Proportionality-based association metrics in count compositional data

Compositional data comprise vectors that describe the constituent parts of a whole. Data arising from various -omics platforms such as 16S and RNA sequencing are compositional in nature. In this kind of data, correlations between features on raw counts have no meaningful interpretation. Metrics of proportionality were formulated to address this problem. However, an inherent bias arises when these metrics are calculated empirically on count-based measures due to variability in read depths. We quantify the bias introduced by empirically calculating proportionality-based association metrics in count data. Additionally, we propose a means of estimating these metrics within a logit-normal multinomial model in pursuit of more accurate estimates. The model-based estimates are shown to outperform empirical estimates in simulated data and are applied to a mouse embryonic stem cell single-cell sequencing dataset, as well as a pediatric-onset multiple sclerosis metagenomic dataset.