The loss in power when the test of differential expression is performed under a wrong scale

One of the most common and important goals of microarray studies is to identify genes that are differentially expressed between cells of different conditions. T-test and ANOVA models on the expression data are common practices to gauge the significance of the observed difference in expression levels. Transformation of the microarray data is often applied in order to satisfy the model assumptions being entertained. However, the distributional properties of the expression are gene specific, and it is impractical to find a single transformation that is universally optimal for all the genes. This difficulty results in the situation that some genes have to violate the assumptions of the model (e.g., homogeneity in variance, normality). It is thus the interest of this paper to evaluate the impact on the inference of differential expression when the test is performed under an inappropriate scale. Particularly, we quantitatively assess the loss of power when the test is performed under a wrong scale. Normal distribution and log-normal distribution of the expression data are considered. The loss in power is investigated in two scenarios: a transformation is misused, or a transformation fails to be applied. Log transformation and power transformation are particularly considered due to the fact that Box-Cox types of transformation are commonly used in practice. The impact of using a wrong scale is investigated analytically and based on simulations. The loss in power is assessed both as a function of the degree to which the assumptions are violated and as a function of the effect size. Simulations are conducted to quantitatively assess the power loss when tests are performed under a wrong scale. A public experimental microarray dataset is used to illustrate the impact of transformation on the results of testing differential expression. The results show that the loss of power is a function of CV and fold-change (effect size). The loss in power depends on the true model and on how severely the assumptions are violated.