Analysis of Microbiome Data in the Presence of Excess Zeros

Motivation: An important feature of microbiome count data is the presence of large number of zeros. A common strategy to handle these excess zeros is to add a small number called pseudo count (e.g. 1). Other strategies include using various probability models to model the excess zero counts. Although adding a pseudo-count is simple and widely used, as demonstrated in this paper, it is not ideal. On the other hand, methods that model excess zeros using a probability model often make an implicit assumption that all zeros can be explained by a common probability model. As described in this article, this is not always the case as there are potentially three types/sources of zeros in a microbiome data. The purpose of this paper is to develop a simple methodology to identify three different types of zeros and to test hypotheses regarding the relative abundance of taxa in two or more experimental groups. Another major contribution of this paper is to perform constrained (directional or ordered) inference when there are more than two ordered experimental groups (e.g. subjects ordered by diet or age groups or environmental exposure groups). As far as we know this is the first paper that addresses such problems in the analysis of microbiome data. Results: Using extensive simulation studies, we demonstrate that the proposed methodology not only controls the false discovery rate at a desired level of significance while competing well in terms of power with DSEQ2, a popular procedure derived from RNASeq literature. As expected, the method using pseudo counts tends to be very conservative and the classical t-test that ignores the underlying simplex structure in the data has an inflated FDR.