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Semilinear high-dimensional model for normalization of microarray data: a theoretical analysis and partial consistency; Comment.

Article Excerpt
We congratulate Fan, Peng, and Huang (FPH hereafter) on their interesting, innovative, and important contribution on microarray normalization. In addition to proposing new methodology that addresses several important open problems, FPH also present new asymptotic theory that both validates their approach and provides insight into the normalization process. Such theoretical work has been sparse in the microarray literature, probably because of the nonstandard way in which the number of parameters is large relative to the number of observations. We appreciate the opportunity to comment on this article.

Normalization is the process of removing systematic background noises of gene expression measurements in microarray experiments. Typically, this is done slide-by-slide before conducting a significance analysis of individual gene effects. However, some authors advocate combining normalization and significance analysis to account for the variability of estimators used in the normalization process (Huang, Wang, and Zhang 2003; Huang and Zhang 2003). We revisit this issue later on in this comment. For now, we note that techniques for normalization and significance analysis share a number of similarities for both cDNA and oligonucleotide microarrays. Hence some of the concepts in FPH on cDNA arrays are also applicable to oligonucleotide arrays. However, there are sufficient structural differences between the two kinds of arrays that significant work is needed before these concepts can be applied to the oligonucleotide setting. Thus we restrict our comments primarily to cDNA arrays.

We first briefly outline the key contributions of FPH, then discuss a few useful extensions. We briefly discuss a connection to marginal asymptotics for controlling false discovery rates (FDR) in significance analysis, then give a few comments on computational issues before presenting our closing comments.

1. THE MAIN CONTRIBUTIONS

FPHs main methodological contribution is a nonparametric method of normalizing cDNA microarrays that takes into account intensity and print-tip block effects without limiting the proportion of up-regulated or down-regulated genes. This represents a significant improvement in flexibility over the methods of both Dudoit et al. (2002) and Tseng, Oh, Rohlin, Liao, and Wong (2001). Moreover, the new methods permit the variability of the residual error to depend nonparametrically on the log-intensity of the red and green channels. The fact that estimation is applied in-slide makes it possible to obtain slide-specific gene effects. The proven partial consistency of the procedure makes it possible to proceed directly to significance analysis, after normalization, without requiring adjustments for uncertainty in the in-slide parameter estimates....

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