Resumen de Optimal significance analysis of microarray data in a class of tests whose null statistic can be constructed
Hironori Fujisawa, Takayuki Sakaguchi
Microarray data often consist of a large number of genes and a small number of replicates. We have examined testing the null hypothesis of equality of mean for detecting differentially expressed genes. The p-value for each gene is often estimated using permutation samples not only for the target gene but also for other genes. This method has been widely used and discussed. However, direct use of the permutation method for the p-value estimation may not work well, because two types of genes are mixed in the sample; some genes are differentially expressed, whereas others are not. To overcome this difficulty, various methods for appropriately generating null permutation samples have been proposed. In this paper, we consider two classes of test statistics that are naturally modified to null statistics. We then obtain the uniformly most powerful (UMP) unbiased tests among these classes. If the underlying distribution is symmetric, the UMP unbiased test statistic is similar to that proposed by Pan (Bioinformatics 19:1333–1340, 2003). Under another condition, the UMP unbiased test statistic has a different formula with one more degree of freedom and therefore is expected to give a more powerful test and a more accurate p-value estimation from a modified null statistic. In microarray data, because the number of replicates is often small, differences in the degree of freedom will produce large effects on the power of test and the variance of the p-value estimation. Some simulation studies and real data analyses are illustrated to investigate the performances of the methods.
