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Compositional data sets are ubiquitous in science, including geology,ecology, and microbiology. In microbiome research, compositional data primarilyarise from high-throughput sequence-based profiling experiments. These datacomprise microbial compositions in their natural habitat and are often pairedwith covariate measurements that characterize physicochemical habitatproperties or the physiology of the host. Inferring parsimonious statisticalassociations between microbial compositions and habitat- or host-specificcovariate data is an important step in exploratory data analysis. A standardstatistical model linking compositional covariates to continuous outcomes isthe linear log-contrast model. This model describes the response as a linearcombination of log-ratios of the original compositions and has been extended tothe high-dimensional setting via regularization. In this contribution, wepropose a general convex optimization model for linear log-contrast regressionwhich includes many previous proposals as special cases. We introduce aproximal algorithm that solves the resulting constrained optimization problemexactly with rigorous convergence guarantees. We illustrate the versatility ofour approach by investigating the performance of several model instances onsoil and gut microbiome data analysis tasks.

Regression models for compositional data: General log-contrast formulations, proximal optimization, and microbiome data applications