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Abstract:
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Regression analysis that integrates microbiome data with another omics data type is challenging due to the high-dimensional nature of both data types. It requires simultaneous estimation of a massive number of unknown association parameters between individual microbial taxa and omics variables from the other data type (e.g. metabolomics). In regression models where both the response and the predictor data are high-dimensional, reduced rank regression (RRR) is often a useful tool since it reduces the number of parameters to be estimated by imposing a low rank structure on the coefficient matrix. However, the compositionality of microbiome data is not captured by current RRR models. In this paper, we propose a novel reduced rank regression framework tailored for associating microbiome relative abundance data with metabolomic data. We also provide an iterative convex optimization algorithm and show that it attains a global optimum. Simulation studies demonstrate that the proposed approach has superior performance compared to the standard RRR model in terms of both estimation precision and prediction accuracy.
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