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Multifactorial experimental design and the transitivity of ratios with spotted DNA microarrays.

Townsend JP - BMC Genomics (2003)

Bottom Line: Multifactorial experimental designs using DNA microarrays are becoming increasingly common, but the extent of the transitivity of cDNA microarray expression measurements across multiple samples has yet to be explored.A strong correlation between direct and transitive inference for significantly differentially expressed genes is demonstrated, using subsets of a dye-swap loop design.In experimental design, opportunities for transitive inference should be exploited, while always ensuring that comparisons of greatest interest comprise direct hybridizations.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Plant and Microbial Biology, 321 Koshland Hall, University of California, Berkeley, CA 94720, USA. townsend@nature.berkeley.edu

ABSTRACT

Background: Multifactorial experimental designs using DNA microarrays are becoming increasingly common, but the extent of the transitivity of cDNA microarray expression measurements across multiple samples has yet to be explored.

Results: A strong correlation between direct and transitive inference for significantly differentially expressed genes is demonstrated, using subsets of a dye-swap loop design.

Conclusions: In experimental design, opportunities for transitive inference should be exploited, while always ensuring that comparisons of greatest interest comprise direct hybridizations.

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Related in: MedlinePlus

Correlation of direct and indirect estimates of gene expression level. Log-log scatter plot of estimates of gene expression level for the 87 genes with non-overlapping credible intervals, comparing estimates from direct comparisons (X-axis) to estimates from independent, transitive comparisons (Y-axis). Excluding the two outliers (open circles) in Cartesian quadrant IV, which represent estimates different not just in magnitude but also direction, the regression is y = 1.001 × - 0.06, with a correlation r2 = 0.8 (P << 0.001).
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Figure 3: Correlation of direct and indirect estimates of gene expression level. Log-log scatter plot of estimates of gene expression level for the 87 genes with non-overlapping credible intervals, comparing estimates from direct comparisons (X-axis) to estimates from independent, transitive comparisons (Y-axis). Excluding the two outliers (open circles) in Cartesian quadrant IV, which represent estimates different not just in magnitude but also direction, the regression is y = 1.001 × - 0.06, with a correlation r2 = 0.8 (P << 0.001).

Mentions: All of the experimental designs in Figure 1 rely on transitive inference, in different ways, and each implicitly assumes that the ratio measurements from microarray experiments are not nonlinearly compressed or stretched compared to the true values. If compression of true ratios is nonexistent or linear, then the results of direct comparisons should be highly and linearly correlated with results arrived at indirectly from another (independent) subset of the same design (Figure 2). In the set containing the direct comparison (Figure 2A), ratios of gene expression of two samples are estimated from two direct hybridizations. In the set comparing the focal samples indirectly (Figure 2B), ratios of gene expression of the same two samples are estimated by transitive inference. With the indirectly estimated ratio between two samples on the y-axis, and the directly estimated ratio on the x-axis, the slope of gene expression level estimates should have a highly significant linear regression. Its slope should be one, though increased variance may arise along the y-axis associated with transitive inference. This expectation is observed in Figure 3, which plots, for all statistically significantly differentially expressed genes, the Log2 ratio of estimates of expression levels from the direct competitive hybridizations of strains M2-8 and M1-2 on the DNA microarray, against the Log2 ratio of the purely transitive estimates of expression levels of M2-8 compared to M1-2. Results obtained from an indirect series of comparisons corroborate results obtained from direct comparisons.


Multifactorial experimental design and the transitivity of ratios with spotted DNA microarrays.

Townsend JP - BMC Genomics (2003)

Correlation of direct and indirect estimates of gene expression level. Log-log scatter plot of estimates of gene expression level for the 87 genes with non-overlapping credible intervals, comparing estimates from direct comparisons (X-axis) to estimates from independent, transitive comparisons (Y-axis). Excluding the two outliers (open circles) in Cartesian quadrant IV, which represent estimates different not just in magnitude but also direction, the regression is y = 1.001 × - 0.06, with a correlation r2 = 0.8 (P << 0.001).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC239860&req=5

Figure 3: Correlation of direct and indirect estimates of gene expression level. Log-log scatter plot of estimates of gene expression level for the 87 genes with non-overlapping credible intervals, comparing estimates from direct comparisons (X-axis) to estimates from independent, transitive comparisons (Y-axis). Excluding the two outliers (open circles) in Cartesian quadrant IV, which represent estimates different not just in magnitude but also direction, the regression is y = 1.001 × - 0.06, with a correlation r2 = 0.8 (P << 0.001).
Mentions: All of the experimental designs in Figure 1 rely on transitive inference, in different ways, and each implicitly assumes that the ratio measurements from microarray experiments are not nonlinearly compressed or stretched compared to the true values. If compression of true ratios is nonexistent or linear, then the results of direct comparisons should be highly and linearly correlated with results arrived at indirectly from another (independent) subset of the same design (Figure 2). In the set containing the direct comparison (Figure 2A), ratios of gene expression of two samples are estimated from two direct hybridizations. In the set comparing the focal samples indirectly (Figure 2B), ratios of gene expression of the same two samples are estimated by transitive inference. With the indirectly estimated ratio between two samples on the y-axis, and the directly estimated ratio on the x-axis, the slope of gene expression level estimates should have a highly significant linear regression. Its slope should be one, though increased variance may arise along the y-axis associated with transitive inference. This expectation is observed in Figure 3, which plots, for all statistically significantly differentially expressed genes, the Log2 ratio of estimates of expression levels from the direct competitive hybridizations of strains M2-8 and M1-2 on the DNA microarray, against the Log2 ratio of the purely transitive estimates of expression levels of M2-8 compared to M1-2. Results obtained from an indirect series of comparisons corroborate results obtained from direct comparisons.

Bottom Line: Multifactorial experimental designs using DNA microarrays are becoming increasingly common, but the extent of the transitivity of cDNA microarray expression measurements across multiple samples has yet to be explored.A strong correlation between direct and transitive inference for significantly differentially expressed genes is demonstrated, using subsets of a dye-swap loop design.In experimental design, opportunities for transitive inference should be exploited, while always ensuring that comparisons of greatest interest comprise direct hybridizations.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Plant and Microbial Biology, 321 Koshland Hall, University of California, Berkeley, CA 94720, USA. townsend@nature.berkeley.edu

ABSTRACT

Background: Multifactorial experimental designs using DNA microarrays are becoming increasingly common, but the extent of the transitivity of cDNA microarray expression measurements across multiple samples has yet to be explored.

Results: A strong correlation between direct and transitive inference for significantly differentially expressed genes is demonstrated, using subsets of a dye-swap loop design.

Conclusions: In experimental design, opportunities for transitive inference should be exploited, while always ensuring that comparisons of greatest interest comprise direct hybridizations.

Show MeSH
Related in: MedlinePlus