High-Dimensional Equivalence Testing Using Shrinkage Variance Estimators

• Activity Number: 642
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Yue Qi*+ and Jing Qiu and Xiangqin Cui
• Companies: and University of Missouri and University of Alabama
• Keywords: Equivalence test ; High dimensional tests ; p-values ; Shrinkage variance estimators

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. The 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. However, due to the "large p and small n " feature of the genomics data, the variance estimator in the TOST test could be unstable. In this paper, we aim to apply a shrinkage variance estimator to the TOST test and derive analytic formulas for the p-values of the resultant shrinkage variance equivalence tests. We study the effect of the shrinkage variance estimators on the power of the high dimensional equivalence test through simulation studies and data analysis.