  Identifying which taxa in our microbiota are associated with traits of
interest is important for advancing science and health. However, the
identification is challenging because the measured vector of taxa counts (by
amplicon sequencing) is compositional, so a change in the abundance of one
taxon in the microbiota induces a change in the number of sequenced counts
across all taxa. The data is typically sparse, with zero counts present either
due to biological variance or limited sequencing depth (technical zeros). For
low abundance taxa, the chance for technical zeros is non-negligible. We show
that existing methods designed to identify differential abundance for
compositional data may have an inflated number of false positives due to
improper handling of the zero counts. We introduce a novel non-parametric
approach which provides valid inference even when the fraction of zero counts
is substantial. Our approach uses a set of reference taxa that are
non-differentially abundant, which can be estimated from the data or from
outside information. We show the usefulness of our approach via simulations, as
well as on three different data sets: a Crohn's disease study, the Human
Microbiome Project, and an experiment with 'spiked-in' bacteria.
