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Abstract:
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Modeling longitudinal microbiome compositional data, which is semi-continuous in nature, is challenging in several aspects: the overabundance of zeros, the heavy skewness of non-zero values bounded in (0, 1), and the dependence between the binary and non-zero parts. Besides, the microbiome compositional data has unit-sum constraint, indicating the existence of negative correlations among taxa. We propose a two-part linear mixed model with shared random effects to formulate the log-transformed standardized relative abundances rather than the original ones. Such transformation is called “additive logistic transformation”, initially developed for cross-sectional compositional data. We extend it to analyze the longitudinal microbiome compositions and show that the unit-sum constraint can be automatically satisfied under our approach. Model performances of our method are compared with existing methods in simulation studies. Under settings adopted from real data, our method has the best performance and is recommended for practical use. An oral microbiome example shows that our method can estimate the correlation structure in the binary and the continuous parts, suggesting its usefulness.
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