Correlation and association analyses are one of the most widely used statistical methods in research fields, including microbiome and integrative multiomics studies. Correlation and association have two implications: dependence and co-occurrence. Microbiome data are structured as phylogenetic tree and have several unique characteristics, including high dimensionality, compositionality, sparsity with excess zeros, and heterogeneity. These unique characteristics cause several statistical issues when analyzing microbiome data and integrating multiomics data, such as large p and small n, dependency, overdispersion, and zero-inflation. In microbiome research, on the one hand, classic correlation and association methods are still applied in real studies and used for the development of new methods; on the other hand, new methods have been developed to target statistical issues arising from unique characteristics of microbiome data. Here, we first provide a comprehensive view of classic and newly developed univariate correlation and association-based methods. We discuss the appropriateness and limitations of using classic methods and demonstrate how the newly developed methods mitigate the issues of microbiome data. Second, we emphasize that concepts of correlation and association analyses have been shifted by introducing network analysis, microbe-metabolite interactions, functional analysis, etc. Third, we introduce multivariate correlation and association-based methods, which are organized by the categories of exploratory, interpretive, and discriminatory analyses and classification methods. Fourth, we focus on the hypothesis testing of univariate and multivariate regression-based association methods, including alpha and beta diversities-based, count-based, and relative abundance (or compositional)-based association analyses. We demonstrate the characteristics and limitations of each approaches. Fifth, we introduce two specific microbiome-based methods: phylogenetic tree-based association analysis and testing for survival outcomes. Sixth, we provide an overall view of longitudinal methods in analysis of microbiome and omics data, which cover standard, static, regression-based time series methods, principal trend analysis, and newly developed univariate overdispersed and zero-inflated as well as multivariate distance/kernel-based longitudinal models. Finally, we comment on current association analysis and future direction of association analysis in microbiome and multiomics studies.

相关和关联分析是包括微生物组和综合多组学研究在内的研究领域中使用最广泛的统计方法之一。相关和关联具有两个含义：依赖和共现。微生物组数据被构造为系统树，并具有几个独特的特征，包括高维，组成性，带有多余零的稀疏性和异质性。这些独特的特性在分析微生物组数据和整合多组学数据时会引起一些统计问题，例如大p和小n，依赖性，过度分散和零膨胀。一方面，在微生物组研究中，经典的关联和关联方法仍在实际研究中应用，并用于开发新方法。另一方面，已经开发出新的方法来针对由微生物组数据的独特特征引起的统计问题。在这里，我们首先提供经典和新近开发的单变量相关和基于关联方法的全面介绍。我们讨论了使用经典方法的适当性和局限性，并演示了新开发的方法如何减轻微生物组数据的问题。其次，我们强调通过引入网络分析，微生物-代谢物相互作用，功能分析等方法来改变相关性和关联性分析的概念。第三，我们引入基于相关性和探索性类别的多变量相关性和关联性方法。解释性和歧视性分析与分类方法。第四，我们专注于基于单变量和多变量回归的关联方法的假设检验，包括基于alpha和beta多样性，基于计数和基于相对丰度（或组成）的关联分析。我们展示了每种方法的特征和局限性。第五，我们介绍了两种基于微生物组的特定方法：基于系统树的关联分析和生存结果测试。第六，我们提供了用于分析微生物组和组学数据的纵向方法的整体视图，其中包括标准，静态，基于回归的时间序列方法，主要趋势分析以及新开发的单变量过度分散和零膨胀以及多元距离/基于核的纵向模型。最后，