Applying shrinkage variance estimators to the TOST test in high dimensional settings

Abstract

Identifying differentially expressed genes has been an important and widely used approach to investigate gene functions and molecular mechanisms. A related issue that has drawn much less attention but is equally important is the identification of constantly expressed genes across different conditions. A common practice is to treat genes that are not significantly differentially expressed as significantly equivalently expressed. Such naive practice often leads to large false discovery rate and low power. The more appropriate way for identifying constantly expressed genes should be conducting high dimensional statistical equivalence tests. A well-known equivalence test, the two one-sided tests (TOST), can be used for this purpose. However, due to the small sample sizes often associated with genomics data, the variance estimator in the TOST test could be unstable. Hence it would be fitting to examine the application of shrinkage variance estimators to the TOST test in high dimensional settings. In this paper, we study the effect of shrinking the variance estimators in the TOST test in high dimensional settings through simulation studies. In addition, we derive analytic formulas for the p-value of the resultant shrinkage variance TOST test and apply it to a real data set.