  The target of inference in microbiome analyses is usually relative abundance
(RA) because RA in a sample (e.g., stool) can be considered as an approximation
of RA in an entire ecosystem (e.g., gut). However, inference on RA suffers from
the fact that RA are calculated by dividing absolute abundances (AA) over the
common denominator (CD), the summation of all AA (i.e., library size). Because
of that, perturbation in one taxon will result in a change in the CD and thus
cause false changes in RA of all other taxa, and those false changes could lead
to false positive/negative findings. We propose a novel analysis approach
(IFAA) to make robust inference on AA of an ecosystem that can circumvent the
issues induced by the CD problem and compositional structure of RA. IFAA can
also address the confounding effect of library size and handle zero-inflated
data structures. IFAA identifies microbial taxa associated with the covariates
in Phase one and estimates the association parameters by employing an
independent reference taxon in Phase two. Two real data applications are
presented and extensive simulations show that IFAA outperforms other
established existing approaches by a big margin in the presence of confounding
effect of library size.
