Zhan et al. () presented a kernel RV coefficient (KRV) test to evaluate the overall association between host gene expression and microbiome composition, and showed its competitive performance compared to existing methods. In this article, we clarify the close relation of KRV to the existing generalized RV (GRV) coefficient, and show that KRV and GRV have very similar performance. Although the KRV test could control the type I error rate well at 1% and 5% levels, we show that it could largely underestimate p-values at small significance levels leading to significantly inflated type I errors. As a partial remedy, we propose an alternative p-value calculation, which is efficient and more accurate than KRV p-value at small significance levels. We recommend that small KRV test p-values should always be accompanied and verified by the permutation p-value in practice. In addition, we analytically show that KRV can be written as a form of correlation coefficient, which can dramatically expedite its computation and make permutation p-value calculation more efficient.
Bibliographical noteFunding Information:
This research was supported in part by NIH grant GM083345 and CA134848. We would like to thank the reviewers for their valuable comments, which have greatly improved the presentation of the article. We acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this article.
© 2017, The International Biometric Society
- Gamma distribution
- RV coefficient