Functional ANOVA Normalization of Two-Channel Microarrays
We present a new, general method for normalizing two-channel microarray data, partially drawing on ideas from two widely used approaches. Whereas the ANOVA approach carefully distinguishes different sources of signal and bias through explicit terms in its model, the MA-plot based approach takes into account the fact that sources of bias may be intensity-dependent. However, both approaches suffer from serious drawbacks, as we have shown in previous work. The fixed (non-intensity-dependent) coefficients in the ANOVA approach tend to under- or over-fit the data, and the MA-plot based approach assumes that all intensity-dependent trends are due to unwanted bias, each leading to inaccurate normalization in fairly common scenarios. Our proposed approach, called eCADS, captures the strengths of these previous approaches, while avoiding their weaknesses. We replace the fixed coefficients in the ANOVA model with functions of underlying RNA amount, thereby incorporating intensity-dependent relationships like those evident in MA-plots. The normalization method fits this "functional ANOVA" model and subtracts off terms representing bias to retain the biological signal of interest. By requiring a simple balance in experimental design, we show that our method preserves differential expression relationships in expectation. A consequence of this work is the statistical justification of a more efficient dye-swap design that requires only one array per sample pair. We demonstrate our new method on an experiment measuring expression in developing mice.
Bioinformatics | Computational Biology | Microarrays | Statistical Methodology | Statistical Theory
Dabney, Alan and Storey, John D., "Functional ANOVA Normalization of Two-Channel Microarrays" (April 2006). UW Biostatistics Working Paper Series. Working Paper 285.
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