Normalization for cDNA microarray data: a robust composite method addressing single and multiple slide systematic variation

Abstract

There are many sources of systematic variation in cDNA microarray experiments which affect the measured gene expression levels (e.g. differences in labeling efficiency between the two fluorescent dyes). The term normalization refers to the process of removing such variation. A constant adjustment is often used to force the distribution of the intensity log ratios to have a median of zero for each slide. However, such global normalization approaches are not adequate in situations where dye biases can depend on spot overall intensity and/or spatial location within the array. This article proposes normalization methods that are based on robust local regression and account for intensity and spatial dependence in dye biases for different types of cDNA microarray experiments. The selection of appropriate controls for normalization is discussed and a novel set of controls (microarray sample pool, MSP) is introduced to aid in intensity-dependent normalization. Lastly, to allow for comparisons of expression levels across slides, a robust method based on maximum likelihood estimation is proposed to adjust for scale differences among slides.

Figure 1

Within-slide normalization. (A) MA-plot demonstrating the need for within-print tip group location normalization. (B) MA-plot after within-print tip group location normalization. Both panels display the lowess fits (f = 40%) for each of the 16 print tip groups (data from apo AI knockout mouse number 8 in experiment A).

Figure 2

Within-slide normalization: box plots displaying the intensity log ratio distribution, for each of the 16 print tip groups before and after different normalization procedures. The array was printed using a 4 × 4 print head and the print tip groups are numbered first from left to right, then from top to bottom, starting from the top left corner (data from apo AI knockout mouse number 8 in experiment A). (A) Before normalization. (B) After within-print tip group location normalization, but before scale adjustment. (C) After within-print tip group location and scale normalization.

Figure 3

Within-slide normalization: MA-plot for comparison of the anterior versus posterior portion of the olfactory bulb. These samples are very similar and we do not expect many genes to change. The cyan dots represent the MSP titration series and the cyan curve represents the corresponding lowess fit. The red curve corresponds to the lowess fit for the entire dataset. Control genes are highlighted in yellow (tubulin and GAPDH), green (mouse genomic DNA) and orange (an approximate rank-invariant set of genes with P = 0.01 and l = 25). (Left) MA-plot before normalization. (Right) MA-plot after within-print tip group location normalization.

Figure 4

Within-slide normalization: MA-plot for comparison of the medial versus lateral portion of the olfactory bulb. The cyan dots represent the MSP titration series and the cyan curve represents the corresponding lowess fit. The red curve corresponds to the lowess fit for the entire dataset. The green curve represents the composite normalization curve. Control genes are highlighted in yellow (tubulin and GAPDH), green (mouse genomic DNA) and orange (an approximate rank-invariant set of genes). (A) MA-plot before normalization. (B) MA-plot after composite normalization.

Figure 5

Within-slide normalization. (A) Density plots of the log ratios M before and after different normalization procedures. The solid black curve represents the density of the log ratios before normalization. The red, green, blue and cyan curves represent the densities after global median normalization, intensity-dependent location normalization, within-print tip group location normalization and within-print tip group scale normalization, respectively (data from apo AI knockout mouse number 8 in experiment A). (B) Plot of t-statistics for different normalization methods. The numbers 1–8 represent the differentially expressed genes identified in Dudoit et al. (10) and confirmed using RT–PCR: indices 1–3 represent the three apo AI genes spotted on the array. Empty circles represent the remaining 6376 genes where no effect is expected. Only t values less than –4 are shown.

Figure 6

Multiple slide normalization: box plots displaying the intensity log ratio distribution for different slides/mice for experiment A, after within-print tip group location and scale normalization. The first eight box plots represent the data for the eight control mice and the last eight represent the data for the eight apo AI knockout mice.