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A two-way semilinear model for normalization and analysis of cDNA microarray data.
- Article from:
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Journal of the American Statistical Association
- Article date:
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September 1, 2005
- Author:
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Copyright informationCOPYRIGHT 2005 American Statistical Association. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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A basic question in analyzing cDNA microarray data is normalization, the purpose of which is to remove systematic bias in the observed expression values by establishing a normalization curve across the whole dynamic range. A proper normalization procedure ensures that the normalized intensity ratios provide meaningful measures of relative expression levels. We propose a two-way semilinear model (TW-SLM) for normalization and analysis of microarray data. This method does not make the usual assumptions underlying some of the existing methods. For example, it does not assume that the percentage of differentially expressed genes is small or that there is symmetry in the expression levels of ...
<[infinity]) when P{|[x.sub.ij] - [[mu].sub.i]|><[x.sub.ij] [less than or equal to] x) [greater than or equal to] [h.sub.J]J}, k [greater than or equal to] 1, where [I.sub.i] [??] [x.sub.ij] are as in Example 1 and [s.sub.i0] = [min.sub.j][x.sub.ij]. Clearly, [K*.sub.J,n] [less than or equal to] d* + 2/[h.sub.J], so that Condition III holds for 1/[h.sub.J] = o([J.sup.1/2]). For intervals I, let [F.sub.[alpha],M](I) be the Sobolev space of functions f in I, for example, satisfying [[integral].sub.I]([f.sup.([alpha])])[.sup.2] [less than or equal to] [M.sup.2]/[I.sup.2[alpha]-1] for integers [alpha]. If [f.sub.i] [member of] [F.sub.[[alpha].sub.i],[M.sub.i]]([I.sub.i]), with [[alpha].sub.i] [less than or equal to] [d.sub.i] + 1 and ([[alpha].sub.i], [M.sub.i]) dependent on [I.sub.i], then [[rho]*.sub.J,n] [less than or equal to] M* [max.sub.i[less than or equal to]n] E[M.sub.i.sup.2][h.sub.J.sup.2[[alpha].sub.i]]. In particular, for [h.sub.J] [??] [J.sup.-1/(2[alpha]+1)] with [alpha]>
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