Sample size calculation for microarray experiments with blocked one-way design

Abstract

Background: One of the main objectives of microarray analysis is to identify differentially expressed genes for different types of cells or treatments. Many statistical methods have been proposed to assess the treatment effects in microarray experiments.

Results: In this paper, we consider discovery of the genes that are differentially expressed among K (> 2) treatments when each set of K arrays consists of a block. In this case, the array data among K treatments tend to be correlated because of block effect. We propose to use the blocked one-way ANOVA F-statistic to test if each gene is differentially expressed among K treatments. The marginal p-values are calculated using a permutation method accounting for the block effect, adjusting for the multiplicity of the testing procedure by controlling the false discovery rate (FDR). We propose a sample size calculation method for microarray experiments with a blocked one-way design. With FDR level and effect sizes of genes specified, our formula provides a sample size for a given number of true discoveries.

Conclusion: The calculated sample size is shown via simulations to provide an accurate number of true discoveries while controlling the FDR at the desired level.

Figure 1

Monotone relationship between n and marginal power β_i (α) with α = 0.05 and = {k - (K + 2)/2}/K for 1 ≤ k ≤ K.

Figure 2

Hierarchical clustering dendrogram. kA means site A (= E, C or M) for patient k (= 1,..., 5).

Figure 3

Expression patterns of six genes that are significantly differentially expressed in three sites.