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 (AAs) 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 issues of overdispersion and handle zero-inflated data structures. IFAA identifies microbial taxa associated with the covariates in Phase 1 and estimates the association parameters by employing an independent reference taxon in Phase 2. 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 unbalanced library size. Supplementary materials for this article are available online.
Keywords: Compositional data; Differential abundance analysis; High dimension; Microbiome regression; Zero-inflated data.