  One fundamental statistical task in microbiome data analysis is differential
abundance analysis, which aims to identify microbial taxa whose abundance
covaries with a variable of interest. Although the main interest is on the
change in the absolute abundance, i.e., the number of microbial cells per unit
area/volume at the ecological site such as the human gut, the data from a
sequencing experiment reflects only the taxa relative abundances in a sample.
Thus, microbiome data are compositional in nature. Analysis of such
compositional data is challenging since the change in the absolute abundance of
one taxon will lead to changes in the relative abundances of other taxa, making
false positive control difficult. Here we present a simple, yet robust and
highly scalable approach to tackle the compositional effects in differential
abundance analysis. The method only requires the application of established
statistical tools. It fits linear regression models on the centered log-ratio
transformed data, identifies a bias term due to the transformation and
compositional effect, and corrects the bias using the mode of the regression
coefficients. Due to the algorithmic simplicity, our method is 100-1000 times
faster than the state-of-the-art method ANCOM-BC. Under mild assumptions, we
prove its asymptotic FDR control property, making it the first differential
abundance method that enjoys a theoretical FDR control guarantee. The proposed
method is very flexible and can be extended to mixed-effect models for the
analysis of correlated microbiome data. Using comprehensive simulations and
real data applications, we demonstrate that our method has overall the best
performance in terms of FDR control and power among the competitors. We
implemented the proposed method in the R package LinDA
(https://github.com/zhouhj1994/LinDA).
