Measures of association in microbiome and other count-based platforms

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The human microbiome is the collection of organisms residing in or on the human body and plays an integral part in human health. A typical microbiome dataset consists of a count matrix where rows correspond to samples from different microbial populations and columns correspond to microbial taxa (e.g. species, genus, family). Microbiome sequencing data are compositional in nature, meaning that the count of a taxon in a sample should not be interpreted in absolute terms; rather, it should only be interpreted relative to one or more of the other taxa. This makes measuring associations between different taxa difficult, since correlations on the raw taxon proportions will be negatively biased. In this proposal I will extend existing multinomial model to estimate covariance matrices in compositional data as a function of covariates.  To do this, I will modify previous models I have developed to handle a more flexible covariance structure.  Relatedly, statistical techniques have been developed to address the pitfalls of compositional data, for example, the log-ratio transformation. However, the log-ratio transformation is scale invariant, whereas count-based sequencing platforms are not. Recently, (Lovell, Chua, and McGrath 2020) published an important paper exploring the negative effects of applying standard compositional techniques compositional data from count platforms, demonstrating a need for new statistical techniques that will account for differences in count totals across biological samples. A common measure of association in compositional data is the "variation matrix", which contains the variances of the pairwise log-ratios of the parts of the composition. There is a lack of statistical theory surrounding estimation of the variation matrix in count-based compositional data.  Relatedly, zero counts are often very prevalent in microbiome data. It has been shown that measures of association and diversity are sensitive to the choice of procedure used to handle zero counts. However, Bayesian non-parametric models such as the hierarchical Pitman-Yor (HPY) process have recently proved successful in modelling species abundance distributions in microbiome data.  I will additionally develop measures of association in the context of the HPY process, which will allow estimation of association when there are zero counts present in the data.  Finally, I will study the applicability of these methods on other count-based compositional platforms such as single-cell RNA sequencing. This work will provide new methods of estimating measures of association and diversity in metagenomic data that will account for differences in the count totals over biological samples as well as the abundance of zero counts. Though this problem has recently gained attention, there remains a lack of sound statistical theory in this context. Furthermore, these methods will be applicable to many other kinds of platforms such as single-cell RNA sequencing datasets.