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Register a new userRobust Differential Abundance Test in Compositional Data
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Shulei Wang
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
Authors
Shulei Wang
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Differential abundance tests in compositional data are essential and fundamental tasks in various biomedical applications, such as single-cell, bulk RNA-seq, and microbiome data analysis. However, despite the recent developments in these fields, differential abundance analysis in compositional data remains a complicated and unsolved statistical problem, because of the compositional constraint and prevalent zero counts in the dataset. This study introduces a new differential abundance test, the robust differential abundance (RDB) test, to address these challenges. Compared with existing methods, the RDB test 1) is simple and computationally efficient, 2) is robust to prevalent zero counts in compositional datasets, 3) can take the datas compositional nature into account, and 4) has a theoretical guarantee of controlling false discoveries in a general setting. Furthermore, in the presence of observed covariates, the RDB test can work with the covariate balancing techniques to remove the potential confounding effects and draw reliable conclusions. Finally, we apply the new test to several numerical examples using simulated and real datasets to demonstrate its practical merits.
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Robust real-time monitoring of high-dimensional data streams has many important real-world applications such as industrial quality control, signal detection, biosurveillance, but unfortunately it is highly non-trivial to develop efficient schemes due to two challenges: (1) the unknown sparse number or subset of affected data streams and (2) the uncertainty of model specification for high-dimensional data. In this article, motivated by the detection of smaller persistent changes in the presence of larger transient outliers, we develop a family of efficient real-time robust detection schemes for high-dimensional data streams through monitoring feature spaces such as PCA or wavelet coefficients when the feature coefficients are from Tukey-Hubers gross error models with outliers. We propose to construct a new local detection statistic for each feature called $L_{alpha}$-CUSUM statistic that can reduce the effect of outliers by using the Box-Cox transformation of the likelihood function, and then raise a global alarm based upon the sum of the soft-thresholding transformation of these local $L_{alpha}$-CUSUM statistics so that to filter out unaffected features. In addition, we propose a new concept called false alarm breakdown point to measure the robustness of online monitoring schemes, and also characterize the breakdown point of our proposed schemes. Asymptotic analysis, extensive numerical simulations and case study of nonlinear profile monitoring are conducted to illustrate the robustness and usefulness of our proposed schemes.
Identifying which taxa in our microbiota are associated with traits of interest is important for advancing science and health. However, the identification is challenging because the measured vector of taxa counts (by amplicon sequencing) is compositi
onal, so a change in the abundance of one taxon in the microbiota induces a change in the number of sequenced counts across all taxa. The data is typically sparse, with zero counts present either due to biological variance or limited sequencing depth (technical zeros). For low abundance taxa, the chance for technical zeros is non-negligible. We show that existing methods designed to identify differential abundance for compositional data may have an inflated number of false positives due to improper handling of the zero counts. We introduce a novel non-parametric approach which provides valid inference even when the fraction of zero counts is substantial. Our approach uses a set of reference taxa that are non-differentially abundant, which can be estimated from the data or from outside information. We show the usefulness of our approach via simulations, as well as on three different data sets: a Crohns disease study, the Human Microbiome Project, and an experiment with spiked-in bacteria.
Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to open the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.
Significant phylogenetic codivergence between plant or animal hosts ($H$) and their symbionts or parasites ($P$) indicate the importance of their interactions on evolutionary time scales. However, valid and realistic methods to test for codivergence are not fully developed. One of the systems where possible codivergence has been of interest involves the large subfamily of temperate grasses (Pooideae) and their endophytic fungi (epichloae). These widespread symbioses often help protect host plants from herbivory and stresses, and affect species diversity and food web structures. Here we introduce the MRCALink (most-recent-common-ancestor link) method and use it to investigate the possibility of grass-epichloe codivergence. MRCALink applied to ultrametric $H$ and $P$ trees identifies all corresponding nodes for pairwise comparisons of MRCA ages. The result is compared to the space of random $H$ and $P$ tree pairs estimated by a Monte Carlo method. Compared to tree reconciliation the method is less dependent on tree topologies (which often can be misleading), and it crucially improves on phylogeny-independent methods such as {tt ParaFit} or the Mantel test by eliminating an extreme (but previously unrecognized) distortion of node-pair sampling. Analysis of 26 grass species-epichloe species symbioses did not reject random association of $H$ and $P$ MRCA ages. However, when five obvious host jumps were removed the analysis significantly rejected random association and supported grass-endophyte codivergence. Interestingly, early cladogenesis events in the Pooideae corresponded to early cladogenesis events in epichloae, suggesting concomitant origins of this grass subfamily and its remarkable group of symbionts. We also applied our method to the well-known gopher-louse data set.
We present the $U$-Statistic Permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearsons chi-squared test of independence, or the $G$-test, are typically used for this task, but we argue that these tests have serious deficiencies, both in terms of their inability to control the size of the test, and their power properties. By contrast, the USP test is guaranteed to control the size of the test at the nominal level for all sample sizes, has no issues with small (or zero) cell counts, and is able to detect distributions that violate independence in only a minimal way. The test statistic is derived from a $U$-statistic estimator of a natural population measure of dependence, and we prove that this is the unique minimum variance unbiased estimator of this population quantity. The practical utility of the USP test is demonstrated on both simulated data, where its power can be dramatically greater than those of Pearsons test and the $G$-test, and on real data. The USP test is implemented in the R package USP.
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