Ranking analysis of F-statistics for microarray data

Abstract

Background: Microarray technology provides an efficient means for globally exploring physiological processes governed by the coordinated expression of multiple genes. However, identification of genes differentially expressed in microarray experiments is challenging because of their potentially high type I error rate. Methods for large-scale statistical analyses have been developed but most of them are applicable to two-sample or two-condition data.

Results: We developed a large-scale multiple-group F-test based method, named ranking analysis of F-statistics (RAF), which is an extension of ranking analysis of microarray data (RAM) for two-sample t-test. In this method, we proposed a novel random splitting approach to generate the null distribution instead of using permutation, which may not be appropriate for microarray data. We also implemented a two-simulation strategy to estimate the false discovery rate. Simulation results suggested that it has higher efficiency in finding differentially expressed genes among multiple classes at a lower false discovery rate than some commonly used methods. By applying our method to the experimental data, we found 107 genes having significantly differential expressions among 4 treatments at <0.7% FDR, of which 31 belong to the expressed sequence tags (ESTs), 76 are unique genes who have known functions in the brain or central nervous system and belong to six major functional groups.

Conclusion: Our method is suitable to identify differentially expressed genes among multiple groups, in particular, when sample size is small.

Figure 1

Profile of estimates of FDRs for a series of thresholds. λ_1k and λ_2k are two threshold functions from simulations 1 and 2 and were used to construct an estimation interval for estimate of FDR at threshold Δ_k. λ_k and ${\hat{\lambda }}_{\text{k}}$ are true and estimated FDRs at threshold Δ_k, respectively, where k = 1, 2,...,L.

Figure 2

The dot-plot of F-values versus $\overline{f}$-values. F-values and $\overline{f}$-values obtained from the simulated microarray data of 3770 genes were ranked where $\overline{f}$-values were yielded by the random splitting approach. All ranked F - $\overline{f}$ dots roughly fall on a diagonal line as expected by two sets of the same ranked distributions.

Figure 3

The scatter plot of F-values versus $\overline{f}$-values. F-values were observed from real microarray data set and $\overline{f}$-values yielded by random splitting approach are an estimate of null f-distribution.

Figure 4

Comparison between the observed (red) and simulated (blue) plots of F-values versus $\overline{f}$-values. F-values were observed from real (red) and simulated (blue) microarray data sets of 3770 genes and 6 replicates. $\overline{f}$-value yielded by randomly splitting approach is an estimate in null f-distribution. F-distribution from simulated data set without treatment effects is null distribution. Ranked F-values corresponds to ranked $\overline{f}$-values.