Two Sample Mean Test in High-Dimensional Compositional Data

• Activity Number: 548
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yuanpei Cao* and Wei Lin and Hongzhe Li
• Companies: University of Pennsylvania and Peking University and University of Pennsylvania
• Keywords: Compositional data ; Two-sample mean test ; Gut microbiome

Abstract

Compositional data with unit sum appear in many scientific investigations. Motivated by research problems arising in analyzing gut microbiome and metagenomic data, we consider the two-sample testing problem for high dimensional compositional data where the dimension of the variable is comparable with or even much larger than the sample size. Motivated by a key insight on the relation between the covariance matrix of centered log-ratio transformation of the compositional data and that of the log of the basis counts, a statistical test for the equality of the means of the basis counts is proposed. This statistic is based on the centered log-ratio transformation of the observed compositional data and is shown to have the the extreme value distribution of type I as its limiting null distribution. In simulations it is shown that the proposed procedure is more powerful than other tests based on the compositional data or log of the compositional data, and in data analysis the procedure is used to show difference in gut microbiome compositions between lean and obese individuals.