Computational method for reducing variance with Affymetrix microarrays

Abstract

Background: Affymetrix microarrays are used by many laboratories to generate gene expression profiles. Generally, only large differences (> 1.7-fold) between conditions have been reported. Computational methods to reduce inter-array variability might be of value when attempting to detect smaller differences. We examined whether inter-array variability could be reduced by using data based on the Affymetrix algorithm for pairwise comparisons between arrays (ratio method) rather than data based on the algorithm for analysis of individual arrays (signal method). Six HG-U95A arrays that probed mRNA from young (21-31 yr old) human muscle were compared with six arrays that probed mRNA from older (62-77 yr old) muscle.

Results: Differences in mean expression levels of young and old subjects were small, rarely > 1.5-fold. The mean within-group coefficient of variation for 4629 mRNAs expressed in muscle was 20% according to the ratio method and 25% according to the signal method. The ratio method yielded more differences according to t-tests (124 vs. 98 differences at P < 0.01), rank sum tests (107 vs. 85 differences at P < 0.01), and the Significance Analysis of Microarrays method (124 vs. 56 differences with false detection rate < 20%; 20 vs. 0 differences with false detection rate < 5%). The ratio method also improved consistency between results of the initial scan and results of the antibody-enhanced scan.

Conclusion: The ratio method reduces inter-array variance and thereby enhances statistical power.

Figure 1

Individual arrays vs. mean of all arrays A. Scatter plot of signals from 4629 probe sets on a typical array vs. mean signals from all 12 arrays. Line of identity is shown. B. Worst-case scatter plot. Same as plot A, except vertical axis represents a different array, the one with the most consistent deviation from the mean of all 12 arrays at high expression levels. Note that almost all signals > 10⁴ arbitrary units are below the line of identity.

Figure 2

P_detection vs. signal Signal, in arbitrary units, is the average PM-MM intensity difference across all 8–20 probe pairs within a set. P_detection is the probability that a target is absent, based on the consistency of PM/MM ratios within a probe set. Values are based on a single array.

Figure 3

Comparison of two arrays by different methods Horizontal axis shows the ratios between two arrays, for 4629 targets, according to the comparative analysis algorithm, which is the basis of the ratio method. Vertical axis shows ratios between the same arrays according to the absolute analysis algorithm, which is the basis of the signal method. Points outside the red lines have more than 1.5-fold divergence between methods.

Figure 4

Frequency distribution of coefficients of variation (CVs) Distribution of 4629 CVs obtained by the ratio method (solid bars) and the signal method (open bars). CVs are average of within-group CVs in young and old groups.

Figure 5

Volcano plot Statistical significance by t-tests [-log(P)] vs. expression ratio (mean old / mean young) for 4629 targets that passed the presence / absence filter. Note log₂ scale on horizontal axis. Vertical lines represent 2-fold difference between young and old. Upper horizontal line represents P = 0.001. Lower horizontal line represents P = 0.01.