Identifying differential expression in multiple SAGE libraries: an overdispersed log-linear model approach

Abstract

Background: In testing for differential gene expression involving multiple serial analysis of gene expression (SAGE) libraries, it is critical to account for both between and within library variation. Several methods have been proposed, including the t test, tw test, and an overdispersed logistic regression approach. The merits of these tests, however, have not been fully evaluated. Questions still remain on whether further improvements can be made.

Results: In this article, we introduce an overdispersed log-linear model approach to analyzing SAGE; we evaluate and compare its performance with three other tests: the two-sample t test, tw test and another based on overdispersed logistic linear regression. Analysis of simulated and real datasets show that both the log-linear and logistic overdispersion methods generally perform better than the t and tw tests; the log-linear method is further found to have better performance than the logistic method, showing equal or higher statistical power over a range of parameter values and with different data distributions.

Conclusion: Overdispersed log-linear models provide an attractive and reliable framework for analyzing SAGE experiments involving multiple libraries. For convenience, the implementation of this method is available through a user-friendly web-interface available at http://www.cbcb.duke.edu/sage.

Figure 1

Comparisons based on simulated data from the beta-binomial distribution. This figure shows the receiver operating characteristic curves (ROC) of the four tests applied to datasets generated from the beta-binomial distribution with various magnitudes of overdispersion (φ) (shown on the top of each graph). For a specific φ, 10,000 observations (tags) are simulated; 5,000 are generated under the assumption that p_A = p_B and the remaining from p_B = 2 p_A, where p_A and p_B are the mean proportions of the two groups and p_A = 0.0002 (i.e. 10 out of 50,000). For figures generated under other conditions, see Additional file 1.

Figure 2

Comparisons based on simulated data from the negative binomial distribution. The ROC curves of the four tests are based on datasets generated from the negative binomial distribution with various magnitudes of overdispersion (φ). The data are simulated by the same strategy as used in Figure 1, except that p_B = 4p_A. Note that the overdispersion parameter here is not directly comparable with that in Figure 1 (the parameter φ for the negative binomial is not directly related to that for the beta-binomial). For figures generated under other conditions, see Additional file 2.

Figure 3

Comparing p-values from the logit-t test and those from the log-t test. Of the top 100 tags (ranked according to p-values) identified by the logit-t test and by the log-t test, 82 are common to both leaving 18 tags from each test that are not within the top 100 identified by the other. The p-values from both tests for these 36 remaining tags are plotted here. The circles represent the 18 in the top 100 by the logit-t test and the triangles those from the log-t test. While all the tags identified by the logit-t test also have reasonably low p-values according to the log-t test, the tags identified by the log-t test show a much wider range of p-values according to the logit-t test.

Figure 4

Plot of standardized residuals against estimated proportions. Standardized Pearson's residuals (y-axis) plotted vs. the proportion estimates (x-axis) for the two groups. The standardized Pearson's residuals are asymptotically distributed as a standard normal. The model fits of two tags (among the list of genes in Table 5) are shown here; the left is from the fit using the overdispersed logistic model and the right from the overdispersed log-linear model. A lower variance of residuals in the group (normal) with lower mean proportion is an indication of poor model fit.

Figure 5

The distribution of overdispersion estimates (). The estimates are from the overdispersed log-linear model fit to the pancreas data. Tags with the overdispersion estimate 0 are not shown in the figure.