Modern methods of microarray data analysis are biased towards selecting those genes that display the most pronounced differential expression. The magnitude of differential expression does not necessarily indicate biological significance and other criteria are needed to supplement the information on differential expression. Three large sets of microarray data on childhood leukemia were analyzed by an original method introduced in this paper. A new type of stochastic dependence between expression levels in gene pairs was deciphered by our analysis. This modulation-like unidirectional dependence between expression signals arises when the expression of a ``gene-modulator'' is stochastically proportional to that of a ``gene-driver''. A total of more than 35% of all pairs formed from 12550 genes were conservatively estimated to belong to this type. There are genes that tend to form Type A relationships with the overwhelming majority of genes. However, this picture is not static: the composition of Type A gene pairs may undergo dramatic changes when comparing two phenotypes. The ability to identify genes that act as ``modulators'' provides a potential strategy of prioritizing candidate genes.