The interactions between microbial taxa in microbiome data has been under great research interest in the science community. In particular, several methods such as SPIEC-EASI, gCoda, and CD-trace have been proposed to model the conditional dependency between microbial taxa, in order to eliminate the detection of spurious correlations. However, all those methods are built upon the central log-ratio (CLR) transformation, which results in a degenerate covariance matrix and thus an undefined inverse covariance matrix as the estimation of the underlying network. Jiang et al. (2021) and Tian et al. (2022) proposed bias-corrected graphical lasso and compositional graphical lasso based on the additive log-ratio (ALR) transformation, which first selects a reference taxon and then computes the log ratios of the abundances of all the other taxa with respect to that of the reference. One concern of the ALR transformation would be the invariance of the estimated network with respect to the choice of reference. In this paper, we first establish the reference-invariance property of a subnetwork of interest based on the ALR transformed data. Then, we propose a reference-invariant version of the compositional graphical lasso by modifying the penalty in its objective function, penalizing only the invariant subnetwork. We validate the reference-invariance property of the proposed method under a variety of simulation scenarios as well as through the application to an oceanic microbiome data set.
翻译:微生物数据微生物分类之间的相互作用一直引起科学界的极大研究兴趣,特别是提出了若干方法,如SPIEC-EASI、GCoda和CD-Trace等,以模拟微生物分类之间的有条件依赖性,从而消除发现虚假的关联性;然而,所有这些方法都建立在CLR(CLR)的中央日志-拉皮欧(CLR)转换基础上,结果产生了一个退化的共变矩阵,从而产生了一个未定义的反差矩阵,作为基础网络的估算值。 江等人(2021年)和天等人(2022年)根据添加式日志-拉皮奥(ALR)转换提出偏差校正图形拉索和成形图形拉索(CD-trax)的参考属性,首先选择参考税号,然后对所有其他分类的丰度与参考值的对比率比重进行计算。 ALR(LR)的一个关切是,估计网络在选择参考值中,我们首先根据ALR-RA(AL)变本的变版数据定义,在后,我们仅根据ALR(A-Restal Stabial)的变版数据定义中建议,将一个变版的变版的变版的刑法目标值的变校正法的变版的变的变的变的变的变版的变法。