We derive a variance component score test, similar to those that have been proposed in other testing situations Wu and others, ; Huang and Lin,that facilitates testing both homogeneous and heterogeneous gene sets simultaneously.
In each case, Tfloormean is computed as for Tmean but with fg in place of zg. We, therefore, allow the possibility of gene weights ag, which are used to weight the zg when the gene set summary statistic T is computed, similar to a suggestion of Jiang and Gentleman Since there is no limit on the number of rotations which can be done, the problem of granularity of P-values in small sample sizes is avoided.
In some cases, the expected direction and magnitude of change may be specified in advance for individual genes. The need to permute samples to obtain P-values severely limits the experimental designs which can be analysed. For each rotation, the gene set statistic T is re-computed, and compared to the observed value.
As genes operate with complex covariance patterns, this will be a simplification of the truth and, again, the method is restricted to experimental designs with a special structure.
Finally, ROAST is used to test the degree of transcriptional conservation between human and mouse mammary stems. The matrix X represents the design of the experiment, and describes how the different treatment factors are assigned to the RNA samples.
Typically, the gene set is chosen to represent a particular molecular pathway.