Normal uniform mixture differential gene expression detection for cDNA microarrays

Abstract

Background: One of the primary tasks in analysing gene expression data is finding genes that are differentially expressed in different samples. Multiple testing issues due to the thousands of tests run make some of the more popular methods for doing this problematic.

Results: We propose a simple method, Normal Uniform Differential Gene Expression (NUDGE) detection for finding differentially expressed genes in cDNA microarrays. The method uses a simple univariate normal-uniform mixture model, in combination with new normalization methods for spread as well as mean that extend the lowess normalization of Dudoit, Yang, Callow and Speed (2002) 1. It takes account of multiple testing, and gives probabilities of differential expression as part of its output. It can be applied to either single-slide or replicated experiments, and it is very fast. Three datasets are analyzed using NUDGE, and the results are compared to those given by other popular methods: unadjusted and Bonferroni-adjusted t tests, Significance Analysis of Microarrays (SAM), and Empirical Bayes for microarrays (EBarrays) with both Gamma-Gamma and Lognormal-Normal models.

Conclusion: The method gives a high probability of differential expression to genes known/suspected a priori to be differentially expressed and a low probability to the others. In terms of known false positives and false negatives, the method outperforms all multiple-replicate methods except for the Gamma-Gamma EBarrays method to which it offers comparable results with the added advantages of greater simplicity, speed, fewer assumptions and applicability to the single replicate case. An R package called nudge to implement the methods in this paper will be made available soon at http://www.bioconductor.org.

Figure 1

Different Normalizations of HIV Data. Different normalizations of HIV data: (a) raw data, (b) data normalized with respect to the variance. The bullets are the positive controls: NUDGE correctly found them all to be differentially expressed. Other genes found to be differentially expressed by NUDGE are indicated by a plus sign, and all genes found not to be differentially expressed by NUDGE are shown by small dots. Negative controls are indicated by a box. No negative controls were found to be differentially expressed by NUDGE.

Figure 2

Overlay of the model's fitted density on the normalized log ratios. Plot (a) shows a histogram of the normalized average log ratios for the HIV data along with a dashed line showing the model-fitted density. Plot (b) shows a close-up of the right-hand tail of the histogram (where the positive controls lie) with a dashed line showing the model-fitted density.

Figure 3

Different Normalizations of Like-like Data. Different normalizations of Like-like data: (a) raw data, (b) data normalized with respect to the mean, (c) data normalized with respect to both mean and variance. Diff. Exp. genes are genes found to be differentially expressed by NUDGE (with posterior probability greater than 0.5).

Figure 4

Absolute mean normalized log ratio versus log intensity for Like-like Data. Absolute mean normalized log ratio versus log intensity for Like-like Data. The loess line in this plot represents the estimate of the gene-specific Mean Absolute Deviation (MAD), a robust estimator of spread.

Figure 5

Different Normalizations of Apo Data. Different Normalizations of Apo data: (a) raw data, (b) data normalized with respect to the mean, (c) data normalized with respect to both mean and variance. Diff. Exp. genes are genes found to be differentially expressed by NUDGE (with posterior probability greater than 0.5).