MOTIVATION: Understanding how bacterial species relate to clinical health indicators can reveal microbiome signatures of disease, offering insights into conditions such as obesity or liver disease. However, analyzing such data requires methods that address compositionality, high dimensionality, sparsity, and outliers. RESULTS: We tackle the challenge of identifying microbiome components linked to health indicators through a robust multivariate compositional regression model. Our method addresses the high dimensionality, sparsity, and compositional nature of microbiome data while maintaining control of the false discovery rate (FDR). By incorporating outlier robustness and a derandomization step, we enhance the stability and reproducibility of results, surpassing current techniques like the Multi-Response Knockoff Filter (MRKF). In simulation studies, our method outperforms MRKF in terms of FDR control, power, and robustness. In real data applications, it leads to valuable biological insights, such as identifying microbial species associated with specific clinical parameters. AVAILABILITY AND IMPLEMENTATION: Software in R code format, along with synthetic data example illustrations and comprehensive documentation, is available at https://github.com/giannamonti/RobMReg.

MOTIVATION: High-throughput sequencing technologies generate a huge amount of data, permitting the quantification of microbiome compositions. The obtained data are essentially sparse compositional data vectors, namely vectors of bacterial gene proportions which compose the microbiome. Subsequently, the need for statistical and computational methods that consider the special nature of microbiome data has increased. A critical aspect in microbiome research is to identify microbes associated with a clinical outcome. Another crucial aspect with high-dimensional data is the detection of outlying observations, whose presence affects seriously the prediction accuracy. RESULTS: In this article, we connect robustness and sparsity in the context of variable selection in regression with compositional covariates with a continuous response. The compositional character of the covariates is taken into account by a linear log-contrast model, and elastic-net regularization achieves sparsity in the regression coefficient estimates. Robustness is obtained by performing trimming in the objective function of the estimator. A reweighting step increases the efficiency of the estimator, and it also allows for diagnostics in terms of outlier identification. The numerical performance of the proposed method is evaluated via simulation studies, and its usefulness is illustrated by an application to a microbiome study with the aim to predict caffeine intake based on the human gut microbiome composition. AVAILABILITY AND IMPLEMENTATION: The R-package 'RobZS' can be downloaded at https://github.com/giannamonti/RobZS. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.