The analysis of ordered changes of gene expression and gene-gene co-expression patterns

Many microarray gene expression data sets have multiple ordered sample groups. Genes showing increasing/decreasing differential expression or differential gene-gene co-expression patterns can be biologically interesting. Statistically, we can conduct the analysis of ordered changes of population means and ordered changes of regression slopes. The well-developed isotonic regression can be considered for the analysis of differential expression. However, its extension to the analysis of differential gene-gene co-expression patterns has not been well addressed in the literature. We pointed out that the traditional isotonic regression can also be simply extended for the detection of differential gene-gene co-expression patterns after a simple data transformation. A prostate cancer data set was considered as an application. An improvement of false positive control was observed when the order restricted hypothesis testing was considered. Several interesting genes were also identified in our analysis.