Non-linear tests for identifying differentially expressed genes or genetic networks

One of the recently developed statistics for identifying differentially expressed genetic networks is Hotelling T2 statistic, which is a quadratic form of difference in linear functions of means of gene expressions between two types of tissue samples, and so their power is limited.

To improve the power of test statistics, a general statistical framework for construction of non-linear tests is presented, and two specific non-linear test statistics that use non-linear transformations of means are developed. Asymptotical distributions of the non-linear test statistics under the null and alternative hypothesis are derived. It has been proved that under some conditions the power of the non-linear test statistics is higher than that of the T2 statistic. Besides theory, to evaluate in practice the performance of the non-linear test statistics, they are applied to two real datasets. The preliminary results demonstrate that the P-values of the non-linear statistics for testing differential expressions of the genetic networks are much smaller than those of the T2 statistic. And furthermore simulations show the Type I errors of the non-linear statistics agree with the threshold used and the statistics fit the chi2 distribution.

Supplementary data are available on Bioinformatics online.