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Abstract
BackgroundMany procedures for finding differentially expressed genes in microarray data are based on classical or modified t-statistics. Due to multiple testing considerations, the false discovery rate (FDR) is the key tool for assessing the significance of these test statistics. Two recent papers have generalized two aspects: Storey et al. (2005) have introduced a likelihood ratio test statistic for two-sample situations that has desirable theoretical properties (optimal discovery procedure, ODP), but uses standard FDR assessment; Ploner et al. (2006) have introduced a multivariate local FDR that allows incorporation of standard error information, but uses the standard t-statistic (fdr2d). The relationship and relative performance of these methods in two-sample comparisons is currently unknown.MethodsUsing simulated and real datasets, we compare the ODP and fdr2d procedures. We also introduce a new procedure called S2d that combines the ODP test statistic with the extended FDR assessment of fdr2d.ResultsFor both simulated and real datasets, fdr2d performs better than ODP. As expected, both methods perform better than a standard t-statistic with standard local FDR. The new procedure S2d performs as well as fdr2d on simulated data, but performs better on the real data sets.ConclusionThe ODP can be improved by including the standard error information as in fdr2d. This means that the optimality enjoyed in theory by ODP does not hold for the estimated version that has to be used in practice. The new procedure S2d has a slight advantage over fdr2d, which has to be balanced against a significantly higher computational effort and a less intuititive test statistic.
Highlights
Many procedures for finding differentially expressed genes in microarray data are based on classical or modified t-statistics
Building on the Neyman-Pearson lemma for testing an individual hypothesis, the author shows that an extension of the likelihood ratio test statistic for multiple parallel hypotheses is the optimal procedure for deciding whether any specific gene is differentially expressed (DE): for any fixed number of false positive results, ODP will identify the maximum number of true positives
In order to compare different fdr procedures, we summarize their results via operating characteristics (OC) curves: for each procedure, we sort the groups of genes as described above by their local fdr, and compute the corresponding global false discovery rate (FDR) as cumulative mean of the local fdrs from the smallest to the largest
Summary
Many procedures for finding differentially expressed genes in microarray data are based on classical or modified t-statistics. Due to multiple testing considerations, the false discovery rate (FDR) is the key tool for assessing the significance of these test statistics. The need to identify a possibly very small number of regulated genes among the 10,000s of sequences found on modern microarray chips, based on tens to hundreds of biological samples, has led to a plethora of different methods. Many competing methods for detecting DE exist, and even attempts at validation on data sets with known mRNA composition [4] cannot offer definitive guidelines. In this context, the introduction of the so-called optimal discovery procedure (ODP, [5]) constitutes a major conceptual achievement. The ODP establishes a theoretical optimum for detecting DE against which any other method can be measured
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