Entropy-based analysis of the non-linear relationship between gene expression profiles of amplified and non-amplified RNA

Two critical issues in microarray-based gene expression profiling with amplified RNA are its reliability and reproducibility compared to the non-amplified RNA. In this study, the non-linear relationship between the two methods was evaluated with the entropy in addition to the linear relationship using correlation coefficients. The correlation coefficients within the amplification method and between the two methods were significantly high, 0.98 and 0.88, respectively. Comparing the entropy as increasing fold-change difference (k), the average entropy value was reduced to 0.02 in the cell line and 0.09 in the tissue samples, indicating that the number of different genes between the two methods was decreased. In addition, the threshold of k according to the percentage of p estimated from entropy values could be used to provide the cut-off line on gene selection. The quantity discordance rate of 0.3-5.4% and the common outlier proportion of 84.2-94.3% between the two methods were detected, according to the expression levels. In summary, we showed a high similarity between the two methods using non-linear as well as linear comparison. Furthermore, we proved that the entropy as the measure of non-linear relationship is useful for analyzing the similarity of replicated microarray data sets.