Normalization of two-channel microarrays accounting for experimental design and intensity-dependent relationships

Abstract

In normalizing two-channel expression arrays, the ANOVA approach explicitly incorporates the experimental design in its model, and the MA plot-based approach accounts for intensity-dependent biases. However, both approaches can lead to inaccurate normalization in fairly common scenarios. We propose a method called efficient Common Array Dye Swap (eCADS) for normalizing two-channel microarrays that accounts for both experimental design and intensity-dependent biases. Under reasonable experimental designs, eCADS preserves differential expression relationships and requires only a single array per sample pair.

Figure 1

Overview of the eCADS model. The left panel summarizes the model of equation 2. The observed fluorescence intensity (y_R or y_G) for agene with x RNA is modeled as the sum of the average dye function d, the function corresponding to the dye used for labeling (δ_R or δ_G), and an array-specific function a. Since we do not know the true RNA amounts x, we warp the x-axis so that every x value is replaced with d(x); these 'warped RNA amounts' are essentially group means adjusted gene-by-gene for bias (see Model formulation). The curves in the right panel are analogously warped versions of the curves in the left panel, now representing deviations from the group mean (the straight line). The warping enables the estimation of the model without affecting the relationships of interest.

Figure 2

Functions used in simulation. Functions used in simulated example for dye (left) and array (right) effects. The actual dye 'effect' functions (the δs in equation 2) are the dye-specific deviations from the average curve. The array functions sum to zero at any point on the x-axis.

Figure 3

Summary of simulated t-statistics. Comparison of t-statistics (averaged across 100 simulations) and true mean differences after MA (left), ANOVA (middle), and eCADS (right) normalization. Black points represent genes for which the sign of differential expression has not been preserved. Plots for MA show systematic shift, indicating bias.

Figure 4

Summary of simulated null histograms. Histograms of null p-values after MA (left), ANOVA (middle), and eCADS (right) normalization in one simulation. Neither the MA nor ANOVA null p-values are uniformly distributed (KS significance approximately zero), while eCADS null p-values are (KS p = 0.86).

Figure 5

MA plots for mouse prostate development study. The three arrays from one dye configuration are in the top row, while those from the reversed configuration are in the second row. There is apparently asymmetric, intensity-dependent differential expression in this example.

Figure 6

Estimated group means and bias functions for mouse data. The left panel is an MA plot comparing the 'warped RNA' (group means adjusted gene-by-gene for bias) for the two comparison groups. The middle panel shows the estimated dye effect functions, and the right panel shows the estimated array effect functions.

Figure 7

Estimated group means and bias functions for MAQC data. The left panel is an MA plot comparing the 'warped RNA' (group means adjusted gene-by-gene for bias) for the two comparison groups. The middle panel shows the estimated dye effect functions, and the right panel shows the estimated site effect functions.

Figure 8

Estimated array functions for MAQC data. The estimated array effect functions by site. Note that site two has substantially more array-to-array variability than the other two sites.