Filtering , FDR and power : Additional File 1
نویسنده
چکیده
1 Study design Here we assume a study setup commonly found in practice, involving gene expression profiles of two groups of independent samples,with the null hypothesis representing no differential expression between the two groups for any given gene, and a corresponding two-sided alternative. With notation, assume that the two independent groups of samples have sample sizes nX , nY (nZ = nX + nY ) and that each sample has a corresponding mRNA profile including m features (probes or genes, say). So the data consists of two matrices, X = [X1, X2, . . . , XnX ] and Y = [Y1, Y2, . . . , YnY ]. Let Z = [X,Y ] be the matrix including all samples from both groups. Gene-wise sample means are represented by m× 1 vectors X̄nX , ȲnY for each group separately, and by Z̄nZ for all samples. Similarly, gene-wise sample variances are represented by m× 1 vectors S X , S Y for each group separately and by S Z for all samples. A test statistic M = M(Z) is computed to test the null hypothesis H0 : μX = μY against the alternative Ha : μX 6= μY . If V is a binary m× 1 vector with Vi = 1 whenever H0 holds for feature i, and Vi = 0 otherwise, then π0 = (1 V )/m represents the proportion of features that follow H0. Then the distribution F of M can be written as M ∼ π0F0 + (1− π0)Fa, (1)
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