Orthogonal projections to latent structures as a strategy for microarray data normalization

Abstract

Background: During generation of microarray data, various forms of systematic biases are frequently introduced which limits accuracy and precision of the results. In order to properly estimate biological effects, these biases must be identified and discarded.

Results: We introduce a normalization strategy for multi-channel microarray data based on orthogonal projections to latent structures (OPLS); a multivariate regression method. The effect of applying the normalization methodology on single-channel Affymetrix data as well as dual-channel cDNA data is illustrated. We provide a parallel comparison to a wide range of commonly employed normalization methods with diverse properties and strengths based on sensitivity and specificity from external (spike-in) controls. On the illustrated data sets, the OPLS normalization strategy exhibits leading average true negative and true positive rates in comparison to other evaluated methods.

Conclusion: The OPLS methodology identifies joint variation within biological samples to enable the removal of sources of variation that are non-correlated (orthogonal) to the within-sample variation. This ensures that structured variation related to the underlying biological samples is separated from the remaining, bias-related sources of systematic variation. As a consequence, the methodology does not require any explicit knowledge regarding the presence or characteristics of certain biases. Furthermore, there is no underlying assumption that the majority of elements should be non-differentially expressed, making it applicable to specialized boutique arrays.

Figure 1

Normalization results for the H8k data set. In A, differences in the total number of identified DE microarray elements between the different normalization methods are displayed for the H8k data set. In B, the TP and TN rates for the H8k data set are displayed based on the DE of the external controls. The TP rates are presented using solid black bars whereas the TN rates are presented using striped bars. Raw refers to the un-normalized data.

Figure 2

Illustration of the array baseline difference. The first Y-orthogonal score vector t_o,1 is shown together with the average A values for each slide. The t_o,1 values (averaged per slide) are displayed using point-up, light gray triangles whereas the average A values are displayed using point-down, dark gray triangles. The Pearson correlation coefficient between the two series is 0.992, suggesting that the score vector captures an array bias.

Figure 3

Illustration of a print-tip group effect. The eighth Y-orthogonal loading vector p_o,8^T displayed using a spatial representation of the array layout. The 48 print-tip groups are delimited using solid lines. Darker areas denote higher absolute loading values whereas brighter areas denote lower absolute loading values. One distinct print-tip group with high-magnitude loading values can be seen in the upper right corner of the figure (indicated by the arrow), capturing a print-tip group effect.