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Summary We discover a connection between the Benjamini–Hochberg procedure and the e-Benjamini–Hochberg procedure (Wang & Ramdas, 2022) with a suitably defined set of e-values. This insight extends to Storey’s procedure and generalized versions of the Benjamini–Hochberg procedure and the model-free multiple testing procedure of Barber & Candés (2015) with a general form of rejection rules. We further summarize these findings in a unified form. These connections open up new possibilities for designing multiple testing procedures in various contexts by aggregating e-values from different procedures or assembling e-values from different data subsets. 

ABSTRACT In many applications, the process of identifying a specific feature of interest often involves testing multiple hypotheses for their joint statistical significance. Examples include mediation analysis, which simultaneously examines the existence of the exposure-mediator and the mediator-outcome effects, and replicability analysis, aiming to identify simultaneous signals that exhibit statistical significance across multiple independent studies. In this work, we present a new approach called the joint mirror (JM) procedure that effectively detects such features while maintaining false discovery rate (FDR) control in finite samples. The JM procedure employs an iterative method that gradually shrinks the rejection region based on progressively revealed information until a conservative estimate of the false discovery proportion is below the target FDR level. Additionally, we introduce a more stringent error measure known as the composite FDR (cFDR), which assigns weights to each false discovery based on its number of null components. We use the leave-one-out technique to prove that the JM procedure controls the cFDR in finite samples. To implement the JM procedure, we propose an efficient algorithm that can incorporate partial ordering information. Through extensive simulations, we show that our procedure effectively controls the cFDR and enhances statistical power across various scenarios, including the case that test statistics are dependent across the features. Finally, we showcase the utility of our method by applying it to real-world mediation and replicability analyses. 

Abstract MotivationGenomic data are subject to various sources of confounding, such as demographic variables, biological heterogeneity, and batch effects. To identify genomic features associated with a variable of interest in the presence of confounders, the traditional approach involves fitting a confounder-adjusted regression model to each genomic feature, followed by multiplicity correction. ResultsThis study shows that the traditional approach is suboptimal and proposes a new two-dimensional false discovery rate control framework (2DFDR+) that provides significant power improvement over the conventional method and applies to a wide range of settings. 2DFDR+ uses marginal independence test statistics as auxiliary information to filter out less promising features, and FDR control is performed based on conditional independence test statistics in the remaining features. 2DFDR+ provides (asymptotically) valid inference from samples in settings where the conditional distribution of the genomic variables given the covariate of interest and the confounders is arbitrary and completely unknown. Promising finite sample performance is demonstrated via extensive simulations and real data applications. Availability and implementationR codes and vignettes are available at https://github.com/asmita112358/tdfdr.np. 

Abstract SummaryDue to the sparsity and high dimensionality, microbiome data are routinely summarized into pairwise distances capturing the compositional differences. Many biological insights can be gained by analyzing the distance matrix in relation to some covariates. A microbiome sampling method that characterizes the inter-sample relationship more reproducibly is expected to yield higher statistical power. Traditionally, the intraclass correlation coefficient (ICC) has been used to quantify the degree of reproducibility for a univariate measurement using technical replicates. In this work, we extend the traditional ICC to distance measures and propose a distance-based ICC (dICC). We derive the asymptotic distribution of the sample-based dICC to facilitate statistical inference. We illustrate dICC using a real dataset from a metagenomic reproducibility study. Availability and implementationdICC is implemented in the R CRAN package GUniFrac. Supplementary informationSupplementary data are available at Bioinformatics online. 

Sparse canonical correlation analysis (sCCA) has been a useful approach for integrating different high-dimensional datasets by finding a subset of correlated features that explain the most correlation in the data. In the context of microbiome studies, investigators are always interested in knowing how the microbiome interacts with the host at different molecular levels such as genome, methylol, transcriptome, metabolome and proteome. sCCA provides a simple approach for exploiting the correlation structure among multiple omics data and finding a set of correlated omics features, which could contribute to understanding the host-microbiome interaction. However, existing sCCA methods do not address compositionality, and its application to microbiome data is thus not optimal. This paper proposes a new sCCA framework for integrating microbiome data with other high-dimensional omics data, accounting for the compositional nature of microbiome sequencing data. It also allows integrating prior structure information such as the grouping structure among bacterial taxa by imposing a “soft” constraint on the coefficients through varying penalization strength. As a result, the method provides significant improvement when the structure is informative while maintaining robustness against a misspecified structure. Through extensive simulation studies and real data analysis, we demonstrate the superiority of the proposed framework over the state-of-the-art approaches. 

It is well known that the microbiome data are ridden with outliers and have heavy distribution tails, but the impact of outliers and heavy-tailedness has yet to be examined systematically. This paper investigates the impact of outliers and heavy-tailedness on differential abundance analysis (DAA) using the linear models for the differential abundance analysis (LinDA) method and proposes effective strategies to mitigate their influence. The presence of outliers and heavy-tailedness can significantly decrease the power of LinDA. We investigate various techniques to address outliers and heavy-tailedness, including generalizing LinDA into a more flexible framework that allows for the use of robust regression and winsorizing the data before applying LinDA. Our extensive numerical experiments and real-data analyses demonstrate that robust Huber regression has overall the best performance in addressing outliers and heavy-tailedness. 

Summary In this paper, we develop a systematic theory for high-dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new U-type statistic to test linear hypotheses and establish a high-dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be used to deal with the classical one-way multivariate analysis of variance, and the nonparametric one-way multivariate analysis of variance in high dimensions. To implement the test procedure, we introduce a sample-splitting-based estimator of the second moment of the error covariance and discuss its properties. A simulation study shows that our proposed test outperforms some existing tests in various settings. 

Abstract Differential abundance analysis is at the core of statistical analysis of microbiome data. The compositional nature of microbiome sequencing data makes false positive control challenging. Here, we show that the compositional effects can be addressed by a simple, yet highly flexible and scalable, approach. The proposed method, LinDA, only requires fitting linear regression models on the centered log-ratio transformed data, and correcting the bias due to compositional effects. We show that LinDA enjoys asymptotic FDR control and can be extended to mixed-effect models for correlated microbiome data. Using simulations and real examples, we demonstrate the effectiveness of LinDA. 

Abstract Summary PERMANOVA (permutational multivariate analysis of variance based on distances) has been widely used for testing the association between the microbiome and a covariate of interest. Statistical significance is established by permutation, which is computationally intensive for large sample sizes. As large-scale microbiome studies, such as American Gut Project (AGP), become increasingly popular, a computationally efficient version of PERMANOVA is much needed. To achieve this end, we derive the asymptotic distribution of the PERMANOVA pseudo-F statistic and provide analytical P-value calculation based on chi-square approximation. We show that the asymptotic P-value is close to the PERMANOVA P-value even under a moderate sample size. Moreover, it is more accurate and an order-of-magnitude faster than the permutation-free method MDMR. We demonstrated the use of our procedure D-MANOVA on the AGP dataset. Availability and implementation D-MANOVA is implemented by the dmanova function in the CRAN package GUniFrac. Supplementary information Supplementary data are available at Bioinformatics online.