How many replicates of arrays are required to detect gene expression changes in microarray experiments? A mixture model approach

Abstract

Background: It has been recognized that replicates of arrays (or spots) may be necessary for reliably detecting differentially expressed genes in microarray experiments. However, the often-asked question of how many replicates are required has barely been addressed in the literature. In general, the answer depends on several factors: a given magnitude of expression change, a desired statistical power (that is, probability) to detect it, a specified Type I error rate, and the statistical method being used to detect the change. Here, we discuss how to calculate the number of replicates in the context of applying a nonparametric statistical method, the normal mixture model approach, to detect changes in gene expression.

Results: The methodology is applied to a data set containing expression levels of 1,176 genes in rats with and without pneumococcal middle-ear infection. We illustrate how to calculate the power functions for 2, 4, 6 and 8 replicates.

Conclusions: The proposed method is potentially useful in designing microarray experiments to discover differentially expressed genes. The same idea can be applied to other statistical methods.

Figure 1

Sample standard deviations of expression levels and their loess smoothers as a function of the average expression levels for the two conditions respectively.

Figure 2

Histograms and estimated distribution density functions. (a-d) Two, four, six and eight replicates (z2 - z8), respectively. In (a), the solid and dotted lines are the fitted one- and two-component mixtures. In (b-d), the solid and dotted lines are the fitted and the theoretically derived mixtures.

Figure 3

Power (d, ) as a function of the magnitude of expression changes d and the number of replicates, with the gene-specific Type I error rate = 0.09% for the middle-ear data.

Figure 4

Power (d, ) as a function of the magnitude of expression changes d and the number of replicates, with the gene-specific Type I error rate = 0.05/1,000 for the middle-ear data.

Figure 5

Power (d, ) as a function of the magnitude of expression changes d and the number of replicates, with the gene-specific Type I error rate = 0.05/5,000 for the middle-ear data.

Figure 6

Power (d, ) as a function of the magnitude of expression changes d and the number of replicates, with the gene-specific Type I error rate = 0.05/10,000 for the middle ear data.