Response to comments on "Bayesian Hierarchical Error Model for Analysis of Gene Expression Data"

We greatly thank the authors of this letter for pointing out the significance of our original contribution of the hierarchical error model (HEM) in Cho and Lee (2004). As the authors suggested, we agree that an extension of HEM can be made for gene expression data with biological and/or experimental correlations. However, we here discuss several issues in response to some of the points raised in this letter. First, in this letter the simplified posterior distributions were derived under the assumption of the same numbers of biological and experimental replicates for all conditions, i.e. m ij ¼ m and n ijk ¼ n. However, in practical microarray studies, the numbers of replic-ates can often differ among different conditions (e.g. m i1 ¼ 5 and m i2 ¼ 6). Thus, in our original HEM model we considered this kind of heterogeneous sample sizes among different combinations of genes and conditions. Furthermore, expression values can be completely missing for a certain combination of gene and condition, i.e. n ijk ¼ 0, owing to quality control and other experimental reasons. In this case the posterior probability of x ijk has to be defined with a reduced form x ijk j : Nðm þ g i þ c j þ r ij ‚ s 2 bij Þ, which is a logical imputation for the missing combination from the available information of the corresponding gene and condition. Thus, we respectfully argue that our simplified form of Equation (6) is appropriate for the aforementioned general cases. Also, we note that the case that n ijk ¼ 1 for all i, j, k was presented in the section entitled 'Hierarchical error model with no replicates' in our original paper. however, occurred while we attempted to simplify notations in our paper, and it was irrelevant to claim a mistake in our actual derivation and implementation of the corresponding posterior distributions. For example, our HEM methodology was a further extension from a previous study in Lee et al. (2001), in which similar expressions have been shown without such simplification. Therefore, all the results in Cho and Lee (2004) were obtained from the correct posterior distributions, which can be performed by our software HEM available at the BioConductor website (http://www. bioconductor.org). Third, we again completely agree that the extension of this letter addresses the important issue of biological and experimental correlations in practical microarray studies. However, we cautiously point out …