Variable selection in regression with compositional covariates

Motivated by research problems arising in the analysis of gut microbiome and metagenomic data, we consider variable selection and estimation in high-dimensional regression with compositional covariates. We propose an l(1) regularization method for the linear log-contrast model that respects the unique features of compositional data. We formulate the proposed procedure as a constrained convex optimization problem and introduce a coordinate descent method of multipliers for efficient computation. In the high-dimensional setting where the dimensionality grows at most exponentially with the sample size, model selection consistency and l(infinity) bounds for the resulting estimator are established under conditions that are mild and interpretable for compositional data. The numerical performance of our method is evaluated via simulation studies and its usefulness is illustrated by an application to a microbiome study relating human body mass index to gut microbiome composition.