method in terms of mean square errors for estimated gene effects. The results of analysis of the real data set also show that the proposed method yields more consistent results between the direct and the indirect comparisons and also can detect more differentially expressed genes than the LOWESS method.

Conclusions: Our simulation studies and the real data example indicate that the proposed robust TW-SLM method works at least as well as the LOWESS method and works better when the underlying assumptions for the LOWESS method are not satisfied. Therefore, it is a powerful alternative to the existing normalization methods.

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Figures

Figure 1
Figure 1
Study designs for cDNA microarray experiments among the human placenta, the universal reference, and the Probe Set.
Figure 2
Figure 2
An example of R-l plots for twelve blocks of slide one with no-dye bias for two channels, 10% genes are differentially expressed.
Figure 3
Figure 3
An example of shaped R-l plots for twelve blocks of slide one with the dye bias for two channels, 10% genes are differentially expressed.
Figure 4
Figure 4
Consistency analysis based on cutoff p-value 10-5. Both x and y axes are estimated log intensity ratios. (a)-(b) between the direct design and the indirect design for the robust TW-SLM and the LOWESS normalization method, respectively; (c)-(d) between the LOWESS method and the robust TW-SLM for the direct design and the indirect design, respectively.
Figure 5
Figure 5
Consistency analysis based on cutoff p-value 10-3. Both x and y axes are estimated log intensity ratios. (a)-(b) between the direct design and the indirect design for the robust TW-SLM and the LOWESS normalization method, respectively; (c)-(d) between the LOWESS method and the robust TW-SLM for the direct design and the indirect design, respectively.
Figure 6
Figure 6
A boxplot for comparing mean square errors among normalization methods for the case that 70% genes are all up-regulated (Table 3).
Figure 7
Figure 7
A boxplot for comparing biases among normalization methods for the case that 70% genes are all up-regulated (Table 4).
Figure 8
Figure 8
Slide-wise normalization curves based on different methods for one slide of the human placenta vs. the probe set hybridization in the example.
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