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Abstract MotivationDifferential abundance analysis is an essential and commonly used tool to characterize the difference between microbial communities. However, identifying differentially abundant microbes remains a challenging problem because the observed microbiome data are inherently compositional, excessive sparse, and distorted by experimental bias. Besides these major challenges, the results of differential abundance analysis also depend largely on the choice of analysis unit, adding another practical complexity to this already complicated problem. ResultsIn this work, we introduce a new differential abundance test called the MsRDB test, which embeds the sequences into a metric space and integrates a multiscale adaptive strategy for utilizing spatial structure to identify differentially abundant microbes. Compared with existing methods, the MsRDB test can detect differentially abundant microbes at the finest resolution offered by data and provide adequate detection power while being robust to zero counts, compositional effect, and experimental bias in the microbial compositional dataset. Applications to both simulated and real microbial compositional datasets demonstrate the usefulness of the MsRDB test. Availability and implementationAll analyses can be found under https://github.com/lakerwsl/MsRDB-Manuscript-Code. 

Summary Phylogenetic association analysis plays a crucial role in investigating the correlation between microbial compositions and specific outcomes of interest in microbiome studies. However, existing methods for testing such associations have limitations related to the assumption of a linear association in high-dimensional settings and the handling of confounding effects. Hence, there is a need for methods capable of characterizing complex associations, including nonmonotonic relationships. This article introduces a novel phylogenetic association analysis framework and associated tests to address these challenges by employing conditional rank correlation as a measure of association. The proposed tests account for confounders in a fully nonparametric manner, ensuring robustness against outliers and the ability to detect diverse dependencies. The proposed framework aggregates conditional rank correlations for subtrees using weighted sum and maximum approaches to capture both dense and sparse signals. The significance level of the test statistics is determined by calibration through a nearest-neighbour bootstrapping method, which is straightforward to implement and can accommodate additional datasets when these are available. The practical advantages of the proposed framework are demonstrated through numerical experiments using both simulated and real microbiome datasets. 

Summary Differential abundance tests for compositional data are essential and fundamental in various biomedical applications, such as single-cell, bulk RNA-seq and microbiome data analysis. However, because of the compositional constraint and the prevalence of zero counts in the data, differential abundance analysis on compositional data remains a complicated and unsolved statistical problem. This article proposes a new differential abundance test, the robust differential abundance test, to address these challenges. Compared with existing methods, the robust differential abundance test is simple and computationally efficient, is robust to prevalent zero counts in compositional datasets, can take the data’s compositional nature into account, and has a theoretical guarantee of controlling false discoveries in a general setting. Furthermore, in the presence of observed covariates, the robust differential abundance test can work with covariate-balancing techniques to remove potential confounding effects and draw reliable conclusions. The proposed test is applied to several numerical examples, and its merits are demonstrated using both simulated and real datasets. 

In observational studies, balancing covariates in different treatment groups is essential to estimate treatment effects. One of the most commonly used methods for such purposes is weighting. The performance of this class of methods usually depends on strong regularity conditions for the underlying model, which might not hold in practice. In this paper, we investigate weighting methods from a functional estimation perspective and argue that the weights needed for covariate balancing could differ from those needed for treatment effects estimation under low regularity conditions. Motivated by this observation, we introduce a new framework of weighting that directly targets the treatment effects estimation. Unlike existing methods, the resulting estimator for a treatment effect under this new framework is a simple kernel-based U-statistic after applying a data-driven transformation to the observed covariates. We characterize the theoretical properties of the new estimators of treatment effects under a nonparametric setting and show that they are able to work robustly under low regularity conditions. The new framework is also applied to several numerical examples to demonstrate its practical merits. 

Self-supervised metric learning has been a successful approach for learning a distance from an unlabeled dataset. The resulting distance is broadly useful for improving various distance-based downstream tasks, even when no information from downstream tasks is utilized in the metric learning stage. To gain insights into this approach, we develop a statistical framework to theoretically study how self-supervised metric learning can benefit downstream tasks in the context of multi-view data. Under this framework, we show that the target distance of metric learning satisfies several desired properties for the downstream tasks. On the other hand, our investigation suggests the target distance can be further improved by moderating each direction’s weights. In addition, our analysis precisely characterizes the improvement by self-supervised metric learning on four commonly used downstream tasks: sample identification, two-sample testing, k-means clustering, and k-nearest neighbor classification. When the distance is estimated from an unlabeled dataset, we establish the upper bound on distance estimation’s accuracy and the number of samples sufficient for downstream task improvement. Finally, numerical experiments are presented to support the theoretical results in the paper. 

Microbiome sequencing data normalization is crucial for eliminating technical bias and ensuring accurate downstream analysis. However, this process can be challenging due to the high frequency of zero counts in microbiome data. We propose a novel reference-based normalization method called normalization via rank similarity (RSim) that corrects sample-specific biases, even in the presence of many zero counts. Unlike other normalization methods, RSim does not require additional assumptions or treatments for the high prevalence of zero counts. This makes it robust and minimizes potential bias resulting from procedures that address zero counts, such as pseudo-counts. Our numerical experiments demonstrate that RSim reduces false discoveries, improves detection power, and reveals true biological signals in downstream tasks such as PCoA plotting, association analysis, and differential abundance analysis.