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Compositional data in which only the relative abundances of variables aremeasured are ubiquitous. In the context of health and medical compositionaldata, an important class of biomarkers is the log ratios between groups ofvariables. However, selecting log ratios that are predictive of a responsevariable is a combinatorial problem. Existing greedy-search based methods aretime-consuming, which hinders their application to high-dimensional data sets.We propose a novel selection approach called the supervised log ratio methodthat can efficiently select predictive log ratios in high-dimensional settings.The proposed method is motivated by a latent variable model and we show thatthe log ratio biomarker can be selected via simple clustering after supervisedfeature screening. The supervised log ratio method is implemented in an Rpackage, which is publicly available at \url{https://github.com/drjingma/slr}.We illustrate the merits of our approach through simulation studies andanalysis of a microbiome data set on HIV infection.

Regression and Classification of Compositional Data via a novel Supervised Log Ratio Method