Empirical characterization of the expression ratio noise structure in high-density oligonucleotide arrays

High-density oligonucleotide arrays (HDONAs) are a powerful tool for assessing differential mRNA expression levels. To establish the statistical significance of an observed change in expression, one must take into account the noise introduced by the enzymatic and hybridization steps, called type I noise. We undertake an empirical characterization of the experimental repeatability of results by carrying out statistical analysis of a large number of duplicate HDONA experiments. We assign scoring functions for expression ratios and associated quality measures. Both the perfect-match (PM) probes and the differentials between PM and single-mismatch (MM) probes are considered as raw intensities. We then calculate the log-ratio of the noise structure using robust estimates of their intensity-dependent variance. The noise structure in the log-ratios follows a local log-normal distribution in both the PM and PM-MM cases. Significance relative to the type I noise can therefore be quantified reliably using the local standard deviation (SD). We discuss the intensity dependence of the SD and show that ratio scores greater than 1.25 are significant in the mid- to high-intensity range. The noise inherent in HDONAs is characteristically dependent on intensity and can be well described in terms of local normalization of log-ratio distributions. Therefore, robust estimates of the local SD of these distributions provide a simple and powerful way to assess significance (relative to type I noise) in differential gene expression, and will be helpful in practice for improving the reliability of predictions from hybridization experiments.