Differential abundance (DA) analysis of microbiome data continues to be a challenging problem due to the complexity of the data. In this article we define the notion of "sampling fraction" and demonstrate a major hurdle in performing DA analysis of microbiome data is the bias introduced by differences in the sampling fractions across samples. We introduce a methodology called Analysis of Compositions of Microbiomes with Bias Correction (ANCOM-BC), which estimates the unknown sampling fractions and corrects the bias induced by their differences among samples. The absolute abundance data are modeled using a linear regression framework. This formulation makes a fundamental advancement in the field because, unlike the existing methods, it (a) provides statistically valid test with appropriate p-values, (b) provides confidence intervals for differential abundance of each taxon, (c) controls the False Discovery Rate (FDR), (d) maintains adequate power, and (e) is computationally simple to implement.

Increasingly, researchers are discovering associations between microbiome and a wide range of human diseases such as obesity, inflammatory bowel diseases, HIV, and so on. The first step towards microbiome wide association studies is the characterization of the composition of human microbiome under different conditions. Determination of differentially abundant microbes between two or more environments, known as differential abundance (DA) analysis, is a challenging and an important problem that has received considerable interest during the past decade. It is well documented in the literature that the observed microbiome data (OTU/SV table) are relative abundances with an excess of zeros. Since relative abundances sum to a constant, these data are necessarily compositional. In this article we review some recent methods for DA analysis and describe their strengths and weaknesses.

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