Issues in cDNA microarray analysis: quality filtering, channel normalization, models of variations and assessment of gene effects

Abstract

We consider the problem of comparing the gene expression levels of cells grown under two different conditions using cDNA microarray data. We use a quality index, computed from duplicate spots on the same slide, to filter out outlying spots, poor quality genes and problematical slides. We also perform calibration experiments to show that normalization between fluorescent labels is needed and that the normalization is slide dependent and non-linear. A rank invariant method is suggested to select non-differentially expressed genes and to construct normalization curves in comparative experiments. After normalization the residuals from the calibration data are used to provide prior information on variance components in the analysis of comparative experiments. Based on a hierarchical model that incorporates several levels of variations, a method for assessing the significance of gene effects in comparative experiments is presented. The analysis is demonstrated via two groups of experiments with 125 and 4129 genes, respectively, in Escherichia coli grown in glucose and acetate.

Figure 1

Quality index (CV) versus average intensity (Cy5_i + Cy3_i)/2 in the 125 gene project. The curve indicates the 10th upper percentile in the moving window containing the 50 nearest genes. Genes with a quality index (CV) larger than this curve will be filtered out. Only slides C1S2 and C2S1 are shown here. Genes with a low CV have high agreement in duplicate spots, hence representing high experiment quality. Thus slide C1S2 shows higher quality than slide C2S1.

Figure 2

M–A plot for the 125 gene project where M represents the log ratio of two dyes and A the averaged logarithmic intensity. Only slides C1S1 and R1S1 are shown here.

Figure 3

Cy5 intensity versus Cy3 intensity of the aceE gene on slide C2S2 for the 125 gene project. Spot 1 is a contaminated spot.

Figure 4

M–A plot of two slides in the same calibration experiment. The upper plot shows different patterns of M–A plot on slides C1S1 (open circles) and C1S2 (crosses) for the 125 gene project. The lower M–A plot for calibration 4 shows the same situation. Thus the normalization curve is slide dependent and should be estimated and applied within the same slide.

Figure 5

Normalization curve for M–A plots in comparative experiments for the 4129 gene project. The darker points are genes of the rank invariant set selected in an iterative manner. (P = 0.02)

Figure 6

QQ plots and histograms of normalized log ratios in calibration experiments for the 125 gene project. There are ∼100 genes on each slide after quality filtering. The distributions of normalized log ratios are centered, normal-like and consistent across slides. Thus the distributions will provide good prior information for comparative experiments.

Figure 7

The orange and green rectangles show the 95% posterior interval for the underlying expression level θ_g (see text) for the 125 and 4129 gene projects (green, 125 gene project; orange, 4129 gene project). Rectangles of gene 54 (aceA) are below –1.0 and do not appear on the graph.

Figure 8

M–A plot for the 125 gene project. There is an increasing trend in both the first and second plots. When applying reverse labeling design the trend is largely cancelled.